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<h2>HL Paper 3</h2><div class="specification">
<p>A mass-spring system is forced to vibrate vertically at the resonant frequency of the system. The motion of the system is damped using a liquid.</p>
<p style="text-align: center;"><img 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UghoHAzJAFAdKXr7bHHHlPWrFmjyOehQ4eUS5cuqZ9yfP36de+Zm08rRen/oqQXnVaavaZoVq4eWK5YMEqZW3rOI03becty5cDVZkW5ekDJtUCx5B5QrnqU02wvUtKRpOQeuKgoykXlQG6SAi2Plk7Na2mzQSv3RaW0/qaWwndejxTcDW8CbHmF8f9SMii/cuVKdQUhWXRWlkqTT3nGUaZPeN3MQ/HIEyNRmf8blFfbUGbr1H1zZ3oI40fdh/YLyIyo2DgkNlSiouayO1WvdqKsSEgETtidcOEyaioq0ZA4FqMs/T2Ki0JswgiPY+5GGoH2ay/SPI8Af31NlZCHtH2/VWIgkl7ZAfsH43CldB2emZKAaJOMXRXD5mjyg5oTx881enQv/cjCJCTQCwIUr15AM0IWmSohD2YfPHhQXbBj0qRJyM3NxXPPPefHorMxiE/Lwtx1Fa1jUDUF+PGFzZiS+is/BsetGDN8sEeLzAi0aKMRCXCGvRGj5ofN0i3MyclR3+EljwXJCtuNjY1qi0vuPPq/9YclKRMLs2uwaXsdzl24hWQ181nY611A/IC2olrgqq/DCUs68pK7Xsnb/7ol5SAkZ6TDUlKHelcL4mO0/29dqLefBRDXs+KYOmwIULwMEEp5PvHjjz++zdKnn37afe7BBx/Epk2b3Medd2S8S/663VrOoHj6kygZsx6/XpWJ+Cgz4HJgf0UtMHcRMuIGAPVSSi3Wr96EcbGvIis+Cq4zJVgyezemF/wXUkVg/OlhdmuMJDAjJnURCqY/g9VrkhGr2uSCo2wTVq+vBSzpfpXCROFHQPtvLPw8CyOPpKUk41SyeKz2J+5p+/J57dq1Dh53niohXUaZs5WZmdn1VAnzSLyw7UMsGbILqdH9WuddRc/EriGLsPvNJzHMfcWkI3fOQzi7ZjxMpn6ITrMh8f1SbMn6fuC7jObvI2vLDqxw2zQea84mY8mGzA4+8yDCCIT3zdTw8S4lJUWR6RHe/oYOHarY7fbbnJUpETk5Oe6pEjI94tixY2oZPqdK3FZK5xPaVImZSpH9u85fBvH4O8VeNPO2qRhBNIBVhZiA+//RCNNsw7n71ltvYejQoV7tfvLJJ73OnJepEhs2bHBPlZB32MuCszIW5nOqhNcaQnmybUa/dR6Kz2h90VtoqC7CmvzrWPbsWMSE0jzWHTICFK+Qoe9ZxWlpaXjggQduyySCJmLkbdOmSsiYmedbJbqeKuGtpFCekzGvJdhd8BAOpv1zazfWdBeS3vkOM3YXYlnSwFAax7pDSIAPZocQfk+rlpWxf/rTn+LChQvurPJW1MLCQvextiN3F++9917Iw9ibN29WJ6uKyMkD23yrhEaJn0YmQPEyWPTGjRsHeZ2zbNLqknlc3h627vxWid5PlTAYIJobMQTYbTRYqD3HvnyNdXlzSaZJiMj1bI6Xt5J4jgT0QYDzvPQRB7+t8Bz78jXWJYV5TpWQYxnz2rNnD+677z71+Ua/K2RCEtApAba8dBqYrsySRWSff/55r91FLZ+0sJxOJ+rr1Rml6ttUz5w5g5dffhkFBQVaMn6SgGEJcMzLsKHr3vCysjIcOXIEr776KqZNm6aOj0kLTAbyL1265N+M++6rYQoSCAkBtrxCgj04lU6fPh1///vfkZeXp74GR+Z5ydiX3KGU5xy5kYCRCVC8jBy9bmwXsZLFN2STuV3SEpM5X1988QXuv//+bnLzaxLQNwGKl77jc8fWydiXDOxbrVa4XC5ERUVh79696tsm7rhwFkACISTAMa8Qwg9W1dqEVUWRxxq5kUB4EKB4hUccu/Wiu6XSui2ACUhAZwTYbdRZQGgOCZCAfwQoXv5xYioSIAGdEaB46SwgNIcESMA/AhQv/zgxFQmQgM4IULx0FhCaQwIk4B8Bipd/nJiKBEhAZwQoXjoLCM0hARLwjwDFyz9OTEUCJKAzAhQvnQWE5pAACfhHgOLlHyemIgES0BkBipfOAkJzSIAE/CNA8fKPE1ORAAnojADFS2cBoTkkQAL+EaB4+ceJqUiABHRGgOKls4DQHBIgAf8IULz848RUJEACOiNA8dJZQGgOCZCAfwQoXv5xYioSIAGdEaB46SwgNIcESMA/AhQv/zgxFQmQgM4IULx0FhCaQwIk4B8Bipd/nJiKBEhAZwQoXjoLCM0hARLwjwDFyz9OTEUCJKAzAhQvnQWE5pAACfhHgOLlHyemIgES0BkBipfOAkJzSIAE/CNA8fKPE1ORAAnojADFS2cBoTkkQAL+EaB4+ceJqUiABHRGgOKls4DQHBIgAf8IULz848RUJEACOiNA8dJZQGgOCZCAfwQoXv5xYioSIAGdEaB46SwgNIcESMA/AhQv/zgxFQmQgM4IULx0FhCaQwIk4B8Bipd/nJiKBEhAZwQoXjoLCM0hARLwjwDFyz9OTEUCJKAzAhQvnQWE5pAACfhHgOLlHyemIgES0BkBipfOAkJzSIAE/CNA8fKPE1ORAAnojADFS2cBoTkk0HcEWuByVGDjih1wtPSglpYzKM6wwppnQ1MPsvV1UpOiKEpfV8LyQ0/AZDKBoQ59HEJrQSNsedMw5fj/gX3PXMQbvOlicPNDeymwdhIggdARoHiFjj1rJoFWAi0NqH0/D5NNJkgL2Zq9Gfscnh20JjhsxcibbFW/N5kykFdsg8Ol9f2kRZUMU8Y7sFWXtKezZmPjPgdcai1tra71tUDlPCT0S0aerVH9pqWhFmUbs2Ftq/+28jt0G1vQZFsBq+lZFNqq8H5eRptNicjeWOFhkxR9Cw21Hvb4sntyHgq1+q0rYGvS/GrF4+tfipcvMjxPAsEg0PIVyhakI3lbPyyxX4WiXIVt0klkp65A2flbAJpwpvhlpM4+iKHratGsKGh2voahB5ci4aktqHULGIDKNVhd+k+Yt7seinITzg9G4JP0ZXi39gqAwUhbtxcHcpOA9CLYm2uwLm0w4KrGplmLsKvfQtQ2K+rQQrPzFfQrWYhF79a0CZ83EB9h4epKRM/7qC3PJgz75EWPPLdwvmwZkp7a77ZbufbvSDi4FKlLy3HeU5+qfo9Dg3LgEJurFiElxk9ZkjEvbuFPAJBrjJveCDTbi5R0JCm5By62m3b1gJJrsSjpRaeVZnV/lDK39JzS3J5CUTzTKBeVA7lJCizLlQNXPVJ1SCOZ29KlFyl2NVmzcvXAcsXSOZ/ynWIvmqlAS9d8WilKtyiW3APKVaUtT2ebO5d9W91txqvnNX992O3pZxf7fkqcN+XlORIggTsjcAN1h/aiEiOQEBvVXlRMGtY5naiYGw9XzX6UNDyE8aPuQ4cfa5QVCYnACbvTd+uo2zRmxKSthdP5JlIufIqysjKUlf0OxXkzkDDvo3Z7/NqLQmzCCOBEHepd/40m1W4rxgwf7MVuJ0oq/nzHdy478PDLRiYiARIIEoFbuHCuDg1d1NZw/BwueHbBukjr9SvXSRRnP4LohFnYevQSADMGZqxHTdHMNiG6k8JrsX7KkLYxsdbxPFO/hzCvsiuPvFrp9eT3vJ7lSRIgAR0Q6I+hw+NgQZ1PWyxjhmOoGaj3maKrL27AsfOXmLdvEkrrNyFrWP+2xDK4fxZAXFeZ/fhuJors2zE3foCPtK03DHx82e1ptry6RcQEJNBXBAYgbsI0pOMs7PWt9wTVmtru7pkytuHCo1Mxx3Iah09+iw5tIJcT9hNAYoIVHh3OHhrqQr39LJA4FqMsmnABaPkHrjTe7GFZnsnNiEn2ZXc1Nk6OQ0bxmY7+eGb3c5/i5ScoJiOBOyFw+fJlHD58GGvXrkVKSgoKCgrU4sxxGchbfi/Wr34Htga5u3gLDVUfoqRyLDaszUL8/0jGz95MwZ7Fr2FLdUPrD166ekuWYn1CDtY+G99xTKlLI9vGpdQ0N+ByxSA5Ix2Wyg+xrep8a9ktDaje8hoWF5/ssqRuv4yZgJcKJnWy+wzKVq9CDl7sod3eawsb8ZL5MdxIoDcE+uraOX78OLZv347MzExMmzYNBw8eRHJyMvbu3YvFixe3mmoehrQ3t6HmhetYbb0LJtNdsK6+jhdqCrEsaSCAGIycuxlVH0zChbwk9JO5WNG/gH3SFth3L0VSVE9+wgMQN30Blt/KR0K/EXhm51lEpS7B7m1j8Kcpsa1lx76KT+/PRnlpLiy9genO0x/DstZ2snsmdg1ZhJodL/bQbnehHXbC5vEgPv7SIa63HZDPbUjcJwLFpr6+HqdOncL+/fuxYcMGzJ8/HxMnTsTjjz+O+Ph4d33cCQwBildgOOq+lED9QHXvaC8M7C2b7777Dp9//jmOHTumtrCsViumTp2KRx99FGPHjsXdd9/dC2uYxV8CFC9/SRk8XW9/oAZ32y/ze8LG4XDgyJEj+Oyzz/Dee+8hJydHFayHH34YsbGxftXHRIEhQPEKDEfdl9KTH6junQmwgV2xkYH2mpoa9W/lypXuruDo0aMxZsyYAFvC4npCgPO8ekKLacOegHQF7XY7Dh06pI5dOZ1OdcB90qRJuHTpEgYNGhT2DIziIFteRonUHdrZVeviDos2fHZhU1paij179ri7gjLILlMa2BXUb3gpXvqNTUAto3j5xilstm7digkTJiAhIYED7b5R6eobipeuwtF3xlC8fLMlG99s9PxNT2a46dkP2kYCJBBhBCheERZwuksC4UKA4hUukaQfJBBhBCheERZwuksC4UKA4hUukaQfJBBhBCheERZwuksC4UKA4hUukaQfJBBhBMLq8aDy8vIIC1/P3CWfnvFian0TYMtL3/GhdSRAAj4IULx8gOFpEiABfROgeOk7PrSOBEjABwGKlw8wPE0CJKBvAhQvfceH1oU1gRY02VbAanoaG8vKsDE7sW2B1gzkvV+NhiYH9m3MhlUW3TAlInvzYTR4rH/W0lCLMvf3kiYDecU2OFxaoha4HDYU52W0L/w6OQ/FNkf7KtsuB2zFeZis1uGtDP0GgOKl39jQsoghUI6crTUYsfIwFOUmnAd+iOoXxsE6cg1O/uhXqFeace30K8CGnyO//Ku25c+qsWnWIuzqtxC1zQoURUGz8xX0K1mIRe/WtIqTqwbvLsrFwYR/xzVF0tyEc9U9KJmSj52OGwCuoPbdZZh98GH8x7XmDmUs2em443UV+zp8FK++JszySaBbAknIXbUMWfExAPrDkjwRKRYL0t9cjqUpFphhRlT8OExKvIQ9R/8CF1rQVF2OTfZ0ZM/7V1jafsVmy0S8MGcsqvadhLMFaHGexL6qEZg0Ia5tYdr+sKS9jj8oO1tXsW65gC/2nUHipHGIb1tCzWx5Amv/UIeKuSN7sB5ktw72SYKwmufVJ4RYKAnojoAZMWlr4XRKt/BTlO2/LMtc48rRQsxbXwmkT1MtNltH4YnUfOQX/RdGZQyAK/ZHSFMFss0h81A88sRIzMv/DcpHZQCuWKSnxd/BCtzBBcWWV3B5szYS8EJgBBJio7yc7+KUrJqd/QiiE2Zh69FLAMwYmLEeNUUzgRN1qJdxr6gUvLK7Ch+M+ztKVy/ElIR/7jQuNhBJr+yA/YNxuFK6Ds9MSUC0yYrJecWwOZq6qFwfX1G89BEHWhFBBGRFIvnr/XYDjp2/xLx9k1Bafw5/WLcAWVlZyEobhqv2sx2LjYpHWtYCrPuDE0qzEzWlT+BC/hSkrq5CqzzFID4tC3PXVbSOidUU4McXNmNK6q9ga9IG/jsWqZcjipdeIkE7wpaArKRdWVmJtWvXqisR3XvvvaiqqroDf12oF5FKHItRlv7t5bT8A1cab7Yfd94zW5CU9QKy5ySh4fg5XLhNm/rDkpSJhdlPwdJQh3MXbnUuQVfHFC9dhYPGGJ2ALJ12/PhxlJWVITc3V52isHjxYshitcnJySgoKFDv6klLqffbICRnpMNS+SG2VZ1vvSvY0oDqLa9hcfFJd7EtjmJkyPSJsjNtUyNax8gqqoG5i6YgDmdQnBGHyXll7dMrXA7sr6gF5qI9PkQAAAjOSURBVP4bMuIGuMvS4w7FS49RoU2GIaC1qkSUMjMzcc8992DHjh2q/bNmzcL169chD8SLgKWnpwdoKTUzYlKXYPe2MfjTlFj0kzlasa/i0/uzUV6aC0sbPXP8bGyrWYQhu2YiWp3H1Q/RqbswZMmv8Wbm92E2j8QL2z7EkiG7kBrdr3UuWPRM7BqyCLvffBLDdK4OYbV60Mcff2yYiz7Yhj799NMgH+/UhY3Mk+pu0xakPXv2LI4cOYINGzZgxowZ6vqO0qoaPnw44uPjuyuG3weIAKdKBAgkiwk/AtKq+uqrr3Ds2DF88cUX7gVpR40aBWlVvfrqq1xBO4Rhp3iFED6r1g8BaVV98803OHnypNqq0gbUpSsorSrp8hUWFurHYFoCihcvgogkcOnSJVy8eBHSBZRNxqrmz5+PiRMnql1Btqr0f1lQvPQfI1oYAAJOpxNff/01pCt49OhRtcRx48a5B9D9GfMKgBksIoAEKF4BhMmi9EHg2rVrOH/+PBoaGnDq1Cns378fU6dOxcMPPwwZr8rIyEB0dLQ+jKUVvSZA8eo1OmbUCwFvrSoRqYSEBMidxAULFqB/f4/JnHoxnHbcEQGK1x3hC11m+VH2dOtpHj1OrZBWVWNjI86dO6d2A2UOlbSqHnzwQbVVNXnyZMgMdm7hT4DiZeAY9+U4jclk0gUZaVX97W9/Q11dHb788kv1mUCtVfXEE0/gueeeY6tKF5EKvhEUr+AzZ40+CHhrVaWkpOCRRx5BXFwc2KryAS5CT1O8IjTwenBbpivI3CppXckk0OrqavURGxmr+tGPfsRWlR6CpGMbKF46Dk44mXbr1i31DuC3334Lu92uPu+ntaqsVitk2sLy5cvDyWX60scEKF59DDhSi/fVqnrggQfYqorUiyLAflO8Agw0EouTVpXcAZRJoJ6tqh/84AfqWNWYMWPYqorEC6OPfaZ49THgcCze89Gav/71r+okUHkGUGtVybuqOAk0HCOvL58oXvqKh+6s6dyqkgeXZZMxKrkDKK2qF198UXd206DwJ0DxCv8Y98hDebf66dOn1TzvvPNOh0drRLDYquoRTibuQwIUrz6Ea4Si5fXE0po6c+aMegdQbJYuoGwyI5+tKiNEMTJtpHhFUNy1VtVf/vIXfPbZZ+rL9eQ1MDIJdNKkSfj5z3/ufrneypUrIVMYuJGAXglQvPQamQDaJa+B0RZ8SE1NxeOPP46cnBy8/fbbuPvuuwNYE4sigeARoHgFj3XIaoqNjVVXs5FPbiQQLgR0vj5IuGAOvR8UrtDHwJsFrcuTPYtixw0AN+AofhYm64rAL/jaIsucWWHNs7UtNuvNmkbY8pJhyiiG47Y1Hb2lD+05trxCy5+1k4AHgQGIn7sTylyPU4HaNY/E3Aon+qLoQJnY03LY8uopMaYnARLQBQGKly7CQCNIQAh46zbeQkNtGTZmJ7YuCmvNxsaK32GjuwvYgibbClhNycizNXpgbOsCal1QL93GloZalG3MhlVdkDYR2Rv/E59fuOlRhr53KV76jg+ti2gCLXDVvoNZyb/GxRkf4ZqioLl2IfrteAM5lQ13RsZVjU2zfoKtF2eg6lozFOUwVo6owyfbW5+guLPCg5Ob4hUczqyFBHpB4DKqd/4W9tw8rMwaiSgAZst4LF35MtJ7UVp7lhY0VZdjk/1ZrFqZifgokYEYxGctw6rcpPZkOt+jeOk8QDQvggk0/RkVJU4kJlhV4dJImON+iJ+kW7TDXnxeRk1FJRoS4xCrCpdWRBRiE0ZoB7r/5N1G3YeIBoYTAW1lbvEpPj4+NK61NOLccWdo6g5grWx5BRAmiyKBzgTkkazjx49j+/bt6hJssjL3hg0b1NW6O6cN2rF5MIaPMf6jXxSvoF0xrCgSCMijWIcPH0ZBQYH6gLssw7Zjxw5ERUWpj2Rdv34dhYWFGD9+fPc4YkYjY44VJw6fQoPnpFGXE/YT2oC9GVGxcUjsvjSPFIOQnJEOy4k61Ls6FIx6+1mPdPreZbdR3/Hp0jq9LE/WpZFh/qW8lUPWkKypqenwVo7k5GRVvGRdyd5vg5H60gpMf+x1rNgWj3fmjkKU6wzK1qzD+gZAG/VqHQPLR/77n+BnKXMwMsoFR9kmrF5fC1i8De2bEZO6CAXTn8TsJQmwvdMpj7csvXeiz3JSvPoMbd8WrMcFYfvW49CXLuNV8prrs2fP4siRI2r3b8aMGeqit53fyhEoa83DMrGlaiB2Fv0C0aZKAOnILXoauaknUKJVYo7Hs1t/g8trXsFD0S+0ptm2HKv+Xx2qXtcSdfo0fx9ZW0oR/e4apEW/gAZYkJq7Dks2ZKJqX6e0Oj00KX25cmkQnZZWCH/QQQQeRlXJe8u8/Qx8vUJo4sSJGD16NGSJtpC8lUMmnE5PQ/6YD3BmXRpiwigWPXGFLa+e0GLasCYg41WnTp2CdAX379+vrifp+QohGaviph8CFC/9xIKWBJmALHYrKx7JJmtIyssX5VMbr+KbOIIckB5WR/HqITAmNyYBbdFbGVwXwZKB9KlTp+LBBx9UHdq7d6/7LbK69zAM3xDRG+Yc8+oNNebRPYFr166pK3TL4Hrn5dmGDx+OYcOGoX///qofvsa8dO9khBvIlleEXwDh5L5MBq2rq8OXX34JGWyX1Y6k68fl2cIpyu2+ULzaWXDP4ARu3LihriU5efJkyORQbuFNgOIV3vGNKO9kYRFukUOAjwdFTqzpKQmEFQGKV1iFk86QQOQQoHhFTqzpKQmEFQGKV1iFk86QQOQQoHhFTqzpKQmEFQGKV1iFk86QQOQQoHhFTqzpKQmEFQGKV1iFk86QQOQQoHhFTqzpKQmEFYGwejA7rCJDZ4JKwNvLCINqACvrMYGweTyIF1+PY88MJGBoAuw2Gjp8NJ4EIpcAxStyY0/PScDQBChehg4fjSeByCVA8Yrc2NNzEjA0AYqXocNH40kgcglQvCI39vScBAxNgOJl6PDReBKIXAL/HxGoRpZdlu22AAAAAElFTkSuQmCC"></p>
<p>At time <em>t</em>=0 the vibrator is switched on. At time <em>t</em><sub>B</sub> the vibrator is switched off and the system comes to rest. The graph shows the variation of the vertical displacement of the system with time until <em>t</em><sub>B</sub>.</p>
<p style="text-align: center;"><img 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"></p>
<p> </p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain, with reference to energy in the system, the amplitude of oscillation between</p>
<p>(i) <em>t </em>= 0 and <em>t</em><sub>A</sub>.</p>
<p>(ii) <em>t</em><sub>A</sub> and <em>t</em><sub>B</sub>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The system is critically damped. Draw, on the graph, the variation of the displacement with time from <em>t</em><sub>B</sub> until the system comes to rest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>i</p>
<p>amplitude is increasing as energy is added</p>
<p> </p>
<p>ii</p>
<p>energy input = energy lost due to damping</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>curve from time <em>t</em><sub>B</sub> reaching zero displacement</p>
<p>in no more than one cycle</p>
<p><img 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D44XvZdFg3gfrl20ob9uDYaLNhEcdZg5WPjrsuKCVeY3IYtNzkJ6/nnn6dZs2bxx8FW2rAf1yiTDfZzkzbYLyfbSRu8j+IMP599tpLWLnueoejD/+tPx+z9afp9nFiPP/54i/VuJWfGwn5uPhvoDL25+WyeeeYZwh+3XG00nDVYMj6YD7bcJBb2u5/jfSYs1w6xC1/cfFjSjw9Lw1lisR+XjwZL+vFxxr6ouJecfXw0fjQ2knM+WOU0idASv3CmrbVSoF27dlZIxQqpBHHhKz6QLuCwZQ397yyi4ZPPoW/Wb6BT/+cZ+snAYbRf29YFCnx+ZGEBn02cRRXcwgI+LMkHAkg7WTBBfo5jpI3PjxYrirMGKx+bTz9tOYgMgqIS//nwPrroxPvoIu7bPufQpH9t43e2NQVMAVOghQI2ibCFHPaGFbBJhKyEbTMr0DyxcPIhtBiFVbYsogm9f0+9Ft/zxWPxzAfbJ6ZAYhRADnTv7xDd/+ov6GjcVtryEs388Xfpyq6/o1cnD6LOiWFqREwBUyApClgKR1LOhPEwBcpOgY9pxbz51DAfk7HaUJvdB9OUhqV0/9INNpmw7M6lEW6hQMfedMbQE6jh/U/pXy0+sDemgClgCjQpYANoiwSvAlZIJbp4h8xB8wmpsYmrGALya7GgfVjT2HDOXZgfcK7/2yyaPGsILdzU2DTxKpWixrpJRFc2TSbU+NHYxMVZU1hAw0dTNEBjo8HScNZgxWWDmIiKaQ1njZ9i2/zrXy/RP95/vynst7xKT8xdQUNOPpz2bdoT/BvVdy1nTUxrsOL67tDEooazxo8mPuLC0sR9XJzjwtL40cSZRmeNH41NXJyBVU450DaAxhmzZgqYAlkrsGHZEqJJI2hg5y++Rtr2/CZNuHBNi8mEWTu2A0yBUijw/t10+gE1TUvZdRpCs7pOpFu+3dPWOi/FuTBMU6AMFLAc6DI4SaWgaDnQpVDdME0BU8AUMAVMAVOgHBSwVTjK4SwZR1MgQQrgx9VLL70UrE7Rs2fPBDEzKqZA9gr8+9//piVLlgQHnnTSSfSlL30peyd2hClgClSdAjaArrpTbh02BXJXYP78+XTaaadRTU0NNTQ00NKlS+mEE07I3aEdaQqUUAEMnn/yk58Q4hrtqKOOoj/96U82iC7hOTFoU6BcFGh39dVXX10uZI1n/ArgP44XX3yR1q1b1+Lv6aefpr/97W80cuTIABQLpWPAhL/a2tr0PixS379//zQxtmMbLByPBd3dtXJzseGF2lEljH1LP5g08eCDDwb/CTIhaaPxAxvckfr444/poIMOSvfV7Tt2osBFWN81WPBz5513EtbaPfjggzNiQefXXnuNDj300Iw2mHQUxVljkwlrzz33pJ/97GcEnYGDO3UffvghnX/++UFRCKlPJj98/tARjY3kjOOgbbZ+ENOLFy9Oxwd8yJiWfHxYMqZ9fqQN+3E1CsN69tlnadq0afTDH/6QHn30Udq8eTMdcsgh9Morr7TirMHK14Z1wha8w65DqbOv73xtxHH93HvvvcG62zvvvHOQv8zng+ODsXycEcs/+tGPaNOmTcFfXV0djRgxgvbaay9vTMd1zcuYlpyhGbB8nLlfsNF8d2iwZCz6+MTlR8YHY7nXhsTiGHL7nomz60fGvQ9L+vFhaThLLPbj8tFgST8+ztgHX2HXj+Ts46Pxo7GRnPPBuu++++j444+Hi8S3L2b/JJ6qESy2Atu3by82pOElVIFt27YFd+pQYGeXXXYJWOL1Z599RmeffXYwkE4o9bKihR8k0BOrEFxwwQXBjPTBgwcTUmVOP/10QmVCay0V2Lp1K3Xo0CEYPLf8JPwdtPz+97/fyqhtW/tvsZUotsMUMAVaKWCTCFtJYjuggE0itDhgBfgx96hRo4I78v/93/8d3BX9xje+Qbfffju9/fbbNHXq1OCO6f7778+H2TZLBd577z265JJLaNy4cd60GJyHq666ig488MDALkv3Zu4ogLv7ePJ28803B0+t+Enb17/+dfrpT39KQ4YMcaztpSlgCpgCrRWwAXRrTWyPDaAtBhwFrrvuOurcuXPooG316tXB3bwnn3ySunTp4hxtLzUKICUGd5jvuOMO6tevX+gh48ePD1KikGpgLXsFHnroIXriiSeCwbOcMIg4RlYj1le2ZgqYAqZAmAL2rCpMnSr+zAqpRBclQZ5eVNPYxFUMQVN8QGPjFhbAgGL58uU0ZsyYFl2VnDHo++Uvf0nXX3992s71k94pXmhssuUsINJvNYUFNHw0RQM0Ni7WhAkTAv3k4NnH+ZprriEMAnFu0DRYcdkALyqmfZzTJ8F5EeVHg5WtDZ6sIUZx51kOnhHTXbt2DRjCztfi4qyJaQ2WvA59nDVYbiz6fGBfXH408REXlibuNX3XcI4LS+MH5yMqPjScNX40NnFxBpYVUoEK1kwBU6DsFcDdOPzJwYavY8OGDaNPPvkkvaKBz8b2tVYAE3kxQRP6aRrOxZQpU4I7/kjrsKZXAHfvcZc/LJ5xZ59X5dB7NktTwBSoNgUshaPazriyv5YDrRSqgs2wEsTcuXODwZq2m4ib4cOHB3erwgYpWn+VbocB8Mknn0xYSSLbNbWRWtO7d2/1wLvStYzqH+7aY0Ug/PgIa5xOgycv1kwBU8AUyKSApXBkUsb2mwJVrgAmBg4dOjQrFTAIxCoSyDG1Fq0AdMIdz2wHz/CMJe7OOeecYEnBaKTqtsAPFaRujB07NlII5PD37ds3nSITeYAZmAKmQFUqYAPoqjzt1mlTIFwB3H1Gy6VIyrnnnhsMViy9IFxjHtRhubpcGgZ6t9xyS7AiSi7HV9MxL7zwAg0cOFD9Q+W8884LigRVk0bWV1PAFMhOARtAZ6dX1Vhv3LiR1qxZk+4vJnXwH+/EezmRQdosWLCAHn74YT4k2OZiw1jYcpN+MGkCxQfcJm00fmADzuDOTfrB/qi+a7DgB5zd9X19WPg8ykbDWWMDnJtuuikoMAF+Pj5hnHE3FYMVLBUWxTmXfjEnbLlp/MDGjQ/uF7bcpB/sdz/HexnTPj/Shv24vn77298GS9K5q5a4n+OYKM4YfCOVIyoWNXw0NuAHLJcnXrvvJWdf39kPPuMm/bCN61va4NiovuMYFADq1asXQ0XG9DHHHEO33npri35psaL0gR/NdajxE3Ydcmc1WDLufTrH5UfGB2Nhy01iYb/7Od5n4uzayZj2YUk/mbCivjskFvtx+WiwpB8fZ+yLinups4+Pxo/GRnLOB6ucJhFaKW+caWutFECxjPbt26f3u5UEeSf2YdDqNmnXo0cPevPNN12TFlUJ8YHGhrFc/+5rBujUqRO/DLbSRuMHNqtWraLu3bunfUk/6Q+cF9JGg4XDwRkacJN+sJ9XBwizgZ8ozhob5C7PmTOHZs2aFcD5+ERxRurHFVdcQYMGDWLKrc57rv3CcZKTRh9ovGXLlqz4+LBkvEouOEba+Pw89dRTrQp5SF9RnDH4Rg71hg0b0v3yYWn4aGzAD9e8y9N9zX13dfbxYT8uaemHbdz97mv3WPe1tOFcfKQWcZM22O/GNHTFIBqVAMOa9IP3UfowVtS1CjvXv/uaObmcpb1rE4WluX403x0aP1ExDd4Sy9c3LZb7/49PQ+nHh6XhrLl+tFhRnDnO+BxrOPtsNH40Npq+a/zABpUPy6XZJMJyOVNF5mmTCIsseILg7rnnnqB0NIp65NMGDBgQLLdmxVVaq4jrCytCYBmyfBvSbe666y6aPn16vq4q8ng8CcE65tmum42VOHCe8r0OKlJU65QpYAqQpXBYEJgCpkALBbBawYknnthiXy5vMPCIY4CYC3bSj8HgTLtsXVRfkKeOqnqoZGitpQLIM7/00ksJVTOzbYcffjjhx6Q1U8AUMAV8CtgA2qeK7SMrpFKdhVRQnAOPDzt06BB6FWgKOKDkNNbcDWuaIgbIwcNC/WFN4weP1qMG9Bo/mqIBUTYYmEEf4IU1DWdgfeUrX6FFixZldBXFBwdqbGAncy8lqIazxk8cNpg8iJU3kKMZ1WRM48lJbW1tcBeaj43qu5azJqY1WJIz83S3GixN3MflRxMfcWFpYlrTdw3nuLA0fjRxpuGs8aOxiYszsMopB9oG0Dhj1kwBUyBQYOnSpZTrqhBSQuT7ffnLX7blwIQw+JGCgZkvH1KYqt/26dMnSJdRH1AlhhiIYUWNXBueEmDtaGumgClgCkgFLAdaKmLvAwUsB7o6AyHuvOW48qkr6WzkmpMbpUHc5y4Krxw+z1eTOHPVy0Ev42gKmAJ6BewOtF4rszQFKloB3BlFi3PS35FHHklYbcLaFwpAj+OOO+6LHTG9wiS5sDSOmGDKxg3f6c8nnrEkY319veWXl81ZN6KmQPEUsAF08bQ2JFMg0Qpg3e9sVyqI6lC/fv1sAOKIhIl+GJDlUnnQceN9edRRR9GSJUu8n1XjTsRzHBM1cU288sor1Sih9dkUMAVCFLABdIg41fwRCqm4/2nwRAt30hNey4kubMfaYU3Hxx9/nN8G21xsGAtbbtIPJk3w2sWZbDR+YAPO7nqUEgv+o/quwYIfcHbzLH1YzzzzDOGPm89GwznMhlff0GBlwxnr7yKWfJw1WJIzNIAvt2n8QGM3PpiP60v68WHJmPb5kTbsZ968eUGpc7zXYGk4M1b//v2DQjEff/xxK63ZxtWMefM+jQ2OQdy7mkk/kjP3XR4T1/WTyQ9+TOAJiIYzOGaKaaxI8+CDDwYyZcJiDbVYMqalhvAXpXMYZ+aDrQZLxqKPT1x+ZHwwFrbcJBb2u5/jfSbOrp2MaR+W9OPD0nCWWOzH5aPBkn58nLEvKhYlZx8fjR+NjeScD5ZNIoR61spagXbt2pU1fyOfnQK4Mzp37lzCHeO4GwpSWBpHk6rPPfdcUKAjbo3hDwVDsOLEunXrCuG+rHxu2rQp+DHhVh/MtQPwgSp0Vpo+VwXtOFOgMhWwSYSVeV7z7pVNIsxbwrJygHWJV6xYQRMnToydN+6I7rXXXpFV3WIHTqDDNm3aBMvFueW746SJpwhIEan24h9xF5dB0RtU18Sa29ZMAVPAFIAClsJhcWAKmALBHWKUhC5Ew2ARgw/8KKvmhv5Dh0INnqEtSuHa3X6iVatW0UknnRRbuJ166qmEJfGsmQKmgCnACtgAmpWwbQsFrJBKdPEOmYPWQsDmNxobTTEEzoPzYfA+TfEBnw0eTU+dOpUOO+ywwJUGK1vOGIC89NJLTDW91WD5OKcdNL/Q+NEUFtD40RQN8Nmg/9CBmwZLw9nFwuREpOLgrr/bXBt3v/taYwP7qJjWcNb4yccGlRmR/8wtijPswmIaaUj4XONHY6OJaY2fMM7cdw2WJhbj8qOJj7iwNDGt6buGc1xYGj84t1HxoeGs8aOxiYszsCwHGipYMwVMgbJQoK6uruB3RjGww6SWam7ofyFW35Cajhs3rqrzoPGDEDnLceQ/s7Z4aoDiNw0NDbzLtqaAKVDlClgOdJUHQKbuWw50JmUqbz+KnaDFvYSdqxQmKWJJseXLl7u7q+p1vkU9tGJVex40vrvwRGX69OlayVR2xbhOVETMyBQwBRKhgKVwJOI0GAlToHQK8HJfhWTAxSwwkK7Ghn7//e9/j7VITSYdu3fvTkhhqNaGVJm+ffvG3n0Uv8GPE2umgClgCkABG0BbHJgCVaxAIR53Z5Jz4MCB9Pbbb2f6uKL3o99IrShGq/Zl1wqVKoP0G6xwIvPLi3FODcMUMAWSp4ANoJN3ThLBCBMQrJDKyvS58E00kZM4pA3ewwZbbtIG+zMVcOBjsJUL8Pv8yOIDGpuHH36YxowZE6whzHgarFw4H3DAAfTkk08yTLDVYMl+4UBXU7zX+JGFBVgf15f048OSRQN8fqTNG2+8Qeh/tlgazhIL60EPHjy4xaoR0ob75fLR2MA+KqYlZx8W+8Fn3LDP5cM2cp/7HpOXEB9uQ4y1b98+vUvjB8TJq0IAACAASURBVMaamO7Ro0ew3CM7h2+XjxZLxrT0A/9ROms5a7Bk3Pv4xOVHxgdjYctNYmG/+zneZ+Ls2smY9mFJPz4sDWeJxX5cPhos6cfHGfui/v+RnH18NH40NpJzPlg2iRDqWTMFTIGiKrBt2zbKtgAOim4U4nG3r+NI48CXcTU2pBVwGksx+n/88cfTa6+9VgyoRGHg7vDatWupa9euBeGFlWpsmcCCSGtOTYGyU8AmEZbdKSsOYZtEWBydS42CMttTpkwpyuoQSBfZddddq7KgSqELqMg4KmRhHImVpPerV6+m2bNnBzFdCF4cw59//nmLpzaFwDKfpoApkGwFLIUj2efH2JkCBVMAgwGsGVyMpdXQCaQWVGNBFUwgPPbYYwtaQEUGSbdu3apyxZM333wzKCYj9YjrPZdLf+GFF+JyaX5MAVOgTBWwAXSZnrhC07ZCKuVXSEXmxPlixC1QgPWffRPbkGYRlWqhKeDg84Ol3DZs2JCm5rNJf9j8wuUsP+P3Gj+awgIaP5qiAa4NJhBiAqVsGiwNZxeLMfCjCD+O8CMJzWfDtrzV2MA2Ks40nDV+NDaSM/I+fekbUZyBpYlp+DnvvPOCSoc4xtc0WJqY1vjRcNZgaWIxLj+a+IgLS8aH73xp+q7hHBeWxg/6ERUfGs4aPxqbuDgDy3KgoYI1U8AUSLQCa9asISzNVczWu3dvwhd7NTVMICy2ztB37Nix9O6771aT1EG5eNx9L2Q7/PDDideELiSO+TYFTIFkK2A50Mk+PyVjZznQJZO+aMAXX3xxcAe6WCkc6Fihc1SLJl4WQOPHjw9SV0444YQsjsrfdNq0aUH1PBSwqZaGXPNUKlXw7hZz7kDBO2MApoApkJMClsKRk2x2kClQ3grg0T7KHWNptWK2Aw88MKgSV0zMUmMtXryYDjrooKLTQOlpPJ6uloYf/cixL0bDjxKki1gzBUyB6lXABtDVe+6t51WsAB7t4xE/JkUVs3Xp0iWAq5ZiFPihUqwKhPI8HnHEEfTWW2/J3RX7Hrn1yLEvRrOqhMVQ2TBMgWQr0O7qq6++OtkUjV0pFEB+LMrWDh8+PIDHpA5MhsIf5xhi37Jly1rMemc7tlmwYAHBF9ZP5ZaLDWNhsgL7ln6QW3vfffdR//79GSooJuHjHOYHfletWkVYPQGFE9AkFvZhEgcGKdykDd5DnzAsHIs7wQ0NDenVMKQf2Dz22GPBur6cbuGzAZ8oLBROQb/wV1NTQ59++mmLc6rFyofzPvvsQ7gTjclemn4xZz4X4Ij+cxxoOQMLhQw4PlhDNz4kHx+WjGmfH7bZZZddaOvWrfTNb36zVQxpsDScGUteY4iFyy67jPAVn8nG7bvGBn2NimnJmTV0sdhPvtcP+jhv3rzg++XZZ58NUlY+/PDDFjHNWFHXhiam+Zrfa6+9gslOe+65J3300UfpWNRiyZjGca4+0ExzPWs4a7BkLPr4xOVHxgdjuf2XWBxDmmve9SNj2ocl+54JK+q7Q2KxH5ePBkv68XHGvqj/e6XOPj4aPxobyTkfLIw7sI59ObSdyoGkcSy+AviP363m5f5Hx2ywT04Ik3YY9GBpKbflYsNY7rHua/bfqVMnfhlspY3GD2wwgO7evXval/ST/sB5IW00WDgcnN3BofQDG7mygM8Gdu5+9zXTBBb69fvf/54uuOACbwqHBisfzvgPBTHRr18/Vb+YM/dB9hPvNZyh8ZYtW9JufPpIPz4sGdM+P2yDu6IHH3xwgCnttFhRnBkr3TEnDrB8Hv8QLNZ1KHX2aQgtor472MbVzX3N/UV8oKFYjS+ms/ED7tx8WPwZtiNGjAjeunbZYGm+X6RvFx+vNdehvH5cn+xPxqLPJi4/Mj40WOAp7TSc5bUhfcCv9OPD0nCWWD4/Wiz3WvVxxr6o60dy9vHR+NHYaPqu8QMbVDUsl2aTCMvlTBWZp00iLLLgRYbDZKtSFYOopiIfWK2hY8eOVKqJfJjAiEElfqxUekP6Bu5eFaviIybE3nrrrTR9+vRKl9b6ZwqYAh4FLAfaI4rtMgUqWQHckcRkq2LnP7OmeAxbLbm5uCvq3mlkDYq1Ra6uezerWLilwCl2rnmvXr2C9KtqyecvxTk1TFMgyQrYADrJZ6eE3KyQSuUWUsHqAaeeemrG6NIUFtAUcMjkByt/IHcTLZONSw45eMhfDWsaP3jkCd5hTeMHXMAprLENVuDYe++9vaYaLA1nxvKB7LvvvoHGYTZ8nMYGtsjNDWsazho/GhvmjCdmmBSbqUVxxnGamHb94AfotddeS+vWrWsB69q0+MB5o4lpjR8NZw2WJhbj8qOJj7iwOD4c6Vu91PRdwzkuLI0fdCIqPjScNX40NnFxBpYVUoEK1kwBUyCRCqCwB09GLAVBDDw4N7cU+MXELPZdUdk3TNishrv9mMiHCX3FbieffHLkj6liczI8U8AUKI4Cdge6ODobiimQGAVwdwfV1ErZUNoaOdiV3JAqE3ZXtBh9xw8lvttfDLxSYXzwwQclqfaIFV2uuOKKdMn0UvXfcE0BU6D4CtgkwuJrXhaINomwLE5T1iSxLvGuu+5alGptYeRKPbkujFtcn2FZtblz59KUKVPicpmTH1TNQ1XCYk2uy4lkngddd911hLvBxa72CNqlxM5TNjvcFDAF8lDA7kDnIZ4dagqUmwIooDJu3LiS08bKFPX19SXnUUgCpborKvuEu9CVfrcf65kjXaUUzdI4SqG6YZoCpVfACqmU/hyUlAHunvzlL38JCi2gmAfyYzEpZuHChbRo0aL0I2hMVuHJFr179w44Yx/s3OpfbMc2mOiASWtcvAIH5mLDWBh0sW/pB5MmZs2aFeTXsqjSRuMHNkuXLg0Kl2BdSh9n3KE//fTTCQUVsM7vzjvv3KpfGiz4vv322wPdM2HBBv1CQZq+fft6+WAnltQK0wc2v/rVr6hdu3Z02mmnZfSjwcqXMzg8/fTTwVqmUf1CCsJrr73WYh1YaMtxgI5oOKPIzpIlS9LxAR8ypqUf+JZYMqZ9fmDzpz/9ib72ta8FRWPgB+ub4hpDiW20xx9/POjXoYceGrxnG/4c76ERJiIeddRRgQ37cP2gwAOuMY4f9sM22P7tb38LsDPZ4JgoP+wXvFOpVLofzIl5S858HPPh9/Djfi9IP3gfhQVf0BoFY3CnH9dhrn7uvPPOoLAQr9st/QALsSg5NzY20ve+9z2aMGFCcI1qOWP1Di7xngkrTGfw0XCGPlFY4IxrjGPRxycuPzI+GMuND4nFMcMxhveZOLt+ZEz7sKQfH5aGs8RiPy4fDZb04+OMffAlY9HFkpx9fDR+NDaScz5Y+J62QipQ0FriFTj33HPTHLHkFre2bdsGi/TzeyyHJRv2oQKR26QdBnwYlLstFxvGco91X7N/OZFI2mj8wAZfGlgcnpvrB4/mf/7znwePjOvq6ujJJ5+km2++uVUOpgYL/sHZHdi4WIzP/7Hxe59N586dW3Dw2aBKG/6z5+az0WDlyxkrU2BgKNdH9vFBxUT3XIC7tNNwhsZujEsf8Cv9+LBkTPv8wObBBx8s2V1RPr/YongDCgP5+ubalevr7du3B9RLtSwjik5hNY4XXniBOnToUK4yGm9TwBTIUgHLgc5SsGoxtxxo/5lGDjEe2boFG3AXH4PXSy65xH9QgvbiaQEmEZZqsOFKgWIuuMNWqa2UxWpcTSv9Wk5C//CjGtfVxIkTXenttSlgClSwApYDXcEn17oWvwJPPPFEUMLXnZD1wx/+kC699NLgMWn8iPF5xGNcPAJNwuAZvcIKFRj8VGLDDy20JGjNd/srUWf0CUvY7bHHHiXtHh6l22ocJT0FBm4KFF0BG0AXXfLyALRCKv7iHddffz1hVQM05OmhdenShW655RZ69NFHg/fuP2zj7pOvkUOL/O2wxrm6YTZRWMhtx0QrLHof1jRYcXBGGsjLL78c5CGH8YmrqIKmsICm75qiAWvXrqXzzz8/rFvp/OswIw3nKD6IT6xHDR3DWpQfPjYqzjSc4SvKj8YGnDFXw82HZ57uVoOlielMfvBDidM4Mtm4fDQxrfGj4azB0sR9XH408REXliamNX3XcI4LS+NHc23ExVmDFRdnYFkhFfebwl6bAhWiwOrVq4M7uO7dZ+7aiSeeGKR18PskbpGLjvLDSWnIHcZayZXY8B8KVhpJShs+fHjFav3OO+8QKi6WuiG166677io1DcM3BUyBIilgOdBFErrcYJKQV5g0zbB2MdqIESO81JBf7OZGe41KuHP8+PFB2kQpqxC63Z8/f36QwlEOueMub81rxAGanCSpObYQNsjT//rXv079+vUrhPuS+kxKXPP8CEwqxl1/a6aAKVDZClgKR2WfX+tdjApgCbQjjzwyo0cMrF955ZWMn5f6g6lTp5a0hLfsf7du3Qh3DyuxYTnBJNwVZW2R4vDmm2/y24raYjWXAw44oOR9QhoHvgPAx5opYApUvgI2gK78c2w9jEEB3F3CGrBhKRBYq3fFihUxoMXvIgllpWWvKnlyG34YlKqwh9QZ7yu5cA3yu5MwWRM6I5WLn1T5zoPtMwVMgcpRwAbQlXMuY+0JJiC4d1N5ogW23PBaTnRhO7bhRdj5Pba52DAWttykH3BGIQy3SRuNH9j87//+LyHnmRsmtQwePLjFf9Sy7zvttBNhEXhuGizYgjMKYXCTnLEfC9Xjj5vPBnywn5trg3OJtYmx+D7OCTfXhvdpsOLgzJPbovolOYOn20+813CGxm58cN9dX9KPD0vGtM/PY489Fqy9zJqyn2yxNJwlHx/Wv/71r1Z3Rpk3c9T4wTFhcQZfkrOPD/th7DAbVzPJGZM1uSgQ+5I2jBXmB8dqYlpe8xIL60Bv3LgxWBs+Ex/slzEt/cAmSmctZw2WjHsfn7j8yPhgLGy5SSzsdz/H+0ycXTsZ0z4s6ceHpeEssdiPy0eDJf34OGNfVCxKzj4+Estno8GKyw+wbBIhzoI1U6CMFcAdZ7coAqp0RVVH2n333YMeJ3FiHHLauZpdkk7LmWeeGSxDliROcXDBD5ZOnTrF4SoWH4hNDDYrreE6TdJkTej71a9+lbAutDVTwBSobAVsEmFln9+ce2eTCFtKh0lYyCONmhSGCU1Dhw6lE044oaWDEr+7+OKL6aqrriLfCiKlpJaUCWBxaoAfUNdccw1Nnz49Trd5+6rEwjVJm6yJk4T11vfaay/6/PPPWzyxyvsEmgNTwBRIlAKWwpGo02FkkqrAW2+91aLcdiaeWJrtgw8+yPRxyfYjfztpg2eIAb3c8tolEyhGYAycZEn5GN3n7AqFa5L4dCTnDiX0QKQmYU1oTDq2ZgqYApWrgA2gK/fc5tWzai+kIvPLMACVM/2lDQTv3r17i3xmn408MZpiCJwHJ49132fCwtOEcePGBaZxFSiIizPyRfEX1uLirCksoNE5qmjAhg0bCCuMgHdY02BpOEfxAQfYbNmyJbgrmomTxg+OzRRn7FfDWeNHY4MVL5DGEdWiOON4TUxr/MAGSwbedtttGWlpYlqDpeGswdLEYlx+NPERF5YmpjV913COC0vjB4EVFR9xcdZgxcUZWJYDnfFrwz4wBcpPAdy1O/bYY1WPY5O4sgQGdEcccUQihT/00EPpxRdfTCS3XElhoLrbbrvlenjBjjv88MMr7m5/wcTK0zGvt40fr9ZMAVOgMhWwHOjKPK9598pyoL+QMFstkGuapPzHadOmBRMIk5aXDYXx4+Tmm2+mKVOmfCF4mb9KatGSJOYL53uqUbxo+fLl+bopyPEoFPTUU09VVGwXRChzagqUqQKWwlGmJ85oF08B5OgeeOCBakDkmr777rtq+0Ib4j/xgw46qNAwOflHXjYKvFRS+/TTT2nXXXdNXJfwFAJLW1VSwxrQSW0nnXRSsHSg5Z0n9QwZL1MgPwVsAJ2ffnZ0lShQW1ur7unBBx+cmKXZkB86d+7cRE4gZEGRHqPJY2X7pG+TUhkv6Trlyw8DU87tz9dXIY5HcZdf/vKXQW51IfybT1PAFCitAjaALq3+iUXHxK41a9ak+WFSB//xTryXExmkzYIFC+jhhx/mQ4JtLjaMhS036QeTJjDZz23SRuNH2uCu3SeffNJqUlimvmO5O6zEIf2Al+SDfeCMwhvcfDb4PMoGfHAsN7zGY3t3kIFzgXPCLVesuDijT7i7z3fsfXwkZ3B3+4n3Gn1g48YHY7m+pB8floxp6Qd3RZcuXRoZ9xosDWfJhzm7/YLNyy+/3OJuP/OGPZrGD47xxZmLJTnDt8RiP03ITf9msnF9uzZIk9q6dWukzoyVyQ9z0MR0pmuefUisM844g2699Vb6y1/+wibBVsa02y82jNIZdhrOGiwZiz4+cfmR8cFY2HKTWNjvfo73mTi7djKmfVjSTyasqO8OicV+XD4aLOnHxxn7omJR6uzjI7F8NhqsuPwAq5wmEe4EwayZAlKBXXbZhdq3b5/e7ZuEhn0YtLpN2vXo0YPefPNN16TVhDaNDWO5/t3XDCCLV0gbjR+fTZ8+fQg8wxpjYVY3vgh+8IMfBPrwfhzrvmZf4Oz69tl07dqVzYOtz0b6h42cQAgsrBTCzedHgxUXZ2Dtu+++6dUhfHwkZ9lPvNdwhsaY4MfNhyX9+LBkvLp+sAYwUnikjc+PFiuKswaLbXC3n5vLG/vYhj/HVtrgPa55d7/7mv24nMP85IOF2MaPVcSH2yQfDWccr4lpFwevo7D4LvSyZcvorLPOSh8uY1r6YUN3v/uaP9dw1mDJWMyEFcd3B+LMjQ8Nlk9rDWcZ0z4s6ceHpeEssXx+tFju/5k+ztin+b/X1dnHR8NZi+Vy9mFp/MAGVQ3LpdkkwnI5U0Xmme3EuSLTKypctgUokqQdJrSdfPLJiSvs4p7ASprclqRz72rMryupcE25xA3Sk3AN3nvvvdSzZ08+FbY1BUyBMlfAUjjK/AQa/eQpkKSl7LBCQVInEPKZQylmeaeEPyu37UcffZTVhNNi92+PPfYoNmTB8Orr61s8TSkYUJ6OcRd60qRJLdJn8nRph5sCpkACFLABdAJOQhIpJKmQCpaDQinqE088McjpzTThDI+0UFggqsncMZ892+COoptD7NqyjbsPr1GJjFcHyGTjHqMphqBZ7F9i+SYQIrUEi96HNQ1WXJyBtWPHjtD1iePirIkPTd/DigYg9x0TTsNsWHsNloazBottkPKQqfIj2zC/TFsZZ9JOwxnHRPmJsnnnnXdo+/btrXJjJZ8oP2yvielcOQ8ZMiSA4bvmmpjWYGk4a7A0sRiXH018xIWliWlN3zWc48LS+NHEdFycNVhxcQZWOeVA2wA6+Fqzf5KoAAaAGDhjGTbklQ4dOpTwZfeTn/wk8as2gGupl6+qq6vLOPhP0vnu0KFDkujkxQV30pHTba3wCuDHLX6slku76qqr6Jxzzin590K56GU8TYGkK2AD6KSfoSrm9+CDDwa9R5GN//qv/woejU+cOJH69u0bDKKLIQ0mKh133HFZQyHXEasElLJhUgcmZSS9YWJNpawFjbu7++yzT2IlRzxUylrQWJ5xzz33TKzWkhjWPJ8zZw5dc801tG3bNvmxvTcFTIEyU8AmEZbZCSsW3VJPhsJqBnvttVfwKNx3lwl3ps877zziR6OF0oUfuQ4bNiwriCRM3sOEMdwJT2IFQilmkivKSa5h76E5npBgsJTEVurrOi5N8HTqu9/9riplKy7MuPwgRrB04yWXXBKXS/NjCpgCJVDA7kCXQHSDjFZg9uzZdMstt2R8RIu85CuvvLLgqRxIGcnlLi6vBR3d08JZoKDHYYcdVjiAGD0PHDiQMLgr94Y76UkdPENbPBmphLv9WDe8XFe0wB3oe+65h5599tlyD3fjbwpUtQI2gK7q05+58yik8sorr6QNeKIFttzwWk50YTu2wZqOjz/+OL8NthqbO+64o8XAlbGwRcN/nlhdAgvuc8OkiVmzZvHbYCuxpB8YhdmgLLPPBvui+g4NYcOcM/kBZ/exuuSD45555pngD6/RfDYuFu7go8jEhx9+2HxE0wbnwl1n0+dHgxUXZw2W5Mz9dzum8QON3fjgvmPLTfrxYcmY9vmRNuwnWywNZw1WXDbg78aZr1+Ss8+G/eAzbqyj+z4MCyuKYPJS1PcLY2HLTWJhvyamwcdt0o8GC6ty8KRonich/QAjrO/MQcNZXj8+LBn3Ppu4/Mj4YCxsuUks7Hc/x/tMnF07Gfc+LOnHh6XhLLHYj8tHgyX9+DhjX1QsSs4+PhLLZ6PBissPsGwSIc6CtbJWoF27diXjjzuRX/7yl1sVx5CEvvWtb7UYQMvP43gPLgcccEDWrnDX+sUXX8z6uLgOwAoFSIsol4Y880yrQ5RLH5Avn2nFliT1ARx54JYkXtlwQazgKU+5tv32249mzJhBSA0r93NRrufAeJsC+SpQATnQm2n9grvorvohNGlkb2pLW2n9zBHU68pDaOGrk2hQ53husu9YP5PO6PUkfafuHhrds3JWDcgUQKXMlcTjTbQRI0ZkohfsRx7krrvumjFPOvRg5YfZFlFht6XUDxxyzd1m/sXelhtfnz6lPuc+Tr59lVBMpRLiBecG33VLliyhm2++mXBn2popYAqUjwLxjC5L2d/NK2jGyOtpZSOT6EA9Rz9AqfrrYhs8s2fbFkcB3F068sgjI8HwH861115LK1asiLTNxQADdEzCy6VhYI8c5FI1PL5zy+6WiocWF3fs8fiunFuuK7YUu8+42w+u5dwQK7nMTUhan3GTgFcVwveNNVPAFCgfBcp/AF0+WpcV01IWUsEkp169erXSS+Z8wQAlcrFONJpm4XjY+fwEDpx/YBM1USnMDyaSoZhKmA3DaYohYMAQNcB0sTB4x0x/2eIqUBAXZ7dfnG9eKM6a+HD5SB78PlPRALeaYiYb9oGtBkvDWYMlbVyuzEna8H65deNMfob3Gs6wi/ITZsOxEhdnYGliOh/OwODmXodYjcM3iNZgaTi7WIwvt5pYjMuPJj7iwtLEh6bvGs5xYWn84PxFxUdcnDVYcXEGluVAO1cnUh9Oa/Ntmrl+q7OXiDYvogm1x9CERf9o2r+jgVbePYFOadOG8Ni8zSkTaOai9bSFjwrsa+mUCTfTDSP7BDa13xtF3+s9mKY0NND8MYdRu9qJtGjz57R+5repTfB6R/PR26lh5SyacEptk+/akXTDAsc34fOH0n69+MzDtgVVAI/BUTRF+zizf//+waoChbh7g3Wcy7H0MSYQovmW/yvoycvDOfLMS3nHPg/q6UOTXFoaJcZ5zWQ8mcCgoZwbvidymZuQ1D67g2i+fpPK1XiZAqZAswKpQrfGdakZQ3qkhsxYl2pMYzWmNi28PFVTc3lq4abGVKpxQ2rO6CNSNSOmpZbVb0ulUo2pz9bdlRpRc0Rq9JwNTcdtWpgaX0MpqhmdmrFuUyrV+EGq7vVNqVSwv8bx/+9U3YzzUsS+U9tS7835caqGhqTGz1mX+qyV78bUZytuTA2sGZG6cVl9M8dtqfqFV6cG0pmpqSs+CVg31s1IDaHzUjPq/p3uRSW/qKurS40bN67oXVy6dGnq2muvzQp37NixqVWrVmV1jMZ4zpw5Kfzl2sALOha7QYtsNSw2Rx8eEfl2l80+XC+lON/ZClSqaztbnmH25R4rmfp2yy23pI499tjUu+++m8nE9psCpkBCFCh8CkfbbnTid/rT/FlP0KotfEf4Y1oxbz7RhafSMZ2JNi/+A10y8zCadMUYGlDTnojaUsfeF9It955FT1zyB1q8mY8jqrnwe3Ru785Ebb9MPXt0jv4htONNmveHh4jGT6ArhvWmjoHvM2nkhbvQzD8spNd3fEzLH/gfqrtwJI0ZUENNgrSnmoHfoQuHvEoLXnyfvkCPhjOL/BR44403sp5df9JJJxGq7iWt8R2/YvOCFuW4QgGePJTz3bdPPvkkmNRa7POdLR7u3OIObrm2fOYmJL3PuBN90003BatzrF69Oul0jZ8pUNUKFH4ATR3okNPOp9F1/0MPLG96tLxj4zP0P7O60mXf7k+dqWkw3VBzCHXrisEzt7bUcf9DqE/DfJq3ouk4/iSb7Y7X/0b3zyfq06uWOqYP3JsGTV5BqXmjqWfbptf1k4+h9xfNDVYveOih6TRh8CAaM7+0pZjTdKvoBSYQZjs5CBMOMWku7hbHRLxSlPMG72w1jFu7XPzhBwdy78u1/fGPf0x0ERXWFelRKINdri1qbkK59ot5o3Io1sH//ve/n15Nhz+zrSlgCiRHgSIMoIna7vdV+t6FRLPmraHNtJVen3cfzewzjL551B5fKNHwGxq8e7umHOXmPOh2vcbQ/C8sCvRqB2159W4aWbs79Rp8Gy37FPebv0yn3f4QzRhCtLau/os87AIxSKJbTEDIVEgF65ZOmzaNjjrqKOrTp0/wmtcylRMyNAusuzbIg917771bTbCCX0yacHM3GQsTDjHxEJzdQhnQlW1Y4zA/0gZ3Q7Gahs8P9slJHBILd/rAB/u5SRvs1xRDkAvw+/ywPtAQ2D4bWaDAZ6PBiouzi4VJj1hRBZzcJjnjM2nj+uHPpQ1+WLjxwX137aQf9uXyceOVP3d9YJ+08dlpsDScc8HC6jLLli1roaPGD/rJccaasI78XnL29Z398DFhNq62eI0nLDw3AZOXEB9uk3wYS/px3+N4TUxHXfNaLBnTOM7l069fP7rooovoT3/6E2HZQXwXSRst5ygs+JGx6MOKy4+MD8Zy+y+xwNH9PIyzaydj2ocl++7D0nCWWOzH5aPBkn58nLEvKhYlZx8fieWz0WDF5QdYNokQZ6FF60LHnDaEaNZTtOLTN2np/S/QkO98hQ5xh+9DZlBdYwpJkOJvBU0etHcLb7G+kd6spwAAIABJREFU2bGeHvjp5bTgjDn0XuM8mjz6XBo2bCgNqv2c6tY2xApVCc4WLFgQPF6sra2l3//+9/Szn/2M8BoFAfItTYtHs1i5ItvJb7ijhgFBQ0O85wuFDsptotKmTZuC86GdhJmkmEQcYUBUjg3Lwo0ZM6ZsqKOSJ1JOyrG99tprZZmilK3W+B684oorgqdJp59+Oq1bty5bF2ZvCpgChVSgaLnYwWS/o1OXTf2VmIzHEwp/nJrzHiYQcmue3McT95onEdaMX5jaxCbYRk0iDCYx1qRaHtc80RC+l/0lNb7GnYTY5LzxvTmp0TWUPs4mEaZSmOAydOhQ7wQXTHrB5BdMAsy15TO5CdzywfZxznei0rx58wLNfL4LtS+XSZiF4pKt31LolS3HTPb5xG4mn4Xcj0mmhZh4W0jO7Dvfyb3sp5y2iC9892Ki6j//+c9yom5cTYGKVcC9B1zIcTpR5/707cu60o3jfk3zh5xOJx7C1fzaUueBP6BpZ/yVLpk4nZY3bCeiHbRl/SP061/cSjT1F/TtsMp/HWupV5+mx+z0+RZKz1Pk3rTtTmdM+AH1mjKZrl+0MZgQuKNhCd016wUaCN8DjqPTLqyl+bPup8UBNtGOhmfpdxOvopnx3tBkRmW5ReUvVM3CI0WscSwb9t17773085//POeJYFhqix/NSv9R73FHDRMQ42pIScGktnxat27dCCW1i9mgwTHHHFNMyNiwSqFXXORxB7qc8s4xyTSJE2815wOPecupSJCmT1E2+H7Ddy9iDHej8X1ciKU7o3jY56aAKfCFAsUbQNMedNQ3h9EQOoJG/2Bwy/SNtgfRsN/NoXtPfocm1O5Cbdq0o04D59I+l95Psy8b4Ez++4J4+lUwQL6QtmMd6N1G0wOvi/WmqT3VDLqcZq8YTo2/PpbatWlD7WpvoMZRs5t9700Df3Yb3TXgbzQ4wG5D+//yOTpg5G00Z/zRaZjkvxBrXbfBmtnTae7KhpxWEXELqWA2+PXXXx98acvUADcPC1/ymEUOW26aBdbZ5oMPPgh9NOtisX/eYvCFnE4UFohqYX742D//+c/pdXN5n9xq/OA/+6imKYYAP1G+wAeTMKFFphZXgYK4OLv9Qr65L60gLs6awgIun0wacry6n6MwSceOX0xT9tm49nitwdJwzhVLFlPR+AHvqLjXcNb4yWSDIio8NyEuzsDSxHRU3zNxxn63aWJaYuG7F5ULMXhGfut3v/vd4LsWeoc1DZYmFuPyo4mPuLA08aHpu4ZzXFgaPzjfMj5kDMTFWYMVF2dghedA4+bqPLph4mxa37w8WlOtEaemiBSigO+LOIAmattzNM1LraUZww5qXi7O6VnHnjRo9GR6mnOg6++mXww7mmqYYedBNLk+RfWTB1HLxeswQL6q+bgHaHTPPTylvNtTzdEX0uSn65vzq+fR5JED0r7b1gygkZPnpXOv6+/+BZ076CQaNnlFGq+JO/zznXOHewJe7tj4KF151r1Eox6heuSSN66kyV2X0n+fdUuLZQCzpYq7HJgNjqWVfHeepb/zzjsvKIiRyzJZ+CLL9c4SBu+33XabpJPze9wNz/eOIiZDuhMxcyaTxYGYTAktyrEhvrCSRTk2FFHZd999y4Y6Yhs/tsqx4bsF11a1NlwnU6ZMCf4efvjhYLIh5p/YHelqjYhq6vfHtHzGFTRu5Rc3SpvGZgWeK5dB4jZITsnwme0uGwW20vqZI6jX/adT3RNYmq+Z+I5XaeYZY6huwtysJ2LiPykMZjilYuLEiWo1+A4JvuSzaRdffDFdddVVqoG6z+/ZZ58drAiiGej7jnf3oQ9omByZT0NVy2JdYkg7ueaaa2j69On5UC7psdALS//JJx0lJaUAx0oJSPkplx8vfH1ne40qpCi4STGvqYJ3JgYAPCGcPXt2cOMCTwC/8Y1vZD0ROwYa5sIUKIIC/6BFE06nwat/1HKsUwRkHwQPtXyf2b6yUWALvVf3JtX060Zd3TPadm/q1m9b8/KB2XcGj9PxWBN5zdm0M844I/gy56XttMfmu47ugAED6O2339bChdrhbni+d6BDAQrwIe529+3btwCei+dy3LhxhHV+y635Uk+S3AcM9PG0otya3WVtfcaw5B1+COFH/+bNm4McadyMmD9/fs7zUVqj2B5ToNQKNA+ep6wkmj+GerVrSttomcIBm2OozWnX00PzbqKRtW2alkY+ZQLdvXIjbUb6x8g+TftqR9JNy0WK644GWnn3BDqleSnlNqdMoJmL1mdcytgdbpVaHcPPVYEd/6ANq+szHt2wegO9n0M5xeXLl9OkSZOyvhuIu4e//OUvVfnITDqOSXuYGIU86jga8izjaFheL9sfErni4q4i1ua2VnwF8OOvXO4+F1+d+BDx4wo/sqy1VgBP3nAHGvnDo0aNCtZU32uvvQiDaUwAR5pHsb6LWrOzPaZAvgqg6N2TtBBz04Jlj0PSNubfTLcsOoiuWN9Iqcb3aOHxq2nUMftT72tfp69ev5JSqU20btJONPXsa+mRjVi4AmtXvE0PXTyEzlp0IE2u30apVCN9dvvh9Nfh59BPH3rbO5dsp3y7ZMcnQIEt9U1rVvfLnst1111HvsEiJuRh3dGnnnoq+MPaq9wOPfTQ4CX2YSKSO2hjO6yffMstt9Cjjz4a2KJaIDe2YT+42/vhhx9S+/btg6IBsJM2jIWJWnycz2bp0qUtqhL6bHjCV5gf3HnHsZlswHHVqlXevrvH4PEqCiKwRpIP/OBOUdeuXYk18tlwLvXhhx8eyOizwWNc3DUP87NmzZpAZy717fOjwYqLs8RauHBhMAA4+eSTg37iH8kZ+8CbdcZ76cfXL/jBxJohQ4YEvtkGb9iX9OPDQrxu3769lc7f+ta30n6kDfvJFkvDOVesgw46iL72ta+lY1PjB5pFXT+Ss6/v7IevizAb95rHNSefMgGPY17rh889n3ccp4lpzTUfpQ+wwBnfd2HXIbDcvufCGT82nnvuOcL3UNu2bWnr1q2E896uXbt0rIKPjHsfloazxg+44Ps+7DqUWHxe3fOVCQu2bCdjmvvl2kg/PiwNZ4nFfrLFkn58nLEv0/+93Hdo6H7f+fhILJ+NBisuP8DCuAP+8mo1o+hXV5xNPTviHnENHXPq0VTzm91p0hVjaEANKl63p54nnkB9Gm6jZXWbadh+XWjz4j/QJTMPo0l1bEPUsfeFdMu9ddR7+B9o8amTaFDnlvecbQCd11kq/4Mxq9tXbhpFLbAkGi/l5pZY5gk82Ie7GrjLyo3tYIP8aeT/YjA9cOBANkmXa2Y/WE4LM4qPPvro9Jeq6wcHMhbK3PJx0mbJkiWEARhz5uOwdY8B5zA/GzduDCrJ4T8f9zjXD16jHHKmvjM2csfBhwcKkjPsUH0Pudaskc8GX+BoeFyLJm3wHyMeyT/wwAOhnFGlEBX/eLKm9APfUViwiYOzDwvlvNHOOeecYIt/JGfsA28+N3iv4Qw/9913Xzo+uO84nn1JPz4sxCuWJ+TzhYFOY2NjcGeU/Ugb9pMtloZzrliY+HjWWWelY1PjB5pFXT+Ss6/v7Cfq+pFYc+bMCb6vLrzwQrgNGvD4XGAHn1c+F4wVds3jOE1Ma655yVnyARY4R12HwIqD8yGHHBKJJeM+V85aP1HXodSHzyufU7zPhIXP2E7GNPfLtZF+fFgypn1+JBb7yRZL+vFhYR/iLOz6kZx9fCSWz0aDFZcfYCHmi98+phXz5lNDzRDq1hUDbG5tqeP+hwQD7XkrLqNBsqhfxa5wXU0d8xaLgQAfpRaOPzpFQ2ak6hqzEwRFLQYMGJDdQcKaF/8Xu71vx44dm4J9Pg3Hd+3aNfX555/n4ybggYIFcTQUeIGWYQ1YcfQ9Ls5hXPmzODizL3dbyEIw0LgQGhXKL3QppG9NbLrnRvu6kJwLWUSlUDGt1S0Xu3LkXMj4yEVDzTHGWaNSPDbhBcxaj2maitwdnRq/8KMMY57mYn1clK+Zpvc4Iiyq4flj/y372PJ+NA+6bVteCgSTBWszcm41uTCjZbwfICd0n332CX4ph3nGxCDkkMZRNht3dfKdhIaiGPATR8OdfDxqK3TDkmTHHXdcoWEK7h/x4kspKjhwHgBY8jCueMmDRtaHFis2syYWcgAe7ZbTcoEhXbGPTAFTIGkKBLnVqfSSxniC3vTnz7e2AXTSTmBOfDrS/r26U6vJgsHkwk+pT6/a8GI0HkysKqBZWSBqMXekJmBCYVhDvvWZZ54ZOVkxCguPf/7zn/9Erm8b5Qd5Y2+99VYY5eCzKD8wwmO2qIa8L3APaxg4hOWFobAC/ES1uAoUxMEZXGW/8OgVkyHdFhdnaBylkeTj8uDXsmgAJq5iMOo2aeN+xq81WBrOuWJhIIo0Dm4aP7CNinsNZ40fnw1+XOFHFre4OMOfJqaj+u7jzFzdrSamNVgazhosTSzG5QfpT1HXYVxYmvjQ9B1za7Zt2+aewlav48LS+AF4VHxorsO4sOLy00rUou3oQsecNoRq1r5ALzVXpG6C3kFbVt5Ep7T5Ns1c/8Xa00wr8wB68yKaUFtLp818tWn2IdYUPq2Waicsos18dN5brF/8bWpz2sx0VZm8XZaVg9ZVdXKj34EOOe18Gr32Jrr2rpeallzZ0UDLf/cbunLtt2nCuT1bF67JDSjro7C0HFrYQBIDaHcSUNYgzgGYdIMvxHwa7ubGcTccHHbfffe8+Wj6gnw3zvvT2CfVpkuXLkFueVL5+XjxpDHfZ0neh4FosUvN56sHftRzFcJ8fdnxpVEAMderV6/SgOeBWm5r0+fR1QQf2nSzsIngVtqy5T8xcW1LnQf+gKad8Ve6ZOJ0Wh4MojE+e4R+/Ytbiab+gr7tKaKXeQAtabXtTaPn1acr88mP7X0uCrSuqpOLFxzTdr9TacK9P6eus4ZQJ6xh2K6Wzl7dh6b95VIaKGaO5oqR63Hnn39+MMHNt4Yr9uGXdP/+/XN13+I4fMlh+b18GgajnTp1ysdF+tjOnTsXPCUBS1PhDih+PFRCO/bYY8tq/dqo8ulJPSeZSqcnlS945btWfJL7ZtxMAVMgSoEOdMgZF9Pl26+kXu260zkPvO5dXi7Ki/fztgfRsN/NoXtPfocm1O5Cbdq0o04D59I+l95Psy8b4H+K3zIl2nm3aWFqfE1NasiMdaks5585TqJe/jtVN+O8nCa5RXkuj89bJ8Qnhfdf//rX1EknnRQbHUx2ufvuu1v5w6SguCZ2vfvuu6lrr702mACQ60TCf/7zn6ljjz22Fc9cd2gmn4AzuOfaCjnxLhOnfDln8ov9hZoYBY0xcS7uVii+4AnOvusmrj6ET9jJDYWvw9yODj+qEHwZsZAxzRhxb8uRMyZVR02sjlunfP2VI+dCXof56hl2/NChQ8M+TtRnSJBOpVLbUvUr5qSmjjiiafZhzYjU1Pumpka4A+hWKz1sStUtnJEaP7CmecZiTWrg+BmphXWbmlzyAPyO+annbhyRqglmNsLmntSK+m1NNinPALqxPrViDrB5JqTw23xkY/2y1F3jhzRjH5EaMfXJVN1nzlAffu4anxrIMyoHjk/NWFiX+qz5+BTzm/pg6smpkt9Hqbr5N6Y51IyYllqW5tzkoCW+5PjFrM87Fj6dgWfz4Jn5kX+WJ9Mt9lYz8MuGEw9M3S9OXOAYrAIrzpbPgGbVqlWxDejRJ+53nP2Tvgq1moLEKdZ7DApwHsqlFXJQV2gNcP3l+mOz0Nyk/7i/k6R/e28KmAKmQDYKtCVCkvStdMExf6CPhj5In2HW4frLqfsLC+ieBu+NbpRsoS0rZ9APhj9LvW5/tWmWYuPf6Vft7qfBl/7ZyWduoPnfv4xup+/TysYUpT5bRJfSvXTMBbfSyi2+0nif0sobL6az5n6JfrwSlWBSlGK/P5iRPmbHxofo4qPPprvoB1T3WSOlPvsTnbz2FzTwp4/QRrhVV5RpoPnjptOi7pfT+lSKGuvvpuOXT6Bjak+ha18aQNe/B85raRL9ns6+8tEm33Af4I+hRV3/P6pHv1Kv0u29nqXhAyfSQ1zVJpDuQfr+r+dTpzEPBn1prL+R9nvsx/SD36+gLZRFVZ1Mp6GA+7EWMhZi54ZJHfzn7pMTGaTNggUL6OGHHybktqLU7G233UYo9Y0CDphgeNNNNwWFEWDjNukH74GFLTdpg8l/eMSLYiJ4rI4mbaL8YD3LnXbaKRILvqP6Diz0/+9//ztTbsUHH4DzY489FmqDzzPZvPjii9StWzcVZ+gMTtykPtgfhsXH5cuZ/fiwsKYyzgM3cF65ciW/DbYyz/2ZZ54h/HHzTQzCRMtZs2axSXoCo+tL+oGx+zneg8vjjz+e9sM2rp3GRoOl4ZwPFuYe8Ko1Gj/oI+Le7Steu+8lZ58+7McVUfphG9f3xx9/3AILk5eizoXPj8QCD8QGuHPz2chrXtposcAZenOTfrA/SmfYaDhrsGQs+vjE5UfGB2Nhy01iYb/7Od5n4uzayZj2YUk/Pizwwbrc3Hx+JBb7cflosKQfHxb2RcWi1NnHR2L5bDRYcfkB1o033sgyJ367E9HHtPyB/6G68VNo7rDeTXkeHXvTsCsm0PhZw6mpfIPsx3aqf/E5WtzndPpDz85NH7bdjwZdNy+4bexa14y+hq776QlUg2xr9tt7PD2w/EI6epDI2dz8Aj1w4/t04b3faa4WEyT30sBR36Ehv3mSXqz/bzq6J9Hr8+6jmTSKFqYrzRxO5448i64cfB/Nm3A6nfueoqJMM8ma8RPoCu53zVF06oBa+k37H9EVac6H0IknH0YNV66gui1n036dP6bFN19HM/v8nOrYhjpT79GT6d6602n4zUvp1MlcNORoGv+ry2hYs0ZtA/970G8WvET1lw2gnvoMdFfSorxGpSpUyuKGQals2IdBq9ukXY8ePdKDIZSaRYU/5CijEtVXvvKVYGCNwZI7YII/6Yex3P3ua+aA3GXg4MsOA3RpE+UHXzqnnHIKbd68ucWx0g/juVtpw1hhNvgMnKETN+kH+1Gp0G1sw0sATp8+PaiMyPth677mY4HFRVQy2WTCYh/Y5sPZ9ePDwjKCbtttt93ct4l6jfzzc889N1GcKpUM4gJFQayZAqVQYOeddy4FrGEmWYF0KoPMdQ5SNnp8kQPdIoWjMfXZihtTA5F2MOeZ1MI5T7dMn8A9cE6R8PqtSdWMX5ja5EvhwLGf1aUWzpmTChbNn8FpGOelZtT9O5Vq5pG5OEhzakTN5amFm5yUjlQq1WLh7IAfNfPgm/a+nOTmNBP25z0Ox7t2/5fatPDyVE2rtAzXBtx8eMyltNtyflyaT9oEHsfj+DgbcrriTlNhfnGnnLDfUm7LKfbKiavvnBayMIkPL5995cQ1n37asaaAKVAeCrTd8f4GWp0xVSPT0L8tdTz6p/SXuhvovz59lH59zinUq1M7anPKBJq5aH3TMmqZDm3e32rN4mD/Znp15hiq7dSLBt+yjD7Fvj3OoNtX3EFD6E2qey+LghQNv6HBu7ejNliRovmvXa8xNL8Fr5qc1kiGi4Ypg2l3x3ebNl+iXmMebOHd3pRGAaSLYFUK3B3MpmH9YZRGxfFxNhSUKVRDmk0lFFAplD6F9vv555+XZRGVQutSCP9Ys9qKqBRCWfNpCpgCuSjQtm3XbtSvJqdDqWPPgTRs9GR6OsgfXkFzznyfrhx8Af16UXhRCKD5quPtWP9n+umY5XTGnA3U+PRkGj1sGA0b9lWq3fQWrc2WYpYVZbJzX0NDZqyjxnSVGq5Wk6JU/XU0qMTLxmXXl8q0PvXUU+mVV17JqnPIm8Zx5dTA2U3JKCfumbjiB8fUqVMzfZyo/Ug9kkVUEkUwggzSfJB3WA4N6we7RVTKgbNxNAVMgcpVoC11PpJOu7CW1tbVt7xzvKWe6tZ+ru5525qjadj3R9KFNfW0esM/mtfma8jgt5YuPO1Ias6ebsbYQVvee53W0mF0whH7OoU//kOffeqUbmnbjU78zolEa1+n95yJiDvWz6TT2qDwy4d0VA4VZdQdZb2efYUaWsyD/JRW3vCNiikKo6liBM3kRAapo6ZCkcZGg4V8bORYox111FH01FNPSTrB+0ycn3jiieA4GGWycR1qbTBI4UmN7vH8GpxlLjl/xlsMcnwDHQw0uSiBhg8mDULvsJYJyz0mH86uHw1WXJzd+HA5uK81fKSNb/1tTUxLPy4Pfq3hnC8Wl07X+AGvqDjTcNb4kTa+IipxcQaWJqaj+i45472vaWJag6XhrMHSxGJcfjTxEReWJj40fcckOfyFtbiwNH7AIyo+NDrHhRWXH/SrnCYRBsvYNb43JzW65ojUiBlrm5Z5+2xdak6wRJyzDnSLHOjmXN6Bl6fm8LJ1qU2pujmXpwbW/Dg1571tzTnQmFM4JDV+zrpmv2tTM0YckaoZPSf1XpCe3OxnyIxUHd43500PvHx+qj74fFuqftm05uXkvljmrbF+furygT1SabvG91ILLx+SooE3plZgKbvGDak5o49IfbH8XGPqs7o5qfE4ZuqyJi7eHG1fTrLMW06l0nrduLSZZ3Pf6czU1BWfINtamQPt9v/fqc8++7/EJP6Ue24nluZCPrN2iS7kPWdjn82JKlTuJs7R2LFjs6FSNrZYihDLHCa95bNkYhL6husjznXPC9mncl4usJC6mG9TwBQojQLBOhBt9zubfrf4Burz1+82VbHr9FNaduxomjpk1ww/uDpQz1G/oxWXdqG5A3dvzjHenQbO7UKX/uUKOns/Xr2hhgaOP5eOffM31BP5wp2+S3/tcwMt/t3ZtJ9vBYrOJ9LP/jKZBjw3kmrbIXf5aPrlM3vTyEcepPFOmknbmq/RpNmzaVTjDU127Y6lXzcOpxWzf0xHd2xLlEtFmQw99e1u0ut3dPL7/6+ZZ3PfV0yny47ew3dIhn2tq+pkMLTdWSqAioRjx46lF154QXXkihUraNy4cVSocq0o9xx3w13tk046KW63ifGH/GJrhVUA8e4us1hYtPy8o0KlNVPAFDAFkqJAG4zbC0Jm8yKa0Hs4rZ60iJ4Y3dtJySgImjmNWQFMqMNav1OmTInZc/HczZ8/P0jj0PTh4osvplGjRtEJJ5wQO8FCaTl+/Phg0mMhOMcuQpYO77nnnmDpviFDhmR5ZHHNBwwYkHfp+OIybo2G2J88eXLsk2dbI+W+p1DXUO6M7EhTwBSodgV894GrXRPrP1GQk+tOwuM8MWy5aRZPj8sGuMj5cvGZE/NBzpdbKAN3Z5EjvGzZMjYJjpd+nnzyycCmf//+gZ0GC4YyB03yYT/uGtfSBn40xRDkAvzwg74ddthh6b7JfvmwZIECn40PC3Zuy5Wz9JMJC3nFfNdecgYPrR+XsywswH13fUk+UVi4e+vzo4l7DZaGcz5Y4L7nnnsS5jxo/MA+Ks4kZ9bQ1Zn9uOcH+3w2cp/7HrmXiA+35eIHx2tiWnvNuxwlH2DJmPbZROms5azBkrHo4xOXHxkfjIUtN4mF/e7neJ+Js2snY9qHJf34sMAHf9x8fiQW+3H5aLCkHx8W9kXFotTZx0di+Ww0WHH5AVY55UDbAJqvCNtWnAJ4PH3llVfSo48+Gtq3P//5z4S7cIVK38AAZfHixaEcsv0QRSUGDx6c6LuG2fbJtcfKIvgyTXLDMolIEyr3hkmuH330UaK7gXi35RoTfYqMnClQdQoULoWj6qSsrA5XyiNTlP49/fTTgzLiqFAoG/o5fPjwoMR2oQbQwMRa5HFmS6EsOtbFveSSS2SXKuJ9OcRfOXDUBANiCQ2VO5PayoFjUrUzXqaAKVAYBewOdGF0Na8JUQBFUSZNmkTXXHMNoey12/Aeg+c77rijYHefJZ77Pp/XeDyHpfoqtR1wwAGEAWqSG+7a+sqlJ5mzjxuKk+DHWJIb+FXaeudJ1tu4mQKmQLQCNoCO1qgqLTTrQGvWfozLBidB5nzJE5Np3UtMROvbty/95Cc/odWrV9MNN9xAzz77LJ188sl00003Ub9+/aSrSCwNH9cGK3y8++67rXCwQ7OWK9IZOKUBA3+Z/+xieUGad8a1vmq2nDNxcvvl2uBpwNy5c4NdcXHOFB8ubiY+PpsPPviAfGtAw1YT9xosDed8sVCcBEVKNH7Qt1yvQ1dDjR/XBvx23bX1qlBxcQaWJqaj+u5yxutMTRPTGiwNZw2WJhbj8qOJ6biwNPGh6TtyfPEX1uLC0vgBj6j40OgcF1ZcftCvcsqB3iksIOwzU6BSFECqAwbPs2fPJhRM2b59O917771UyDLbhdKurq4uyL2Nu+R4ofjm6hf5xUjBSWrDJMcePXoklZ6a19577534u/14GgGe1kwBU8AUSIoClgOdlDORMB6Vkt+ZFFmnTZsWDNbjWJYNS7yhjRgxIindKwgPLNOHQXRSf+QknV82JyXuHP1ssDW2Seen6YPZmAKmQGUpYCkclXU+rTcJVaC2tja9LFu+FJcsWUJHHnlkvm4Sf3zSV4fwlZZOvKgZCA4dOjSxd/uRsgR+1kwBU8AUSJICNoBO0tkwLhWrAHJl45iohZQGFLjp1atXxWrFHYNmyDNOasN58K3sklS+Ybxwlx/zHpLYMHcgqU8hkqiXcTIFTIHiKNDu6quvvro4UIZSTgqsWbMmWPoNq1SgYVLH22+/Hfx169Yt2LdgwQKCnVvMg+3itoFfFETBZAX2LbEwaeK+++4jLoji8naPifKjwYJvTOJwV2GQfFw/WFXi6aefpvbt27fQEH4wEGtoaEgPEqQf2Dz22GP02muvBXex99prL9ptt91a+QGfMH3g5+GHHyasX8y5u2FYPGjx2WTDOcwP98tns23bNnruueeCgZ3LGf0AJz6nrj4+P/gcDVgoZMDxwf1CXLMvyQfH+bBKEGStAAAgAElEQVRefvllQoEcrB/u86O5NrRYUZzzweK+I68ef4jDsOsZfY26fqTOrCFj8Xv40Vw/r7/+ehDvqPrIWvP5QrzPmzcvb87gpInpbK555ig5A0tzHWquZw1nDZaMxVw5a/zI+GAsNz4kZ44Z1hTvM2G5fuS14cOSfnxYOBe45jlefX4kFvtx+WiwpB8fFvZFXT9SZx8fieWz0WDF5QdYWLLy+OOPB5XEN5tEmPhTVBqCu+yySzDYY3T+4uD32GIQ5lbZwz5pF5cN/GKA7Pp3XzOvTp068ctgK200fjQ2LUCa34Rh4TE08sonTJjQ6lBw5gEtPpR+sK9r167BcRgsnHrqqV4beazPD7Dc5cB8NowVAGbgkw3nMD9hWFh14dNPPyXJWfYT78P8MD405uqGPh8+Pz47YGFViIEDBwaufRpq4l5y9mFpOMeBhRQj3O2H1m6TfcP7qOtQcvb1i/1osHbaaScCP58f7IuDM/sBd26y77zf3Uob7pe7333Nx8qY9tnA1t3vvnb9RHHWYMlYzIQVx3eHjA8NltQC7zWcgeX+H+XDkn58WDU1NSx5sPX5kVg+Pxos6ceHhX24Dt0m7aTOPj4Sy2ejxXJ1ztUPsKJWO3H7XOrXNomw1Gcgofg2iTD+ExPHRCj4wCPtSkkdCFMZPzqw1ODy5cvDzEryGa4PVLCcOHFiSfDjBsWyjqtWrUpkYR5MmsXAI44JuHHrZv5MAVOgehWwHOjqPffW8yIrcOyxx+Y1UQvL8GEyVTUMnnFqsBb03//+9yKfJR3cSy+9RL1799YZl4EVrwWdRKrQ2n10n0SOxskUMAWqTwEbQFffOVf1uJIKqcgOI58tqhXCBo/8fRO1NMUQsNj/nDlzQsstazgjxwx5o2FNU1hAyxm+wloUFpaxw53eODjjkSd4h7UoPjgWNhs3bsxYRAU24Autw5oGS8M5Dizk6D/11FORnNGfqDjTcNb4YZuw1U40fWc/2IY1TUxH9R3+NTaa61DjR8NZg6WJxbj8aOIjLixNfGj6boVUwv/P1OisvTbKqZCKDaDDvlHtM1MgRgUOPPBA2rBhQ84eUZnvuOOOy/n4cjxwzz33JEwmTFp78cUXK+quKO72I4UjiQ0T5arlqUsS9TdOpoAp4FfABtB+XWyvKRC7AvmsBb1u3bqAD68yETu5hDrEDwY5OSUJVDdt2uQtLZ0EbrlywIo7H330Ua6HF+Q4VAxF6pM1U8AUMAWSpoBNIkzaGUkIH5tEGP+J4FLiU6ZMydo5KhmioSR5NTUsaYSVM5JWdTGOCaFJO49JrKxo30NJixLjYwqYAqyA3YFmJWxrChRYgb333jtYyi4XGKxEUI2rEGBZI0wiS1LD6iCVeFc0iVrjjjhSn6yZAqaAKZA0BWwAnbQzkhA+mCSFIincMKmD/3gfFk/HgvduK5QN/GJSDbbcJBYmpyBf0m3SRuNHYwMMOcknCgt5nMhjhp3bwBmL3nOTfnDnul27dkEhlUw22B+lD2xwvnDeuEks7AeXMD6wieKs9ROFhbWgkZvrcoZvqWGUH+bjxgf33fUl/fiwZs2a1WJQ5/OjuTY0WLCJ4pwPltv3N954o5Wu3DfogIb3UXEmOfNxLhb7afLa9K8PC08gMImQm7TB5KWo7yDGwpab9IP9mpjO9pqHXx+W5jqM0lnLWYMlYzFXzho/6JerI4olyYl8jz/+eKv1gGHjNhQYwh839uHaYfIffHHz2Ug/sHV94D18RPmRWOzH9aXBkn58nLHP1dCH9fzzzxO+q9zGvnifxPL50WDF5QdY5TSJ0AqpcCTZtoUCGLChah433J2STbMIe1w2wMcA2eXhvmZucRRV0GIxJm8lH58f5JliwpbbwBk6cZN+li5dSmeccUaLwgHSxneszybOogphnMFHFg3w8YmywY8OrA7xhz/8gbsYbKWvKD84CHzjKKSCEuP77rtvmo/kwlgyd1vaSc44TtpoOMMmDqyvfvWrdMcdd6T75eMDflHXoeQc5scFk33H+7vvvjsoHMR20gb747jm2Q+4c/Nh8We8lTZ4H6UPjtVch7Bz/buvGT/qu0OLJWMxE1YchVRkURJMFLZmCpSjApYDXY5nrQicLfewMCIjlxkTAbXpGEgXwF1Y3Gnr0qVLYUgl3OvZZ59NM2fOTEz/cVcUbdiwYQlXLjt6KJd+zTXX0PTp07M7sIDWSczLLmB3zbUpYAqUkQKWwlFGJ8uolr8CGDzjx4m2LVmyhMaNG5eYwaOWd5x20My3fnacGNn4qq+vb3EHOptjk2yLu/1uukgSuC5evJgwd8CaKWAKmAJJU8AG0Ek7I8anohVARTWsIaxtt912W1B9UGtfiXZ4nJzP+tlxa/LOO+8QKvdVYkOlS9yJTkpDJcpqffKSlHNgPEwBU8CvgA2g/bpU/V6rRBheeQkBIidx+IJG2uBuKu7yITWDW6ZqYs8++2xgcsIJJ7SaZMPHuluJ5X7GrzE5COkgYU1ONPHZZuLs2mr8aGzefvttev31113XrV5r/CA3FbzDmsbPk08+2WJim8+fpjKXBkvDOS4s+EF+/ueff+7rUnpfVJxpOMNZlB88qRk0aFAa1/dC03cNFmw0MR3FWYuluQ41WBrOGixNLMblBxPO8BfW4sLSxIem7xrOcWFp/GjiTHMdxoUVlx/0q5wmEVoOdNhVXMWfWQ504U4+8jovuOAC6tevXygIcn+RvoEBdDW3pMViJa4BzfGF5RIxSTIJ+d35rJvO/bGtKWAKmAKFUsDuQBdKWfNrCmRQANX1sLJGWHPvPofZVcNnmESZTd54ITUBj7FjxxYSoqS+MXh2VyopJRmsLFJtpetLqbdhmwKmQHYK2AA6O73M2hTIW4EBAwYQ7vRlakjvmDp1Kl199dWZTKpqP6+fnYROI72hkpfdQr55UgrXYLImBvTWTAFTwBRIogI2gE7iWSkip/nz5xOW5ZJ/yL9bsWJFmgnngLm5a1gUXubpsR0fGJcN/CJ32MWXWMj5uvPOOxk62EobjR+NDZzLFQu0WB988AH17duX+C4zOD/99NNp3hg877fffi1SPORC/hKL+WA/N58NzhfOCTefjQZLcs7VjwYLnE888cQWd6HdfqIvGj/Q2I0P5uz6kn7g2/0cd0WxPjrsuPn8aOI+Cgv+NZzzwXL7Bj8LFy4krHzBjfvmvo+6DiVnHJvJD/v12WACIf5cjtIPjov6DsIxUZzhRxPTuV7zbh+Yc9R1GBfnuK75uPwgb9udi8Dn1NVIYnF8YMtNXj8+P/La8NlIP/DvcsF7DWeJxX5cXxos6cfHGfuiYlFzHUosH2cNVlx+gFVOOdA2gEbEWPMqsH37du9+25m/AqNGjQruMktPGFTjP4/vfe978qOqfn/AAQdETm4rhkC4K9qhQ4diQJUEAyteYNCahIYf8HYHOglnwjiYAqaATwGbROhTxfYFd/vwC3fKlCmmRoEUuPjii4M70ZdcckmAgKcBV155ZfA0AGkL1r5QICnFS6qhsAfiEpNXsWJMqRoXEEqlUqWiYLimgClgCoQqYHegQ+WxD02Bwilw1VVXBWWqv/a1r9HXv/714DWWSLPBc2vNUToby02VuiG9ptILeyDH+6OPPiqp1O+++24wiC8pCQM3BUwBUyBEARtAh4hTzR/ZOtCFWQfajSkMlJFbh7Lev/3tb4O7/ZmKRmjWKkXqR1SLa31V8EbOeVjTcNbYgPPOO+9Mb731VkY4jR/Nuqhhfnjt7g8//DByMK9ZFzUMizuq4RwXFvvByhfI08/UouJMwxm+w/ygcM4ee+wRagMfzDkTV94fhsU2mpjW+NHYaK5DjR8NZw2WJhbj8sM5vay7bxsXliY+NH3XcI4LS+MHmkXFh+Y6jAsrLj/ol+VA+64I22cKmAJeBQ499NCKXtnB2+ksd/bo0aPVpJksXeRtXi13RXG3//nnn89br3wcYCm93r175+PCjjUFTAFToKAKWA50QeUtX+dJK15Rvkoa87gUQGGZadOmlSzFBTnqmNg2ceLEuLqUSD+49pHrjbubpWraYkOl4me4poApYApYCofFgClgCpSFApjUhtSiUjU8Eq2Gu6LQee7cuaWSOcDFIL7Sc81LKrCBmwKmQN4K2AA6bwnNgSlgChRDAeTmYh3mUjUUGOnevXup4IuKO3To0BbrbhcTHLnmGMDbZNpiqm5YpoApkK0C7a62cmfZalYV9qtWraKHH36Yhg8fHvQXkzrefvvt4K9bt27BvgULFtCaNWvosMMOS2vCdnHbwO+yZcuCSUPsW2LhDuF9991H/fv3z8hH40djAwBM4kDlNm6Sj9YPlgtsaGhILxsm/cD/Y489Rq+99lqoDfhgMkcmfeAH5/S9994j5BSj5YoVF2dNv5gzVodAoQ+sWgLe3E+tPsDCgv8cH9x3xDX7knxYI3x+xRVX0EUXXURLlizxngvXj+baCMMKTk7zeY/inA9WJs74oYIS6ogV1waaRV2HUmfW0OfHd/3s2LGDtm7dSrvvvnskFuJ93rx5od9BGs7gqInpuK55jumw61BzPWs4a7BkLPK1wdcF9InLD/r18ssvp787GcuND4nFMeTyycTZ9SOvDR+W9OPD0nCWWOzH5aPBkn58nLEP16Hv+mGNgOV+d/j4SCyfjQYrLj/AwpKlxx9/PKgkvu2UeIZGsCQK4D9PVFzj5l6ovA9f/vKOoLSLywZ+MUB2/buvmVOnTp34ZbCVNho/GpsWIM1vcsHCoeDM/5HivfSDfV27dm1Gadr4bOSxPhtguXdRfTYarLg4a7HA+T//+U/6rqjkrfEDjTE5jZv0gf3SD2uKu6IoMIK7onKFCp8fTdxnwmJ+2Go4x4nF1zNSVXC9nXnmmS6dIDajrkPJmTV0HUEz+HEb64gVDw4++GAVFo6P45pnP+DOjfnwe99W2nC/3P3ua/ahuQ5h6x7rvnb9RHHWYMlYzIQVx3dHTU0N0w+2GiypBd5rOMtrw4cl/fiwNJwlls+PBkv68XHGvkzXD3DR4Mf9vsM+6Uti+Wy0WPzdEYB7sDR+YIPrv1yaTSIslzNVZJ42ibDIghucSoE2bdoEFQm/9KUvqezjMsL1gDWgp0+fHpfLRPtZvXo1zZ49uySFlO65556gAuGwYcMSrZGRMwVMgepWwHKgq/v8W+9NgbJSYOzYsYTl5IrdkP/ct2/fYsOWDA8T+PCDoRStmnLNS6GvYZoCpkA8CtgAOh4dK87L/9/etYZcVbTRIcNK0PBH4SUvKGWFmUaZFZJFdIEo/0T+UAnTIrSgwIj6kQVJSRBEIpSQIIEoJREaqJlYgUR0sTIiMn1T+1eGIkURH2t/PafnfZyz53nfM2efs89ZA6d9e/Zaa9bMHOc9zYUbqaQ3JcG4uFTyxHg2Q/As9u/hwhgzjBstSx6uXJo9XFozOrHoYNnkwcH/8kwtzdYM58SJE2HChAkFbbMYrcmzsYAHx6M5F5fGkQl8v/76q85WcZ6qZx7NAGqGg4775MmTXVxa81lC1Y1mXCqkqBv2f4vr5zj34HhidJ22HHLtwfG0Qw+Xpy7mwvFsSpKLy1M/PHn3aM7F5cHx1EVPO8zFlQsH+eJGKvINwCMdoAN0IKMDWGIN/+BVnb766quzxg9WraFqvtWrV4eBgYFKaTFpEanZjpyViiEZHaADdKDEAf4CXWIOH9EBOtBdDmCG+aefflq5KKx2MGnSpMp5O0mICT12YlC79WDFAnTcmegAHaAD3e4AJxF2ewl1SB8nEXbIeNImHah6IiHaQqd35kua0oaATz75pFiPed26dW1Aj0NiAiHS0qVL4wG8SwfoAB3oEgf4C3SXFARl0AE64HOg6omER44cCXPnzvWJ66GoKVOmhH379lWaI4xvx9JaTHSADtCBbneAHehuL6EO6Tt+/HixSYrQY1KHfOQeFk/Hgvc6tSsGuJhUg6Mky4VJE/hf7TrZGA+OJwYcdpLPcLiAA81Y9F6SxcF9PE/FpPwBzs6dOwetsxmbQIPF9/GRFIvZvHlzOHDggIQU45Lt2GQPjifGasZEQmyeoZMHB3qhW5LkS+u2OIjFxil6C28bE8PBpCPo1kni5J7FwX2tBdceza1waT6Lg4mEWPtad6IRj3qm38O5vraaJV86Bue2/eAeJhCi4y7vpLgweSnls3BZfn0NPk+djmnWOF4uW6fxnsaBnlTevZo9XLYuxvTkxNFlJlw6/5ZL6gOOkppp1ji2Tse4LA7wNQauoSel2XIJjsbycFmcmGbcS9VFTzu0XDHNHq5cOOCq0yRCbqSCGsN0lgMjRozgRipql0GMB00lG4NrdOr1fX0ueLk2JQGextfnwlXlEZuPjBkzJjslJhJu3bo1O24zQHypL1mypNnjnr7/4IMPBqxAUkVCW7nqqqu4hXcVZpODDtCBlh3gGOiWLexNAI6B7s1y7YVcYaUGbLJRxWRC/BGAXTnPnDkTqt68pRvKCtvqogO9atWqtsvZtWtX2LNnT0c2b2l75khAB+hAzznAIRw9V6TMEB3obQdkjWJZ8qyducWmLffee29fdp7hK7ZuxhJ+VST80T5v3rwqqMhBB+gAHWjZAXagW7awNwG4kUqeTVLsOLVYbfFshoBhBPiUJQ8Xxldj3GhZ8nB5NOfiiuEsWLAgHDp0qJENj2bPxgIWB5PabrvttgYPTmzMoIf/Xng2FvDgeDTn4orhzJgxoxijj1/iJaXqmUczsCwOfn22w45sjGiQY0yzPNPHFA5iPXXag+OJidVprRfnHhyPZg+Xpy7mwsF4WXzKUi4uT/3w5N2jOReXB8dTPzztMBdXLhzkq05joNmBLmvFfEYH6EBXOoBfKj/77LO2a8NEnDlz5rSdp1sJMGwFq558//33bZWIHQ/ffffdvltru62mEpwO0IG2OsAx0G21t77gHANd37LrB+Won4sXL277OGisOY1fV/p5Z7wq1mbGmtObNm0Kb7zxRj9UX+aRDtCBHnCAv0D3QCEyC3Sg3xzAShxI7RwHjU46xj/3c+cZHs+aNatYyq+ddeyLL74I8+fPbycFsekAHaADWR1gBzqrnQSjA3SgKgcWLlw4aBx0bt7Y+OfcHHXAk3HQGGbRroTxz+ioM9EBOkAH6uIAO9B1KamKdWIjldgkLUy4kORZPD1XDHgxqUbz28kfmDShN8qAThvjwfHEANtO8hkOF3A8GzjYBfgtl+jBfUmxGLtBQSzGw+XRnIvL4iB/0H3ttdcWy57h2qPZbiwgecdRksZ5//33i/HP+nkZl47z1HvNJfwaA/c8mlvh0nzNcI4ePVqMg/7uu+8K31Pt0GpGPsCjuXAu7UfGP59//vnRGPuevsbwGr3BRRmXfg/n+hrveeq0aEY8ksXBdcofvGfrtMVBjAfHo9nDZetiTE9OHF1mwoWjJMuF+/o5rptp1nG2Tse4LE6MC3pSmi2X4Gg9Hi6LE9OMe6m66GmHlium2cOVCwdcnESIUmCqtQPYSIWJDnSzA+hAY+c6vUJELr3AxA6RV1xxRS7IWuPcddddAcMs2pEwGfSFF15oBzQx6QAdoANtc4CTCNtmbb2BOYmw3uXXL+pXrFgRVq5cGWbPnp01y5zUNtjOdm5es3bt2uL/Jtx+++2DSXlFB+gAHehiBziEo4sLh9LoAB0odwATzz7++OPyoGE8xa+t+NWV6f8OYPOaCRMmhC+//DKrJfil/5lnnik60FmBCUYH6AAdaLMD7EC32eC6wnMjFW6kUlZ3u2UDh1tvvTVgmTUZJ1im2bOxgOAAc+7cuVE4iYk+/PemZ2MBD45Hcy6uFA62T8cfK3bspfXBoxnvAOfzzz8vxlc3W+kkxZXSLNpSOIjz1GkPjifGs1GIB8ej2cPlqYu5cDBeFp+ylIvLUz88efdozsXlwYF3qfrhaYe5uHLhIF8cA13WMviMDtABOpDJAfllFBPcciVg4ddW2TI8F27dceSPlZz5QEfpvvvuywlJLDpAB+hAJQ5wDHQlNtePhGOg61dm/ar4nXfeKX6Bfvrpp7NY8Nprr4UxY8aEpUuXZsHrJRAsHbhmzZosY84xfGPUqFF9v1FNL9UP5oUO9JMDHMLRT6XNvNKBHnRgwYIFxTjaHKtxAAPDN+6+++4edKr1LOGPilxjzjF8Y/Xq1X2/UU3rpUIEOkAHOuEAO9CdcJ2cdIAOZHMA42exDNpHH33UMiY6deiQNxuT2zJBzQHgzaOPPppl6UBs3Y2dHpnoAB2gA3V0gB3oOpZaBZqxkcrBgwcbTBirKB+5uXv37rB9+3a5LI7tigEuJk3gKMlyYdIE1u7VycZ4cDwx4LCTOIbDBRxo3rFjR0O2xcEDPE/FpPwBDsoL5SZpuFwezbm4LA60Q7dOo0ePDs8++2zjVrN86fohMRrr+eefDxdddFEDByf6Oa6blYWO87QNi9OMK6W5Fa6hav7666/DokWLwssvv9zwCBgaB/nSmiVfOuatt94KH374Ybjpppua4iA+VacxeSn1HeTBgQhPnc7V5m2dhkbtD/Sk8u7V7OGydTGmJxcO8qV9FC6df8uFvOrnuG6mWcfZthHjsjgxLo9myyU4Wo+Hy+LENOOe9rAZV6odWq4YjocrFw646jSJ8FwYxkQHrAPnnXdeGDlyZOP2zJkzG+dyMn369HD48GG5LI42LlcMcNFB1vj6XESgI6WTjfHgeGI0h5wPhwvvQjN8kmRxcH/cuHHyuDjGYvBA39fn8jK4pk2bJpeD4uWmh8ujOSeX1mzziesbb7wxvP322wHrN6NTFss7PD59+rRk86wYjPv/888/AybL6WSxPP546r3FAaflSmnGOzm5Uu0Z+q6//vqwa9euhkUpzbF8YaKm/fXZ4uC6qjYPjZ463cj0vyetaNZ12uIIj76vz+W5R3O72mFMj63TsZjx48eL/OIYi7GaEWjjPFy2bVgM4FqcGJdHs+WK4Xi4LE5MM+6hbehk44Cjv+9ieixXLMbL5fnuSGkGV2qFFp3nTp9zEmGnS6BL+TmJsEsLhrKaOoDOM3YmxNJew0lPPvlkmDdvXsBybUzlDsArdID1L8jlb/z3FFt333nnncUvihdccMF/D3hGB+gAHaiRAxzCUaPColQ6QAeaO4DOHIZfoCM91IQ/GPHh5ik+55YvXx4ef/zxYY2FfvHFF8NTTz0V2Hn2ec0oOkAHutMBdqC7s1w6roobqXAjlbJK2K0bOGBVh2YdO/zvw2a/TuMXVbx79OjRYkm8srx7Nl7wbCzgwSnTLBpzcXlwwImxl5dddlnAknbbtm0TGY1jmWbsZCh/qNgxnA0AdZKKGYpmBRs99dTplB4Ae2Iw1hPay5IHx6PZw+Wpi7lwPJuS5OLy1A9P3j2ac3F5cDz1rKwdSr3LxZULB7rqNAaaHWipSTzSATpQewfQsVu1alV45ZVX3HnBsnV4bzjDEdwkPRiIP1SwZjY6xJ6EJQIfeuihsG7dOv767DGMMXSADnS1A+xAd3XxUBwdoANDdQA72/30008BG6ykEoZ7oBP43HPPpUL53DiAIRivv/56WLx4ccC45rKEzvNjjz1W/HGDP1bqmPArG5c3rGPJUTMdaI8DnETYHl9rj4pflbAEDn4tYqIDdXNAOmzz589vuqMgOs/4FRUdbW7bPfwSlsmb+EMk5qOUxdVXX110oIfPxDfpAB2gA93jAH+B7p6yoBI6QAcyOYBfR1999dXwzTffhBUrVhQTC9GRQ8I43LVr1wZs5MHOc+uGY+gLxo9j9RL4eezYsQIUv0pjububb765mJyJoTVMdIAO0IFecWDEmjVr1vRKZpiPoTuAjsR7771XbK6BxdDxOXXqVPjggw/C3r17A2bbI2Gyiky2uPzyy4t7mORy4MCBcM011zSIJS53DHCh6cSJE0GwLRcmTWzevDlcd911TfV4cDwxIFi/fn2YO3duS1x4ecOGDeHHH39srHNq84WYN998M3z77bdh1qxZBV8sBnrK/MGL+L8KP/zwQykXPMQmOvjFECnG5dGci8viiCapB7iOaYan2DVv8uTJYc+ePWHZsmXFL85jxowJd9xxR5g4cWLhF+q1YFkcL9dw2oaHa8uWLcUOi1KnpSy0Zk87bMY1VBzwx9rhmTNniu3U8QcLNrTBcA3UoQsvvDC89NJLYWBgoPj+EJ8FJ0f7Qf0o+w4SrlTb8NbpHFy2Tku5ij+od572DM3w9sorr8QrxRq6v/zyS5gwYUJxjf+gfuCPmSlTpjSN2blzZ/G9cOmllzaNyYVj84oJetCsdVsuiEKczlczzRpn//79xb9RskZyjMvixLg8mi2X4Gg9Hi6LE9OMe8DSdVHixCNsVLRv374wZ86cokxjeixXLMbDlQsHXPjOu+GGGxqau/mEG6l0c+lUoG3p0qUB//hJwjkWRD/nnHOKjQXkPtbHtQkdLHRSdLJxuWKAi869xtfnomHs2LFyWhxtjAfHEwNw+7+rh8MFHGiWL3hcWxzcu/jiiwdtthKLQcdQ39fnwEDChgBYPF9SLEb+ES2L8WjOxWVxoMvqLtM8e/bsgM8999xT/CKNnfSQ8AeXTRYHz4fCJXieeu/hQr1Ap1SS1YL7ubg8OOBv1g4xPhjfJ/hHHZrFZ2i0ugVH8lUWo9/V5/Ku3eTCxgiXvq/PBcdbpyW+Vc2pduhpz9A8adIkLYnndIAOVOQAx0BXZHTdaDgGum4lRr10gA7QATpAB+hAVQ5wDHRVTpOHDtABOkAH6AAdoAN0oCccYAe6J4qRmaADdIAO0AE6QAfoAB2oygF2oKtyumY83ImwfCfCnDsvYYJKbDyurjKenbkw8SaVPDgyIa4MK5dmD1cuzZ6duTx6PDGe+uHB8WjOxeXBQZ1I1TOPZg+OJyaXZnCl6nROLk+dTvns0YwYD5enLubCwUQxfMpSLi5PmXny7tGci8uDA/2PLgMAAAw2SURBVO9S9cPTDnNx5cJBvuq0EyHHQJe14j5+xjHQfVz4zDodoAN0gA7QATpQ6gB/gS61hw/pAB2gA3SADtABOkAH6MBgB9iBHuwHr+gAHaADdIAO0AE6QAfoQKkD7ECX2tO/DzF+6tChQw0DZJwYjpIwLgyLueskcXIvVwxwMeZL81suaMaGETrZGA+OJwZjvlJ59+BAKzRjQxpJVjPug0uPG4zFpPzx4mBRfHwkxbhyafZw2bxDFzTp5MGBx7p+SL40lsUZCpfG8dR7D5dHcytcQ9WM+FQ9s5rFQ80lOLoMcS8WY+/p6yrbYU4uW6dt3uFLymfEdLIdxjTbOh2LQd7xkSQxOEqy/uC+fo7rZlw6zraNGJfFiXF5NFsuwdF6PFwWJ6YZ91A/dJI4uedph5YrptnDlQsHXHUaA80OtNQ2HukAHaADdIAO0AE6QAfogMMBTiJ0mNSPIZxE2I+lzjzTATpAB+gAHaADHgf4C7THJcbQATpAB+gAHaADdIAO0IF/HWAHmlUh6gDXgR48vsyalHPdy9T6s+D2rItqx8RZzV4cO5YuhpNLs4fLk3cPjmddVA+OJ8ZTPzw4Hs25uDw4qAupeubR7MHxxOTSDK5Unc7J5anTKZ89mhHj4fLUxVw4GC+LT1nKxeUpM0/ePZpzcXlw4F2qfnjaYS6uXDjIF8dAl7UMPqMDdIAO0AE6QAfoAB2gAzV2gGOga1x47ZTOMdDtdJfYdIAO0AE6QAfoQJ0d4BCOOpcetdMBOkAH6AAdoAN0gA5U7gA70JVbTkI6QAfoAB2gA3SADtCBOjvADnSdS6+N2gcGBsLBgwcbDJjUIR+5uXv37rB9+3a5LI7tigEuJk3gKMlyYdLExo0b5XFUjwfHE4NJE6m8e3AgEpp37NjR0G3zhQfggt+SYjEpf7w40JLSk0uzh8vmHflA/nXy4CBG1w/xUGNZnKFwaRxP2/BypTS3wjVUzYhP1TPrs3iouQRHlyHuxWLsPX1dZTvMyWXrtM07fEn5jJhOtsOYZlunYzHIFz6SJAZHSdYf3NfPcd2MS8fZthHjsjgxLo9myyU4Wo+Hy+LENOOe9rAZl/7uiMVYrliMh8uDs3fv3rB161ZQNJLkTW7guk6TCM8V4TzSAe3AqFGjwsiRIxu3Zs6c2TiXk+nTp4fDhw/LZXG0cbligIsOssbX5yJi9OjRchrV48HxxAA8B5fgwCdJzfI1bdo0CRnkQ+NmCIPuDxdn3LhxGnIQpjxA3nNo9nLpvEODzZsHB3pPnz4tWTgLAw8sTitcqbbh4fJoRkwurhSOp21YzTEPBadRGJEylRhd1vpc3q26HQpvWb60Tn0u70KzrtOxGIsfi+lkO4zpsXU6FjN+/HixoTjGYqw/1gtce7hs24hxWZwYl0ez5YrheLgsTkwz7uHfQ51snKcdWq6YZi9X6rtj6tSp4Z9//tGSz/oOBldqhZZBAB2+4CTCDhdAt9JzEmG3lgx10QE6QAfoAB2gA512gEM4Ol0C5KcDdIAO0AE6QAfoAB2olQPsQNequKoTy41U/hujF3M958LxqQ0cwI+xYeAsS3ZMXCzWg+PZWCCXZg9XLs2ejQU8ejwxnvrhwfFozsXlwUGdStUzj2YPjicml2Zwpep0Ti5PnU757NGMGA+Xpy7mwvFsSpKLy1Nmnrx7NOfi8uB42oanHebi8uB4YpCvOo2BZgcaJcZEB+gAHaADlTmAf0xj40ErE0AiOkAH6ECLDrAD3aKBfJ0O0AE6QAfoAB2gA3SgvxzgJML+Km93bjmJ0G0VA+kAHaADdIAO0IE+c4C/QPdZgTO7dIAO0AE6QAfoAB2gA605wA50a/717NvHjx/nRipqYX9MasFkE0kYw7lz5065LI52MgquMRFIv2dj8OLmzZvDgQMHGlixGHDp9TFjMR4uD87+/fsDPpJiXLk0e7isZuiCJp08OPAYuiVJvjSWxUGsfo5rGxPDQVml6ofFiXF5NLfCpfPmwUF8qp5ZzZKvdnBV2Q5zctk6LXUIXklK+Yy4TrbDmGZbp2MxyLtuGxKDoyTrD+7r57huxqXjbJ2OcVmcGJdHs+USHK3Hw2VxYppxD/VDJ4mTe7nboeDiaLms5uHGALdOkwi5kYquFTxvODBixAhupKI2j5kxY0Y4efJkwx+e0AE6QAfoAB2gA/3rAMdA92/Zl+acY6BL7eFDOkAH6AAdoAN0oI8d4BCOPi58Zp0O0AE6QAfoAB2gA3Rg6A6wAz10z/gGHUhuakKLfA7YsXSxtzybKsTe4z06MFQHsPlEs4Qx0Ex0oBUHPN93reDz3WodYAe6Wr9rw8adCAdP0IgVHDp2qWQnesTiUzug4R1PJ9LD5cHxfMnn0hzzYzj3PJo9O3N5cDwx6Gyl6ocHx6M5F5cHB2WTqme5NHu4cmkGF+p0KqXK1KMZMZ52mPIZOLnaoacuejR7cDDhDJ+ylIvLUz9yafZwleVZnnlxUvWj29qhN191mkTIMdBSa3kc5ADHQA+ygxd0gA7QATpAB+gAHWg4wF+gG1bwhA7QATpAB+gAHaADdIAOpB1gBzrtESPoAB2gA3SADtABOkAH6EDDAXagG1bwRDuA8VOHDh1q3JJxYjhKyrV4ugcHvBjzpflFk+iBZr1RBu7bGA+OJwbjufRmAMPlwnu5NkNI+QMuu0GB9QcxdrH/WEwuzR4uq1m8xlGSB8duLCD5wlGSxcF9/RzXNiaG46nTFifG5dHcCpfOmwcH8al6ZjVLvtrBVWU7zMll67TUIXglKeUz4jrZDmOabZ2OxSDv+EiSGBwlWX9wXz/HdTMuHWfrdIzL4sS4PJotl+BoPR4uixPTjHuoHzpJnNzL3Q4FF0fLZTUPNwa4dRoDzQ60rhU8pwN0gA7QATpAB+gAHaADCQc4iTBhUL8+5iTCfi155psO0AE6QAfoAB1IOcBfoFMO8TkdoAN0gA7QATpAB+gAHVAOsAOtzODpfw5wHejB48v+c+b/Z941Le04NYuD61xruXq4cq2vmkuzHUsX8yeXZs+6qB49nhhP/fDgeDTn4vLgoHxS9SyXZg9XLs2edpiTy1OnUz57NCPGw+Wpi7lwMF4Wn7KUi8tTZp68ezTn4vLgwLtU/ei2dujNF8dAl7UMPqMDdIAO0AE6QAfoAB2gAzV2gGOga1x47ZTOMdDtdJfYdIAO0AE6QAfoQJ0d4BCOOpcetdMBOkAH6AAdoAN0gA5U7gA70JVbTkI6QAfoAB2gA3SADtCBOjtwbp3FU3vrDqxduzacPHnyLKCBgYFw+PDhxn1MGpO0cOHC4hSTGE6dOhWWL18uj4oJcbiQmC1btoQzZ86EZcuWNY3x4ID/+PHjYeLEiQ1s0SRcmDSxffv28MgjjzTl8uB4YkCwcePG0rx7cTZs2BDGjh0bFi1aVOi2+RKu0aNHh/vvv79pzPr160v98eLIZjRLlixpypVLs4cLPuu8QxQ8knLHtQcHdfG3335r1A/xGe8LlsUZCpfG8dRpDxc0//777+Hhhx8GfKN95eIaKo6nTluftW7xedu2bUW+yr47PFzArrod5tKs67TURfEH+fK05062w5hmW6djMZs2bUL2wgMPPFAcJQYXkv9W2rzGse0wxmU1433EiRZcezRbLsHRejxcFiem2dN+PO3QcsU0gx//9q5cuRKPiySaxCMPjkczcNHveOKJJ4Sqq48cA93VxdN+cceOHSs6uDEmNJpbbrmleITOqaRx48Y17v3xxx9h6tSp8ihInI75+++/wyWXXFIa48FBzPnnnx80NkDlGudofNOmTUtyleEgDx6uI0eOJPPuwYHmUaNGNfJhPURmwFWmOWcM6gSSlFlMTy7NHi6bd2iDJl3uHhy8gz/mpH5IvoAnWBZnKFwaB9ipOu3hAs5ff/0VJk2aBPhG+8rFNVQcyVdZXUSM9lnrFp8R4/1eKOMCdtXtMPV952nztk7DD10Wkq9U3jvZDmOabZ2Oxfz8889FXsvqtPUHLwBL6g+um3HhmcThHd0ORY+OsTgxLo9myyU4Q+WyODHNuOdpP552qP2JabZ62h1j8wW+bk3sQHdryVAXHaADdIAO0AE6QAfoQFc6wDHQXVksFEUH6AAdoAN0gA7QATrQrQ6wA92tJUNddIAO0AE6QAfoAB2gA13pwP8AFyFE8LrVxjoAAAAASUVORK5CYII="></p>
<p><em>Award zero if displacement after t<sub>B</sub> goes to negative values.</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A ball is moving in still air, spinning clockwise about a horizontal axis through its centre. The diagram shows streamlines around the ball.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-09-26_om_10.55.18.png" alt="M17/4/PHYSI/HP3/ENG/TZ2/10"></p>
</div>
<div class="specification">
<p>The surface area of the ball is 2.50 x 10<sup>–2</sup> m<sup>2</sup>. The speed of air is 28.4 m<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,">
<mspace width="thinmathspace"></mspace>
</math></span>s<sup>–1</sup> under the ball and 16.6 m<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,">
<mspace width="thinmathspace"></mspace>
</math></span>s<sup>–1</sup> above the ball. The density of air is 1.20 kg<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\,">
<mspace width="thinmathspace"></mspace>
</math></span>m<sup>–3</sup>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the magnitude of the force on the ball, ignoring gravity.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram, draw an arrow to indicate the direction of this force.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>one</strong> assumption you made in your estimate in (a)(i).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>Δ<em>p</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}\rho \left( {{v_T}^2 - {v_L}^2} \right) = \frac{1}{2} \times 1.20 \times \left( {{{28.4}^2} - {{16.6}^2}} \right) = ">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>ρ</mi>
<mrow>
<mo>(</mo>
<mrow>
<msup>
<mrow>
<msub>
<mi>v</mi>
<mi>T</mi>
</msub>
</mrow>
<mn>2</mn>
</msup>
<mo>−</mo>
<msup>
<mrow>
<msub>
<mi>v</mi>
<mi>L</mi>
</msub>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>1.20</mn>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mrow>
<mrow>
<msup>
<mrow>
<mn>28.4</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mn>16.6</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
</math></span>» 318.6 «Pa»</p>
<p><em>F</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="318.6 \times \frac{{2.50 \times {{10}^{ - 2}}}}{4} = ">
<mn>318.6</mn>
<mo>×</mo>
<mfrac>
<mrow>
<mn>2.50</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>2</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mn>4</mn>
</mfrac>
<mo>=</mo>
</math></span>» 1.99 «N»</p>
<p><br><em>Allow ECF from MP1.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>downward arrow of any length or position</p>
<p><em>Accept any downward arrow not just vertical.</em></p>
<p><em><img 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etxpI6ecMIJOW3tzsApsugJmESOqHuEaVmICkTCpuYduEv7OOqoo3KV23L/MVMnb2GbirAbcFk2SNtBXJdvAOyBD3zgzBKR+vH2t789dzrYs6Mq4XR2ZcXpSCpOhkVKPirA3nvyk5+cPfShD12oPUDQGIisg8OcRMJjaNtuu20uhUSBbJQ0OLgQLtRE3GmIcCQSEecbwimBk7773e/OHvzgB5e6/JXz9Kc/Pe9/zgRtWMTEHnnPe96TS9XXvva16+r0CED58iiVi404bZWQZaOAy2CkhlkWQq8ewg5jMxnoQxj1nDCcBUUXPduKO5wKuGjSqgrgpJjFf2g9BG2qyile178ieAJQ7NDtt99+EHOgWNay/h4NXEEQA3aIyWGd+aY3valRpYtym47xSZlwcNgdiB3DbbvDDjs0vb5Q93nXTI4++tGPzj/wNmblqP0/+tGPLrCZT52KPWZdFj3v0cGFAGE3zeqYoNKRYEPYX8AKUNzp5tU4CoBrLNf62AOBmmgSW8iXLygOmah9GKTNXiQ0w4A2kv3Uh55zAZeKBcBm/cIJ+4uqGRKnT6PjHbbhAQcckE/YUgfn6V6POgx5HBpgmJnvXscelTvuuOMgrvEh27zIedXuuDtkxbfeeus8moGUsH7I7z5JFIRQIzvnWm07SzIhTMVZBWChw4UvfOHsxje+cR49YvLVBkF9EkZo8ppdyo66wx3ukM/tzUrvPnUZ+h0Oqxe96EX5zlvsxDHThcbMvJg33ZxzA8B0YJ9EFSH94ouSffLwDlvwNa95Tfawhz1s6SVWSgPSF7MwqW/L7raJmszR85a3vCU7+eST849vPOpRj8qjboYICmhbj7GeMy3wiEc8Il+faIu1vuOvS/0u3OXhIZ5NAVblDm8qRx4GAAL1MaYR2hSBOa9ltbHqaARgmMbBBx+cxzvW7YkeoLKJkGiIMb6ZVlfXoe9RZdNkjLBF7RhmmmCeaTObizeIdBgi7KSuIRo9S/SF961m7jrLboLYwkxc2UT3KieucgPLJj5FNTycFEBlXmrTpk2j93lfWmMA7OMI1GVb8pBKwGRz1Uix/2H8pto++9nPjp+9joMF7kYgrmUSY6w+Tls3K8CodV09kFztBhapuRGSaJnzzjsve9nLXpY3V9sBKpwUpNqiqH0BomLsoYoL2iWRaRqYP7tdarPLFRX5Gc94Rj7hHoHA6xpbaOBTvSScvo/6lb/c8G+W6Avv4mJtJ0/ZWQJfEXrZPYMNZF27jT7Pf/7zs6c+9am59FokUJFG4g4F8dKYqG0kDwD5RBUADRl7GCAzpfCCF7wg9xSvEWqEk83UwmIZKcjG+tqIQU/Md1XxdI49OKh4TSnUQcb+sk0SN7Wt6T4P2ZFHHpm94hWvyG55y1uum6QiNUkOa9ZiCQiVlOcXkMY2RdDJOOAMs5jVJ7DGTI3gisJDhUOAoZf4UwdErONYbaVQ1It3q82uu1RIURnWRXVNbBdSXKjRM5/5zKV0grz//e/Pdt1111aMqCt96p4P6SRMCrDiA4QREV/37rLfaw0uDQ3PkrD9oZf4y7tPeBOpR4Wo+zCDZd444/ve975WgbhUKWrKSSedlHM5v+WBsYiWX8Zk4v1e97pXvpaq6NwYuj0klMj4Ytwh+m2kqI5O4IpOwI3GWOLP81MXsR7lp0cSlZpRF7Hh+0yeuec975m+Wnn+la98JbfNig8Iuxr7yxjFMof8TXpRh4YOj4o6FuMOd9pppw0dyNsLXEFMnkVu3iGlGPc6wLRdXgKQJEyVvUbHtrtSW6kVbXvzm9+cA9320JIdmyycXGb3fUgv3sMhvwOd2uVjfZQ++mWZjjOFP7GRhJDYp4BkwBV9pHyWxFskLwOhzQ5IXLEAvscee5QWG58x2n333UvvV10UR0c6G4j/+c9/cq/kk570pDzEqOqdRb/OQ3qRi1wkX1Y/xCpmoBIFwmHCo2xiXv/NOgbGpiOGiw5jp5nDn7hKSRlrrdhMxRnyPg2wTYB9I6gZs6Zjjz22Enh1eVvpu/fee+cR+PZ4oFKugvseEzLHM0vSxxZqcvIA1UMe8pDRpmpmqWfxXXbzq171qoy6ahXE2GmQ8CdGKi8flyqbadZt0eQHYCZAhfG0MYI5RIrP4agA2tX1zivoXVubARQViqdtFRJaiGjQvjaaQdpmNBbxgPEN/dXQtJyhz4W7UfPTz7ZyUo2dZrK5yioXc0/Uxa5u9WJ+XOckYtNeHLho2dcrud+/853vtHZkKB/RDzrooOzQQw/tPPiK9V/U35iWNVkPeMADWldRvy7SFz1DQ4qQqLQhGEckjOAlL3nJWrhUXO9y7Bv+NIjkSitKTeRVE/nOTU5tKEqU9Pm6cxOegmvZcnUTjFXq2qc//ek8gr6ujOK9U045JZeaXbl6MZ9F/m1/C1uNtQUX20oc6LylFUADj3Co2MuQi1+KGEJ9z/ZPEy0jxhybnDOKHRihT55d1/CntLJ9zqkQQ3xggfcQJ7rb3e5WWQ2rk4sfiAgvIYC1TSG1hMYs6sY0bdvS9Jw1Wm28hgEs9K9jcE3lNd03Xkgjn6YFpNiGDTAwutjLsE84lLFg1flhhx22FhkyD3ANLrmCiDgHRwejF8jautbj/TgKHhYLppOr4htxLxwu7XwraB/0oAdFNq2OlrIrb9WBhRhowx6t8xq6P8vKhSaik0xApG9JlfioOsnD5g7p05RP030288Mf/vB8QyIgC1u66b1Z748GLhVDHHYX9XAWgFEtgbQKXNSCmI8KggCXuLUu6dRTT81j77q8s6zPog3nRBW4RFmwzQxy0mKoBFAcDELKJBuE8mDOI3ojQFanBQ3VTvmMCq6o6KwAA6qYXK4CWJQVR8vU2z4b73CAmGzeCMkmnbHhTFl7zR1ajmLwz5qofMAEzDyVJuLbxIPOWm7V+2OHf0W5M89zRUZNRwAjYUgwxO6acDfSqyzRx1MPkWfOPvvszT7dU/ZuXKPnizTZCCqhNluvZ6lHWWL7+KuL1yx7r3iN9KO1mP+0A68xYAUD7++Q0rBY7qL83gxc1kiREmMk6p1UBZK6MoOD0s+LqWzjlK5L+H2yZ5U9hEWaYSIiUMoS9ZjU6mvzBKhe//rX59nzHov9jD4sK3MVr20GLm5vUsBSjphLGKrh4eQgJXC0rgk4RVoXk3zL6lrloi++77dFezvvvHPZrZW8BlxAVEyAwSbqI7VoJJhzgMqGMKTVoqx0LrZ17N+bgYthyeAzycjFbSK3jxpXVfEAGM+cwN8uiQ0FRIziNFEx0n0U0nvTeTcK6BeLCLtKLZ5F6p+Y0I0OqqD4ZuCKGziX0CMJ0RBvqKTj7H1haUfXfBnDOGsxsSECdCSv7dcWKZlXWobEyWGvwrYJ48WAaSKYMvVvo0qqIs0qweVBIEAsREO8IaUYaRPxgwGKYuXKfnMdhxs3vW+y0VyXZHK0+BXC9Nmycytj/W3kFP3Q1jbyPMYr+ahFOs+4yHTEfAXxjp1qwRWFIxriSUNKMZ3IcLZxSFvVM7xMMRCijjyRwmQkK5MF33ZJAlq7Bvh2yX8ZnqURtKUBx5JV2TQEDLirGrke9NA+KqtxN48V5a3AhRAhxULaMFyHSBER4RM4bZMBUFQNueM5SiTzGHVzOG3L2WjP0QiqJpVTWgCWyA3b03WdS0zzmdc5SWUFufVmlhLNK7UGV1QI6rlWVVg0Ou/SrEmjzUu1dXCYAFV+muyRwZieUj8KhCYQmkFVLgGsrvtFVuU363X15uTyZwqp+Ge/RnGnJ5544gUCd5/4xCdmW2yxRau/vnXsFaHBYLWsnvQyn0SatdXTyypKKpqxJ6rb7ApETU0jnOVZdg3YNsqksI9TWARYjBAvo7drpDx1LlIbldAAHjPWMOpSPDIZgMh0iT71py48xBxZ7G1J24vTL7Z4ML5E0adjZuEDd820s2/EoM26HAHHtGUb+6spyDeIhcCpEY2Ace3xj3983gkbBVzm/7p4+awASFVAKqF9KauSAW5qho3VJN2q8mh7PYCUbhbKQaUvjTdbMLTZaVd5zA4rpS2x8Y3r0047bc18aFufvs/1klxpYXRuNo6FdIgxy/ot7n/7Z4hBa1ogidAcGCm4cC7czTWdgFNtlKiLd7zjHXm0d9o3dedoI2BAMphJgZSWxXcxUAtgx7CxABdTNPBNzahLbBZqzm1WMAvYZcr4w7ztujwPpjszuHSCxvMmihucJfpdXqRXmwWSgFSMhAcoMWySTqEqdd2YJn95yf5FXGRRJaprBpt1n332yR+x7KPuW1VsYeFh1P+hEkABEmZKJaV1iJAZAkx1dfTlTUHd80idHRpVlaKqscMMegDDDfsk9lx8f0sHVCW2WdGp4Vpsk2xN0Omnn171+kpd9wE/H73rktAmpBAnRZVKyWFlsp/KqI9nTQBlztQGMVRZq6J58owdmsusUmrW+g35/mDgikqJJaOK2cO9L8B0OiOVeliVdEJqoHouOka57Akgn8dGJFV1nNd1k/td9lNEE7RBI+DxAYQqhxQuT6rVqYxN7cQkefHEqwIWDcN8k+AEfT0EaJvqsB73NwMXo9VfX2BoBHuJ9AEwunSfRD20uUjV+6lTI83fQGB3ST66IFZulVNI77aTv2iBJr70IlEJqxaVoj1NIFYzdKUj4IaUorqSfpwLJNRGCJHaDFz06pA8CNN3HgtHAjBbrVE7uibE54Gs+zyrehZVP9u7ReT8Xe9619LI7651WeTnOZJSl3qbuoqG32uvvfJHQzUrew/t9WFXyRKgSqPj1XEW6VdWv0W/thm4EJL7kmdF4lzou74LwOxhaG6kD8BwOOphVfllk8nUG+oiVYQEtbp4VVVD7nOSq2q34bLBhxZogjZAgFZlKiGao70+bJvQHENOQbWIS06sYytG+LRtY5fnNgNXvExyIAy9GDD6ru/SOWbz+wLM6mDEKJOgOKHBkd7DHNgSDGdTBKuqGgKJ/fhsvNLFS0glRBO0oRKWLS9BT1+fFNnQNgFjBPEu6pITbnhMxR6XphbGTpXgioINYJ6cWN8lKqPOixfvpUeOhr4A8y53uj0diimAZJCkiQcqVEO7HNnxZ9WSD9lR4bvYWmhgUMWuWBxGZV5CwGrrxGCXYbwkKEa8aJLKtmq0L+1h79mXcl6p9TwXFc0sOe+Rwdr1K5MBME4OqYu6AdgRjV9UYQAJ11S/SJ6xKSkOTPKZRNT5yzqhzG3NG8gGlXwKSIp5qvxHi39ogDGiCYeVydoiPYGFdIu1fFXZygc413Nra22ITUNJ8gjcVmft0D5/Bx988GbNEFvor02ay467VEWGKZWLR1GHG/htDd6+AJM/w5o+j/ukKQVSeKA8T90xSNiP5lHs6vToRz86fXUpzgECrXHfN77xjdlHPvKRfPL8gAMO6KQOaiyGE98X823kMve9zzEBcV2fGtRULOoo2zzoPiZBgRlgqjYNVZdUjTXWtMG6LfOAaJhO3cwjtrBRLSwjmAGNs+EUpFgXt71GUx90dBcnB0lX5txIgZTWVfxZLDtRnnMDddnSUUcdtbYI1B7222yzTf6h7C52ljZrOxqghYFaBq5wHKVaQJFe+oz2oT/kNSawjCt1svqC9Lbvf4AIk8Bo1QED9ceEib9gDmxL71rShLkKcphX6gUulVN5DSO5RLNHx7SpOAKEF7ELMHEm9oDBkaYUSHFdGZLBQC3EqRB5mRI7M8K51JuKg8F0BZZ33/nOd+ZfsEcL4UwkewqMcGIw9quS9zim2HoG8xhJPdj17DjTDNQ93lBOmACSvg3wtK0DJ5f+J5l9F7uLWdK2jOJzrW2u4ovxG5cTdkRNwB0Rvk3Do3G4YNu1QYjKMLU1G8M5UgqkyNc9k5+xU6/n2YziDWOOJ95fxKNBZTCI6Ytk4Llm9XaXwFOrsj3PRpMH7yuPXpoAmZoYtEzvOaeSU7Pb9lXx/abfmCAGLVpEH4+1aSiQvfrVr26qziD3ZwaXWlD1Yl94joe2HRBA6AIwA4v94QOL32kAABeoSURBVJhyXkDSOZGnejkHLrq6QeMDC1Ra789TPejTUxxH6i1xQMSck0WhXSSXtU9stXAkARHva0q7psDcsYAF6ABLG9E/pGHaf33otkjvDP59Lh2lA7t8AA8oELjth+48T0pSE9JElSh6MXFEAAtHiKUZGAA1o8sgTcvpc273py5fXOlTRtk7VuAq20631C10S9fLGeCYDVqWSS3v8Ai27ZuyOhSvKVN/s/uop/4w6FVLvW2uKkJQE+2tQDfH8dokHIsqIJi0aE+Vva8MXD04ezxDehXDpYITApnkm1Q60rd8Vz1RgS90oQvlwNJ+IMH0UrW9Th2Md2gi6Tt96QZUxkQxgmMVgYVGg4NLpogV3kSenjaAYRPFcpWm53U013wTkGIQkGbAHvkef/zxuffIYFvVpG1obw8JTIh3FkhSdZAGwLYTtVBM6TuzDv4qUKV1KZa/Cr9HARfCAECs72rrrg8nBTWuKZFIPgRODU1TEUjuUXfikzl+85iZL6IyrSLATJFgIIKmbcJijofESkFirpJqZvFgMQFD2TvF55p+Y2YATO2UFiUsStSGv7HTaOCKigMMdz2DWoc2JfaAwdFGpeQ2tpDPYIhUBFJct8MUIEUdRGsIITrwwANLNxmN95btiHbPfe5z86/W0wTQnZQP9Vh7TH8Ig3I9BVy0lZSjpqfvxL22RyolpsrGIzGNg/WWVCaUX/jCF2Y2rfEB8rHT6ODSADaSjtShYftUNYzEAzAgwPXqEiBxHxeXbfuWMiClNpl8TROoQ6iHOtzk4uMe97iVkGABrOOOOy53EpQBS9tNm6BbGXg4MKTQIuroX3YPcEk92oc8OErKAFz27ljXAPzZz352xtN6yCGH5MVQh8dOm3kLY/CXEX7WyiC8DtexZXp+mn88W+S66TPODRYcUkemcXLACUhFL1d4zKiskUhJku3YY4/N6xbXhzyO7S20/ET964ClPewwEq0MPEGzPiFN+kGsoTk1UwcYKoY272TcqEssmDURLYAgDX3qWqe+sYWbSS4EITGs+XFMVa6ulSo+j4NREXCSJrUvnm1aqqK+7CxASusKaFQb19MUoE7LN9AMLDZY8fn03UU9N6CpuOazuLXLJJa6R5vLVhajnbaT7l3VN7TD4EhOdhXv79jAUl/lGqMkpWmYV77ylXlUx9e+9rW1NXzUfzZ2MQEc0LT5K77b9vdmkitepFL5rvAYcxE4C7e7eaamiA6SFMCAsk69IJF0bjr3FeUUOXXVdTr5k570pDxKQBxalyiIoFvVcQzJRbUhiXx4gi1hoABImbQHLPRJ57iirkEPAzGYT9yrO3qPWm0rgLIy697tes94tJWecLDYhIhZoM7UPfsYVo0PzgvgP+yww9benUfgbiW4ovE4BPvFn8aI73OcNekYA8EAKevwNP82AIsBQp1N495cN2lc7Px4vgg8HcHYPeaYY/J9AIfamm1ocFED1RETsAGqPf84d4rtRMc6YMV9kRwpY0rpX3YeKiQvLJV6aEll3FmnF2DiGaaN2MbBNmxdpas2YJ60E3bXQoArCGswcntHqMpQIGvq+Ci/DcDCTiMNU/srrhcHXhXAlGkZuGUddiq6xz3uMXO41FDgAgJqENXnta99ba4Gch4Y7GXxeE30pVahbRODi35As5BWRTrHM32P+gndMQ5BytT6WcBUVQ8gk0TMj5kaJVexcMTVkTpUvNsQIDMA2gSFNg0UdQ2OWlQjmwDm3eIAI8U++MEPZkceeWQuEcwJ9VUVZwUXUPHy4bjmjfbbb798AMa6qqJ6HYyjrF3Rp20YVjzrGLQdUlqlgFKGldV2Ah5CO0rrvh7nncGVVlLnDAUyHJRULIIiLc95G4DJy9oluwCn6koATNBvqjrKN2LoyrgxTsdZYD2VGD0OELp+l9QXXOwkUexAdfTRR2ePfOQjc46rja7zzBXbEsDCCKpUti7AGlpaUfkw01hvB1Ci1atspi50XqRnZwJXNCSAMatN1rbD2wCs6hkA456lNvKapeBLObO5sqJeD2Q24ORJpbZ4xgQ5u60pdQEXKUU9svaI3XHooYfmK8CpMQx71yWStDgg0/aVudu915bOnk1pUgXUvDIN/0LjsbeJNlD5rMNbBQlV1fRBwCVzxAubDOGKS0KqKlC8Hh1fJkHSZ6vAkz4DCAZqUd1T13CmFAeoe6QxzqoNVfM1GAqV7A1veEM+wDdt2pSrNAZLGdjqwEU6GXBsDflawyX4ee+9916TSri9yXKesqovygQQyiRz0CXo26QhoMMQtlXqEPO5H1IWY0uZWtRt1Y6bgQvxNTx1CHRpdAxOLvy+k4nqIASnadlKE8DUhctfKgLMtZC4ZYOVBKB2GfQmvf0VJVnQxbwdT51l6HYXAmrOE4tIzz///PwDA4cffnjmjx1nI1PR6iY6TTPYl8RqW/vbq0uqcirflEgbsFOr65hStLcJWMoUFM2mLtpy0eamI6Cjh7ww21VdVlJHh83AhSgGrbTLLrvkhKkaVHUZ41iWMyBu2eCte9c97/GKFT18xfdmBVg6kDCDMjULo/BnJbMvcbRxBcemk+agfMlDRIg5KQlQJTFuKZDyi//TAkgxKpSVuXUSNOhsSqMohSM/R3TSt2UexXgOM5plRyfvK4Pkl6jM7KmNIKWChulxM3DFTYMunUTuqx/H4DVPIdC2i44dDoghAKbDqyZRtTm4epVKGwMn/eQNYNj1t24CM+gpOr0ujAadSDJSW6gOA9+2cXVhaNRwErMunKxJekf9op9IK/v0d2GoygiTQP+SwH01n6jPKhwrwRWNwxmpJFSO0JnrOjzeKx5jIBi8RUdC8dn0dwCsbgB5PiRYE/fWliq1SFu1M6JS6uxGHFrEAJXQwOTgINFEnbC50lXOPoaOg5NG6TfFvMu+Ip28G2A1QOu4vfLCqVHHsNo4NwCjr7Qq0qsvA077e5XOG8GVNhZXxeFDVQGUrhwunAVdVMU2gyQAVgcez4Q9hztzVpSldNCQIL413MSJDVL1dAS6NAERm48TJXV2CNsBorbSHKDDjmmS5trJnqujc19pldKHLVXHhFI6LMI5m5c9aS5N3cdMncAVFdEpqcrY1VhNOW+dpInyHA1azgmDs8rF7LkYVHWGfYDVHoB17mVlprYPZmL75ybJktY7zpvUwniueDSQMYyYEyL167xt6hwMrGpfDM/0kVbLDCp05d316SS0tFmRCJwxUy9wRYUQe5a4w7BzqHyM3zpVSJkBsKaA3wBYHdeWVxdXM0Cac5I3m4hzgxpH+ph/apLgbcGFpubT7CwL2BEGBNRN0jOYRp2Xr4+0WnZQ8fo+7WlPW3MQGUsLFVsYgCo7GqgGAm4o4a5t7TIdx6vI9iju3FRVFlCUzV+lzxtoll402XhULfZaF0Neew3S2FrZORAAnJR6ANlbHB5sqlhTRG2URyRqowS8HD8kozy48tuojPIKh0IVQ/FMMJOqZ6I+cVxEUKmT/eElx9SGdY3TKl0IifnHh/6iXV2PdY6ourxmklxlGePs4YptUmHS90PatI1ba+PAMKBinsucWZV0icGJw/W1IeQB0I6pzRXAYXNFXYQlpTGKYXuZBmiS3inNnLdhDl2dSesJqqBjACfAEgwsmI+2h/MopUkws7hmOsMqZMw/FlC6tzSSKxqSHhFD5LZj3TxN+g7CBnets5ninVArq7x/8VzEDTY5AYqDqqstGeWVHduqhWXvll0L+pL4VZqCZ3gVSdW2WgEgzsJkyupadQ0zogKTPpiQ+oYGEMAJsJD+VcyxKv/0unnH5zznObndRYNYanBFw2IQOLYFGW7Ms9ZGipF4baI5lG9Suk2eQFacfqhzIkRb645DgAvzQRtMxSCsApX6N4VKpXWVb6iV6FMWV5k+3/dcH5AeAST5hArc1nbtW3a8p2w7Y1GNu36CKfJoe9xMLdRxdFaTo328YlUFdwVZFykWwGmaC0vzbJJi0Q7gjYljbnnri9hCxUiOeL7q2Bdc6qx9FkMCvD4RJVJm03qW3WvZv0WeTU4izweo5DvE8qG0/SmY2JPpXF4bJ1Ca1zKebwau4NoQHgTRkYz1rgOqjCBUAZO0BkobSdZWiqk3CdbkSVQnnR6xc20HlIGoLoAWy8xxeVMDwNaktrQFl7qxN84555ycw1NhDEqA0gdlqlEKEg6cNvNOYRtz5LSlQVl/ptf0gTFj9TA1LAXTkIw6LXORzzcDV1pZnRZc08CiisRcT5NbOM2n7BzIIjC2CWTq0cYW81zM8XSx2fpw7bAXgCCi2tFHFIsBK4Xd4JwUCW+q35hXJJpCeBINSM6OAG2dkyMYoaiSrqBSdhs7LOpYdUQHQNIewQUYjrAt7ShjBFX5rOL1WnAVG4yQdGYeGIOhTfxbMY/ib+Bt6/hoK8XiuTbzZynX7wOyYnvQSJ5SeLycF8EVhnq8XweieCaOyohg4rbezZBU8qiy1SL/pmMAqus8XFO+87rP9LF9QzplMkbZncCVViBUgIjcnlWiBcjqvF/KbyvF1K/r/Bn7IyIhgKFKDUvp0Pa8rVpYlZ92YxoGRpfws7Z0rSo3rqeAcm3ZVg8LexLk/KxnPSs/Lo23MNSTGJgIT2r0UQsMhnAf13HYkE5N3j+AQdQuXjB5+45u2A3snT5OjBiYjn3AFYBKHSpNkfJR5hCgGpqBRt3meQQq26rFWrpQv5cGXCmxdGos7qNmVXm20nfKzkONqTO4Q4qdffbZtfaD58IWa7Lv0rrE4Gagc8CYwBSPyGPIdax9bVMbcCmPhChbetJ2KgBjENzbpAHU1bvoIW0TuFyX3yz3jCcJbcom5yPv1G6Na47s4IMPPji91Pl8YSI0ouYxMCNaw8LLqiXz8U7ZkRrEYDeQq9YZhRSjmpJ2VVEOs3LzGPjhxMAFw4ERURfKBrxiYuAH14x7ETHAGQAM1D2qaMQsdnEaBTOSd53Ej7KLx1D7hAtpE6Y4j4WOyjVW0AJAIiIjaIVuHENSaiPRJIqpjNmZpLa/o8/dRp7eW0rJVWyw3wb1qaeemruw23q10nwQn3rHu1g1f+OZ8Cg2zWEVQdZWKqR1ivN0cLgm5tFfMaXhT3GPR9DAAcY2Cy7jvThqc9+YTnl4H2MKO07fDBmVEvV0pGIa6KQPAKFRypyCFgGaMqCk+XU9p+LbPctnlTCxlQFXEAKB2y5GjHfSo/cj8oB6V9xSzLMGSwTili3bT/MLkDnKz+DqYyemeVadt1ELq94tXkeHdDVC15W/GELMNRrEfVX3Yr3idwokUhl9JWUBEU8dZjI0gKL8uiOQCYMSMpd+jKPunb73ensL+xboPcSP8KI+kkxnhdOjbK4mJF3b+R/5xfq0IaYXymgzBLiofryz6tuVbkUpxeHU1+lUbB+wUuuoy5hbUb3dCNEYRZr4vS7giop0BUG8F0eDzWpbHLDMHgNiAGsbDaI+1Kzi9IL8q+y4qEvTsS+4AvjaENssdFFj0/e1YwgpFWBK93EPR8+sXtUmOi7T/XUFVxDKoOb4aLN3RbwTxwBonT0GZLETVVtvoXeE8sSEeTgaDJ4+6kxbcGkPQEQsIQ9l16mNYBIiQnjLZpVSaME+Cq8p2pOcY+zjHv26CseFAFcQsqukifccvZvaY2WeyeDiXUGcDnjGuIHGi8V+4CUEOJKtLvayClykgEgOCy/ZJ/IOIDvW5Zm23zmVLObn2u79UcwjfqOV/RXTOpljmyRTUKj5uFDgiuoacBF32OT5i3fiaFBEOJV3y1SoFMR9VSXl8HxZiwRw4UpXD6AopqK3MJ4PV36sPO4SBqUMtGKkc3CQcn0jSzAQ4AzpFBLT6oguUwLFdm/k3wsJrugQA1j0ulTmuIjnyo4pyKpUwVCfwsaiPuH4XaRFsWx5GvDFVJznapJ0xffT3wGoiO3rW29MhuorAsQRU5ikU0rp2c4XGlzRtNRx0eRej3fimIKszvZIB6x32TlDcu0qtTDq2XRM6zfL6oTIh7rHqxdR7GUSvqlOy3qfpK/a7XjINi0FuDSYRIiFfYzpukiMMgKFKsjearJH0gGY2kB9nRnq0xVc6qvsWD82i5pG3eMgcZQAqc1uUmV0XOZrTA2b1Xzxi19cvUnkITomQNLWvV4sM1TBWFvVtB9+DPLi4sVYcyW6gorX5EGsAxcwc2pE9EK6GJNHjrrWZXJbG8vsp1lV3iItl+F3RMMDFYlFWksrF6ExZGcYkH2dHlEPKmMEGXeZQ/Je6sxIg0bTWDjlRMxhrOeK2Dn3ypwa1nnJowuY5IUJlNlPXYEZtFmvY9FmTdfERZ1SGsa1quM3v/nN/GPs6NM3LVzgbt+GdH3PQI9ojT4Bq8oLTl9c2tFnkKtPmoBQ/gGukHSeadoaIM2n7Jx0Km4eStItov2EGaJDChZ2n5QyJ79Tb2u6mjtoUFxoGtfLjryfL37xi/MPHobU8twkucqoVXFt1qjwyLYINADjJp/1O711amGU3XQEXGFGBiUpNVTdmsptc59kCNUWDQM46inFlEMKlpTRNKnVbepQ90zEFAomQMMJXHXUqrgHZKK8edT6LnNJs06lQxozF5OpbcOiuoLLYI0o8iKYht6ZK21v3TnQkEAhjdUrpA6HC4CEGhzSZVbpXFefPveAzPqu/ffffzUDd/sQpes7uLxlLohpGcUQSykMeB68WM+FK+PI4upEa9QNqCpwhRqZrmeKawZrrO1y3hbIXWlV9rw6pHal3xgWlS2kT0iesaVOWf2W4drSuOL7EhMgYnkGIAy9CBAnj11jw9COgajOwdEjQiM4fbSHaheD1ZFEnCe3TyWk+lvVTUKrV3hE512noM2yH1ceXGkHURmLTouyzTXTd2Y9N3jZIgYrqTdLZMasdQlGEJK3KCFJXstDZolQmbWOq/T+hgJXdJwBT6WLsCeT0n2/uxV5Nh2r1MKm9/reLwJJe0OKhqq5UddZ9aVp1/c2JLhSIqVAI1lMtPaZuE3zLDsfE1wTkMoovv7XNjy40i4AtGLIUYQKzcrlhwLXBKS0xxb7fAJXTf+wSdJ5JQ4RYLMHBE9ZFy9ZV3CFraZ8m7lwNgB+6p1Uh1lBX9P86daMFJjA1YGAwMY9HQ6BGOz2VmTHSDxrUtHjVwRXgMezMW8U3sbUPgoXPyB1XeuVV2T6t24UmMA1I+mpaRGZwM0OIFLqjvfbx61f8YpXrJUWzgUXihOvE4jWyLTUJxO45tR9Rck1p2KnYtaRAhdax7KnoicKrDQFJnCtdPdOjVtPCkzgWk/qT2WvNAUuvNKtW4DGiRw/77zz8poIIo5ksnpKq02ByaExcv9yZGzatCmP0N9jjz3y0k455ZR8BfQEsJGJv87ZT+AauQOOOOKI7LDDDrtAKXvttVf+sYgLXJx+rBwFJnCN3KWWo5gAjmSS2f72k9QKiqzucXJojNy3wpMOOuigtVJ8MGIC1ho5Vvpkklxz6F6OjD333DPbcsst8w/0TeCaA9EXoIjJWziHTgCmfffdNw+ynYA1B4IvSBGT5JpTR9icUtpqq63mVOJUzHpTYALXevfAVP7KUmByaKxs104NW28KTOAatQfOz879zKHZtltskX+IwYRy+rftIZ/Jzh21/Cnz9aTA5NAYlfr/zn57+s+ys+78muzHH3tkdr2JlY1K7UXLfOruMXvk/NOzk95xUnbV3bbLrjJRekxKL2TeU5eP2S1/OzP78Xe3zR6296bsMmOWM+W9kBSYwDVat5yfnfv1T2VvOuva2Y5Xv9RopUwZLy4FJnCN1jf/s7euukO23VUuOlopU8aLS4EJXKP1zd+yX//4F1l21v/J7nDZLS/gJeQxnDyFoxF+YTKevIVjdcW5p2b/901nZnd+zQ+zjz1yp2ziYmMRenHznfp8pL45/7enZ98+a8/sAXtuNwFrJBoverYTuEbpoX9mPzvp49knJntrFOouS6YTuEbpqf9vb131YXfMdr/MROJRSLwEmU49P0Yn/c/euuGO22aTE34MAi9HnlNU/HL001TLJaTAJLmWsNOmKi8HBSZwLUc/TbVcQgpM4FrCTpuqvBwUmMC1HP001XIJKTCBawk7baryclDg/wEGB61VuUQH8AAAAABJRU5ErkJggg=="></em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>flow is laminar/non-turbulent<br><em><strong>OR</strong></em><br>Bernoulli’s equation holds<br><em><strong>OR</strong></em><br>pressure is uniform on each hemisphere<br><em><strong>OR</strong></em><br>diameter of ball can be ignored /<em>ρ</em>gz = constant</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph below shows the displacement <em>y</em> of an oscillating system as a function of time <em>t</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by damping.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the <em>Q</em> factor for the system.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The <em>Q</em> factor of the system increases. State and explain the change to the graph.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the loss of energy in an oscillating system</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Q = 2\pi \frac{{{{16}^2}}}{{{{16}^2} - {{10.3}^2}}} \approx 11">
<mi>Q</mi>
<mo>=</mo>
<mn>2</mn>
<mi>π</mi>
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mn>16</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mn>16</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mn>10.3</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>≈</mo>
<mn>11</mn>
</math></span></p>
<p> </p>
<p><em>Accept calculation based on any two correct values giving answer from interval 10 to 13.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the amplitude decreases at a slower rate</p>
<p>a higher <em>Q</em> factor would mean that less energy is lost per cycle</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A solid cube of side 0.15 m has an average density of 210 kg m<sup>–3</sup>.</p>
<p>(i) Calculate the weight of the cube.</p>
<p>(ii) The cube is placed in gasoline of density 720 kg m<sup>–3</sup>. Calculate the proportion of the volume of the cube that is above the surface of the gasoline.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Water flows through a constricted pipe. Vertical tubes A and B, open to the air, are located along the pipe.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Describe why tube B has a lower water level than tube A.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>i<br><em>F</em><sub>weight </sub>= «<em>ρgV</em><sub>cube </sub>= 210×9.81×0.15<sup>3 </sup>=» 6.95«N»<br><br></p>
<p>ii<br><em>F</em><sub>buoyancy </sub>= 6.95 = <em>ρgV</em> gives <em>V </em>= 9.8×10<sup>−4</sup></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{9.8 \times {{10}^{ - 4}}}}{{{{\left( {0.15} \right)}^3}}}">
<mfrac>
<mrow>
<mn>9.8</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.15</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span>=0.29 so 0.71 <em><strong>or</strong></em> 71% of the cube is above the gasoline</p>
<p><em>Award<strong> [2]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«from continuity equation» <em>v</em> is greater at B<br><em><strong>OR<br></strong></em>area at B is smaller thus «from continuity equation» velocity at B is greater</p>
<p>increase in speed leads to reduction in pressure «through Bernoulli effect»</p>
<p>pressure related to height of column<br><em><strong>OR<br></strong>p=<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\rho ">
<mi>ρ</mi>
</math></span>gh </em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>An air bubble has a radius of 0.25 mm and is travelling upwards at its terminal speed in a liquid of viscosity 1.0 × 10<sup>–3</sup> Pa s.</p>
<p>The density of air is 1.2 kg m<sup>–3</sup> and the density of the liquid is 1200 kg m<sup>–3</sup>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain the origin of the buoyancy force on the air bubble.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>With reference to the ratio of weight to buoyancy force, show that the weight of the air bubble can be neglected in this situation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the terminal speed.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>ALTERNATIVE 1</strong></p>
<p>pressure in a liquid increases with depth</p>
<p>so pressure at bottom of bubble greater than pressure at top</p>
<p><strong>ALTERNATIVE 2</strong></p>
<p>weight of liquid displaced</p>
<p>greater than weight of bubble</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{weight}}}}{{{\text{bouyancy}}}}\left( { = \frac{{V{\rho _a}g}}{{V{\rho _l}g}} = \frac{{{\rho _a}}}{{{\rho _l}}} = \frac{{1.2}}{{1200}}} \right) = {10^{ - 3}}">
<mfrac>
<mrow>
<mrow>
<mtext>weight</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>bouyancy</mtext>
</mrow>
</mrow>
</mfrac>
<mrow>
<mo>(</mo>
<mrow>
<mo>=</mo>
<mfrac>
<mrow>
<mi>V</mi>
<mrow>
<msub>
<mi>ρ</mi>
<mi>a</mi>
</msub>
</mrow>
<mi>g</mi>
</mrow>
<mrow>
<mi>V</mi>
<mrow>
<msub>
<mi>ρ</mi>
<mi>l</mi>
</msub>
</mrow>
<mi>g</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>ρ</mi>
<mi>a</mi>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>ρ</mi>
<mi>l</mi>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>1.2</mn>
</mrow>
<mrow>
<mn>1200</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</math></span></p>
<p>since the ratio is very small, the weight can be neglected</p>
<p> </p>
<p><em>Award <strong>[1 max]</strong> if only mass of the bubble is calculated and identified as negligible to mass of liquid displaced.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>evidence of equating the buoyancy and the viscous force «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\rho _l}\frac{4}{3}\pi {r^3}g = 6\pi \eta r{v_t}">
<mrow>
<msub>
<mi>ρ</mi>
<mi>l</mi>
</msub>
</mrow>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
<mrow>
<msup>
<mi>r</mi>
<mn>3</mn>
</msup>
</mrow>
<mi>g</mi>
<mo>=</mo>
<mn>6</mn>
<mi>π</mi>
<mi>η</mi>
<mi>r</mi>
<mrow>
<msub>
<mi>v</mi>
<mi>t</mi>
</msub>
</mrow>
</math></span>»</p>
<p><em>v</em><sub>t</sub> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{2}{9}\frac{{1200 \times 9.81}}{{1 \times {{10}^{ - 3}}}}{\left( {0.25 \times {{10}^{ - 3}}} \right)^2} = ">
<mfrac>
<mn>2</mn>
<mn>9</mn>
</mfrac>
<mfrac>
<mrow>
<mn>1200</mn>
<mo>×</mo>
<mn>9.81</mn>
</mrow>
<mrow>
<mn>1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.25</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
</math></span>» 0.16 «ms<sup>–1</sup>»</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A sphere is dropped into a container of oil.<br>The following data are available.</p>
<p>Density of oil<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>915</mn><mo> </mo><mi>kg</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math><br>Viscosity of oil<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>37</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo> </mo><mi>Pas</mi></math><br>Volume of sphere<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>7</mn><mo>.</mo><mn>24</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo> </mo><msup><mi mathvariant="normal">m</mi><mn>3</mn></msup></math><br>Mass of sphere<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>12</mn><mo>.</mo><mn>6</mn><mo> </mo><mi mathvariant="normal">g</mi></math></p>
</div>
<div class="specification">
<p>The sphere is now suspended from a spring so that the sphere is below the surface of the oil.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>two</strong> properties of an ideal fluid.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the terminal velocity of the sphere.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the force exerted by the spring on the sphere when the sphere is at rest.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The sphere oscillates vertically within the oil at the natural frequency of the sphere-spring system. The energy is reduced in each cycle by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mo>%</mo></math>. Calculate the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Q</mi></math> factor for this system.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline the effect on <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Q</mi></math> of changing the oil to one with greater viscosity.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c(iii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">incompressible </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">non-viscous </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">laminar/streamlined flow </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>radius of sphere<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>012</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo>»</mo></math> ✓</p>
<p> </p>
<p>weight of sphere<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>6</mn><mi>π</mi><mi>η</mi><mi>r</mi><mi>v</mi><mo>+</mo><mi>ρ</mi><mi>V</mi><mi>g</mi></math></p>
<p><em><strong>OR</strong></em></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfrac><mrow><mfenced><mrow><mn>1</mn><mo>.</mo><mn>26</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo>-</mo><mn>915</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>24</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></mrow></mfenced><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></mrow><mrow><mn>6</mn><mi mathvariant="normal">π</mi><mo>×</mo><mn>37</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>×</mo><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup></mrow></mfrac></math> ✓</p>
<p> </p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>84</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>–</mo><mn>1</mn></mrow></msup><mo>»</mo><mo> </mo></math> ✓</p>
<p> </p>
<p><em><span class="fontstyle0">Accept use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo mathvariant="italic">=</mo><mn mathvariant="italic">10</mn></math> leading to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo mathvariant="italic">=</mo><mn mathvariant="italic">7</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">0</mn><mo mathvariant="italic"> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>–</mo><mn>1</mn></mrow></msup><mo>»</mo></math></span></em></p>
<p><em><span class="fontstyle0">Allow implicit calculation of radius for MP1</span></em></p>
<p><em><span class="fontstyle0">Do not allow ECF for MP3 if buoyant force omitted.</span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>m</mi><mi>g</mi><mo>-</mo><mi>ρ</mi><mi>V</mi><mi>g</mi></math></p>
<p><em><strong>OR</strong></em></p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mfenced><mrow><mn>0</mn><mo>.</mo><mn>0126</mn><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mn>915</mn><mo>×</mo><mn>7</mn><mo>.</mo><mn>24</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>×</mo><mn>9</mn><mo>.</mo><mn>81</mn></mrow></mfenced></math> </strong></em>✓</p>
<p> </p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mn>5</mn><mo>.</mo><mn>86</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>2</mn></mrow></msup><mo> </mo><mo>«</mo><mi mathvariant="normal">N</mi><mo>»</mo></math> ✓</span></p>
<p> </p>
<p><em><span class="fontstyle0">Accept use of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo mathvariant="italic">=</mo><mn mathvariant="italic">10</mn></math> leading to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mn mathvariant="italic">6</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">0</mn><mo mathvariant="italic">×</mo><msup><mn mathvariant="italic">10</mn><mrow><mo mathvariant="italic">-</mo><mn mathvariant="italic">2</mn></mrow></msup><mo mathvariant="italic"> </mo><mi>N</mi></math></span></em></p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mo>«</mo><mn>2</mn><mi mathvariant="normal">π</mi><mo>×</mo><mfrac><mrow><mi>energy</mi><mo> </mo><mi>stored</mi></mrow><mrow><mi>energy</mi><mo> </mo><mi>lost</mi></mrow></mfrac><mo>=</mo><mn>2</mn><mi mathvariant="normal">π</mi><mo>×</mo><mfrac><mn>100</mn><mn>10</mn></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>63</mn></math> ✓</span></p>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">drag force increases </span><em><span class="fontstyle2"><strong>OR</strong> </span></em><span class="fontstyle0">damping increases </span><em><span class="fontstyle2"><strong>OR</strong> </span></em><span class="fontstyle0">more energy lost per cycle </span><span class="fontstyle3">✓</span></p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Q</mi></math> will decrease </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">c(iii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The properties of fluids proved to be a very well-studied topic.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Only those candidates who forgot to include the buoyant force missed marks here.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Continuing from b, most candidates scored full marks.</p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The calculation needed to obtain the Q-factor proved to be known by many.</p>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very well answered.</p>
<div class="question_part_label">c(iii).</div>
</div>
<br><hr><br><div class="specification">
<p>The graph below represents the variation with time <em>t </em>of the horizontal displacement <em>x </em>of a mass attached to a vertical spring.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-13_om_15.49.15.png" alt="M18/4/PHYSI/HP3/ENG/TZ1/11"></p>
</div>
<div class="specification">
<p>The total mass for the oscillating system is 30 kg. For this system</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Describe the motion of the spring-mass system.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>determine the initial energy.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>calculate the Q at the start of the motion.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>damped oscillation / <em>OWTTE</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>E</em> <strong>«</strong>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> × 30 × <em>π</em><sup>2</sup> × 0.8<sup>2</sup><strong>»</strong> = 95 <strong>«</strong>J<strong>»</strong></p>
<p> </p>
<p><em>Allow initial amplitude between 0.77 to 0.80, giving range between: 88 to 95 J.</em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Δ<em>E</em> = 95 – <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> × 30 × <em>π</em><sup>2</sup> × 0.72<sup>2</sup> = 18 <strong>«</strong>J<strong>»</strong></p>
<p><em>Q = </em><strong>«</strong> 2<em>π</em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{95}}{{18}}">
<mfrac>
<mrow>
<mn>95</mn>
</mrow>
<mrow>
<mn>18</mn>
</mrow>
</mfrac>
</math></span> =<strong>»</strong> 33</p>
<p> </p>
<p><em>Accept values between 0.70 and 0.73, giving a range of</em> Δ<em>E between 22 and 9, giving Q between 27 and 61.</em></p>
<p><em>Watch for ECF from (b)(i).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Two tubes, A and B, are inserted into a fluid flowing through a horizontal pipe of diameter 0.50 m. The openings X and Y of the tubes are at the exact centre of the pipe. The liquid rises to a height of 0.10 m in tube A and 0.32 m in tube B. The density of the fluid = 1.0 × 10<sup>3</sup> kg m<sup>–3</sup>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-14_om_09.34.50.png" alt="M18/4/PHYSI/HP3/ENG/TZ2/10"></p>
</div>
<div class="specification">
<p>The viscosity of water is 8.9 × 10<sup>–4</sup> Pa s.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the velocity of the fluid at X is about 2 ms<sup>–1</sup>, assuming that the flow is laminar.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate the Reynolds number for the fluid in your answer to (a).</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline whether your answer to (a) is valid.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}\rho v_{\text{X}}^2 = {p_{\text{Y}}} - {p_{\text{X}}} = \rho g\Delta h">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>ρ</mi>
<msubsup>
<mi>v</mi>
<mrow>
<mtext>X</mtext>
</mrow>
<mn>2</mn>
</msubsup>
<mo>=</mo>
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>Y</mtext>
</mrow>
</msub>
</mrow>
<mo>−</mo>
<mrow>
<msub>
<mi>p</mi>
<mrow>
<mtext>X</mtext>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mi>ρ</mi>
<mi>g</mi>
<mi mathvariant="normal">Δ</mi>
<mi>h</mi>
</math></span></p>
<p><em>v</em><sub>X</sub> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2 \times 9.8 \times (0.32 - 0.10)} ">
<msqrt>
<mn>2</mn>
<mo>×</mo>
<mn>9.8</mn>
<mo>×</mo>
<mo stretchy="false">(</mo>
<mn>0.32</mn>
<mo>−</mo>
<mn>0.10</mn>
<mo stretchy="false">)</mo>
</msqrt>
</math></span></p>
<p><em>v</em><sub>x</sub> = 2.08 <strong>«</strong>ms<sup>–1</sup><strong>»</strong></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>R</em> = <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{vr\rho }}{\eta } = \frac{{2.1 \times 0.25 \times {{10}^3}}}{{8.9 \times {{10}^{ - 4}}}}">
<mfrac>
<mrow>
<mi>v</mi>
<mi>r</mi>
<mi>ρ</mi>
</mrow>
<mi>η</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>2.1</mn>
<mo>×</mo>
<mn>0.25</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>8.9</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span><strong>»</strong> 5.9 × 10<sup>5</sup></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>(<em>R > </em>1000) flow is not laminar, so assumption is invalid</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A driven system is lightly damped. The graph shows the variation with driving frequency <em>f</em> of the amplitude <em>A</em> of oscillation.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-09-26_om_11.02.12.png" alt="M17/4/PHYSI/HP3/ENG/TZ2/11"></p>
</div>
<div class="specification">
<p>A mass on a spring is forced to oscillate by connecting it to a sine wave vibrator. The graph shows the variation with time <em>t</em> of the resulting displacement <em>y</em> of the mass. The sine wave vibrator has the same frequency as the natural frequency of the spring–mass system.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the graph, sketch a curve to show the variation with driving frequency of the amplitude when the damping of the system <strong>increases</strong>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain the displacement of the sine wave vibrator at <em>t</em> = 8.0 s.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The vibrator is switched off and the spring continues to oscillate. The <em>Q</em> factor is 25.</p>
<p>Calculate the ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{\text{energy stored}}}}{{{\text{power loss}}}}">
<mfrac>
<mrow>
<mrow>
<mtext>energy stored</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>power loss</mtext>
</mrow>
</mrow>
</mfrac>
</math></span> for the oscillations of the spring–mass system.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>lower peak </p>
<p>identical behaviour to original curve at extremes </p>
<p>peak frequency shifted to the left</p>
<p><img src="data:image/png;base64,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"></p>
<p> </p>
<p><em>Award <strong>[0]</strong> if peak is higher.</em></p>
<p><em>For MP2 do not accept curves which cross.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>displacement of vibrator is 0</p>
<p>because phase difference is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\pi }{2}">
<mfrac>
<mi>π</mi>
<mn>2</mn>
</mfrac>
</math></span> <em><strong>or</strong></em> 90<sup>º</sup> <em><strong>or</strong></em> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{4}">
<mfrac>
<mn>1</mn>
<mn>4</mn>
</mfrac>
</math></span> period</p>
<p> </p>
<p><em>Do not penalize sign of phase difference.</em></p>
<p><em>Do not accept <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{\lambda }{4}">
<mfrac>
<mi>λ</mi>
<mn>4</mn>
</mfrac>
</math></span> for MP2</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>resonant <em>f</em> = 0.125 « Hz »</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{25}}{{\left( {2\pi \times 0.125} \right)}}">
<mfrac>
<mrow>
<mn>25</mn>
</mrow>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>2</mn>
<mi>π</mi>
<mo>×</mo>
<mn>0.125</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</math></span> = 32 «s»</p>
<p> </p>
<p><em>Watch for ECF from MP1 to MP2.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows a simplified model of a Galilean thermometer. The thermometer consists of a sealed glass cylinder that contains ethanol, together with glass spheres. The spheres are filled with different volumes of coloured water. The mass of the glass can be neglected as well as any expansion of the glass through the temperature range experienced. Spheres have tags to identify the temperature. The mass of the tags can be neglected in all calculations.</p>
<p style="text-align: center;"><img 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"></p>
<p>Each sphere has a radius of 3.0 cm and the spheres, due to the different volumes of water in them, are of varying densities. As the temperature of the ethanol changes the individual spheres rise or fall, depending on their densities, compared with that of the ethanol.</p>
</div>
<div class="specification">
<p>The graph shows the variation with temperature of the density of ethanol.</p>
<p style="text-align: center;"><img 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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the graph, determine the buoyancy force acting on a sphere when the ethanol is at a temperature of 25 °C.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>When the ethanol is at a temperature of 25 °C, the 25 °C sphere is just at equilibrium. This sphere contains water of density 1080 kg m<sup>–3</sup>. Calculate the percentage of the sphere volume filled by water.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The room temperature slightly increases from 25 °C, causing the buoyancy force to decrease. For this change in temperature, the ethanol density decreases from 785.20 kg m<sup>–3</sup> to 785.16 kg m<sup>–3</sup>. The average viscosity of ethanol over the temperature range covered by the thermometer is 0.0011 Pa s. Estimate the steady velocity at which the 25 °C sphere falls.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>density = 785 «kgm<sup>−3</sup>»</p>
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{3}\pi {\left( {0.03} \right)^3} \times 785 \times 9.8">
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.03</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>785</mn>
<mo>×</mo>
<mn>9.8</mn>
</math></span> =» 0.87 «N»</p>
<p><em>Accept answer in the range 784 to 786</em></p>
<p> </p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.87}}{{\frac{4}{3}\pi {{\left( {0.03} \right)}^3} \times 1080 \times 9.8}}">
<mfrac>
<mrow>
<mn>0.87</mn>
</mrow>
<mrow>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
<mrow>
<msup>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.03</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>1080</mn>
<mo>×</mo>
<mn>9.8</mn>
</mrow>
</mfrac>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.87}}{{1080 \times 1.13 \times {{10}^{ - 4}}}}">
<mfrac>
<mrow>
<mn>0.87</mn>
</mrow>
<mrow>
<mn>1080</mn>
<mo>×</mo>
<mn>1.13</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>4</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{785}}{{1080}}">
<mfrac>
<mrow>
<mn>785</mn>
</mrow>
<mrow>
<mn>1080</mn>
</mrow>
</mfrac>
</math></span></p>
<p>0.727 <em><strong>or</strong> </em>73%</p>
<p><em>Allow ECF from (a)(i)</em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of drag force to obtain <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\frac{4}{3}\pi }">
<mrow>
<mfrac>
<mn>4</mn>
<mn>3</mn>
</mfrac>
<mi>π</mi>
</mrow>
</math></span><em>r</em><sup>3</sup> x 0.04 x <em>g</em> = 6 x <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span> x 0.0011 x <em>r</em> x <em>v</em></p>
<p><em>v = </em>0.071 «ms<sup>–1</sup>»</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The water supply for a hydroelectric plant is a reservoir with a large surface area. An outlet pipe takes the water to a turbine.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-13_om_15.42.28.png" alt="M18/4/PHYSI/HP3/ENG/TZ1/10"></p>
</div>
<div class="specification">
<p>The following data are available:</p>
<p><span class="mjpage mjpage__block"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block" alttext="\begin{array}{*{20}{l}} {{\text{density of water}}}&{ = 1.00 \times {{10}^3}{\text{ kg }}{{\text{m}}^{ - 3}}} \\ {{\text{viscosity of water}}}&{ = 1.31 \times {{10}^{ - 3}}{\text{ Pa s}}} \\ {{\text{diameter of the outlet pipe}}}&{ = 0.600{\text{ m}}} \\ {{\text{velocity of water at outlet pipe}}}&{ = 59.4{\text{ m}}{{\text{s}}^{ - 1}}} \end{array}">
<mtable columnalign="left" rowspacing="4pt" columnspacing="1em">
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>density of water</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mn>1.00</mn>
<mo>×<!-- × --></mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
<mrow>
<mtext> kg </mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>m</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>viscosity of water</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mn>1.31</mn>
<mo>×<!-- × --></mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
<mrow>
<mtext> Pa s</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>diameter of the outlet pipe</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mn>0.600</mn>
<mrow>
<mtext> m</mtext>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mtext>velocity of water at outlet pipe</mtext>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>=</mo>
<mn>59.4</mn>
<mrow>
<mtext> m</mtext>
</mrow>
<mrow>
<msup>
<mrow>
<mtext>s</mtext>
</mrow>
<mrow>
<mo>−<!-- − --></mo>
<mn>1</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</math></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the difference in terms of the velocity of the water between laminar and turbulent flow.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The water level is a height <em>H </em>above the turbine. Assume that the flow is laminar in the outlet pipe.</p>
<p>Show, using the Bernouilli equation, that the speed of the water as it enters the turbine is given by <em>v</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2gH} ">
<msqrt>
<mn>2</mn>
<mi>g</mi>
<mi>H</mi>
</msqrt>
</math></span>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the Reynolds number for the water flow.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline whether it is reasonable to assume that flow is laminar in this situation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>in laminar flow, the velocity of the fluid is constant <strong>«</strong>at any point in the fluid<strong>» «</strong>whereas it is not constant for turbulent flow<strong>»</strong></p>
<p> </p>
<p><em>Accept any similarly correct answers.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>P<sub>S</sub></em> = <em>P<sub>T</sub></em> <strong>«</strong>as both are exposed to atmospheric pressure<strong>»</strong></p>
<p>then <em>V<sub>T</sub></em> = 0 <strong>«</strong>if the surface area ofthe reservoir is large<strong>»</strong></p>
<p><strong>«</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}\rho v_s^2">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>ρ</mi>
<msubsup>
<mi>v</mi>
<mi>s</mi>
<mn>2</mn>
</msubsup>
</math></span> + <em>ρgz<sub>S</sub></em> = <em>ρgz<sub>T</sub></em><strong>»</strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}v_S^2">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<msubsup>
<mi>v</mi>
<mi>S</mi>
<mn>2</mn>
</msubsup>
</math></span> = <em>g</em>(<em>z<sub>T</sub></em> – <em>z<sub>S</sub></em>) = <em>gH</em></p>
<p>and so <em>v<sub>S</sub></em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2gH} ">
<msqrt>
<mn>2</mn>
<mi>g</mi>
<mi>H</mi>
</msqrt>
</math></span></p>
<p> </p>
<p><em>MP1 and MP2 may be implied by the correct substitution showing line 3 in the mark scheme.</em></p>
<p><em>Do not accept simple use of</em> <em>v</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {2{\text{as}}} ">
<msqrt>
<mn>2</mn>
<mrow>
<mtext>as</mtext>
</mrow>
</msqrt>
</math></span><em>.</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>R</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{59.4 \times 0.6 \times 1 \times {{10}^3}}}{{1.31 \times {{10}^{ - 3}}}}">
<mfrac>
<mrow>
<mn>59.4</mn>
<mo>×</mo>
<mn>0.6</mn>
<mo>×</mo>
<mn>1</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>3</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.31</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> = 2.72 × 10<sup>7</sup></p>
<p> </p>
<p><em>Accept use of radius 0.3 m giving value 1.36 × 10</em><sup><em>7</em></sup><em>.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>as <em>R</em> > 1000 it is not reasonable to assume laminar flow</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A railway track passes over a bridge that has a span of 20 m.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">The bridge is subject to a periodic force as a train crosses, this is caused by the weight of the train acting through the wheels as they pass the centre of the bridge.</span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">The wheels of the train are separated by 25 m.</span></span></p>
</div>
<div class="specification">
<p><span style="display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;">The graph shows the variation of the amplitude of vibration </span><em style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: italic; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;">A</em><span style="display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"> of the bridge with driving frequency </span><em style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: italic; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;">f</em><sub style="color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 11.6px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;">D</sub><span style="display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;">, when the damping of the bridge system is small.</span></p>
<p><span style="display: inline !important; float: none; background-color: #ffffff; color: #000000; font-family: Verdana,Arial,Helvetica,sans-serif; font-size: 14px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;"><img 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"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Show that, when the speed of the train is 10 m s-1, the frequency of the periodic force is 0.4 Hz.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Outline, with reference to the curve, why it is unsafe to drive a train across the bridge at 30 m s<sup>-1</sup> for this amount of damping.</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The damping of the bridge system can be varied. Draw, on the graph, a second curve when the damping is larger.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">time period </span></p>
<p><em><span style="background-color:#ffffff;">T = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{25}{10}">
<mfrac>
<mn>25</mn>
<mn>10</mn>
</mfrac>
</math></span>» </span></em><span style="background-color:#ffffff;">= 2.5 s</span><em><span style="background-color:#ffffff;"> <strong>AND</strong> f = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{T}">
<mfrac>
<mn>1</mn>
<mi>T</mi>
</mfrac>
</math></span></span></em></p>
<p><strong><em><span style="background-color:#ffffff;">OR</span></em></strong></p>
<p><em><span style="background-color:#ffffff;">evidence of f = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{10}{25}">
<mfrac>
<mn>10</mn>
<mn>25</mn>
</mfrac>
</math></span>✔</span></em></p>
<p><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Answer 0.4 Hz is given, check correct working is shown.</span></span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">30 m s<sup>–1</sup> corresponds to <em>f</em> = 1.2 Hz ✔<br></span></p>
<p><span style="background-color:#ffffff;">the amplitude of vibration is a maximum for this speed<br></span></p>
<p><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p><span style="background-color:#ffffff;">corresponds to the resonant frequency ✔</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">similar shape with lower amplitude ✔<br></span></p>
<p><span style="background-color:#ffffff;">maximum shifted slightly to left of the original curve ✔</span></p>
<p><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Amplitude must be lower than the original, but allow the amplitude to be equal at the extremes.</span></span></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The question was correctly answered by almost all candidates.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The answers to this question were generally well presented and a correct argument was presented by almost all candidates. Resonance was often correctly referred to.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A correct curve, with lower amplitude and shifted left, was drawn by most candidates.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A mass is attached to a vertical spring. The other end of the spring is attached to the driver of an oscillator.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The mass is performing very lightly damped harmonic oscillations. The frequency of the driver is <strong>higher</strong> than the natural frequency of the system. At one instant the driver is moving downwards.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain the direction of motion of the mass at this instant.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The oscillator is switched off. The system has a <em>Q</em> factor of 22. The initial amplitude is 10 cm. Determine the amplitude after <strong>one</strong> complete period of oscillation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>because the mass and the driver are out of phase «by <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\pi ">
<mi>π</mi>
</math></span>» ✔</p>
<p>so upwards ✔</p>
<p> </p>
<p><em>Justification needed for MP2</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Q = 2\pi \frac{{A_0^2}}{{A_0^2 - A_1^2}}">
<mi>Q</mi>
<mo>=</mo>
<mn>2</mn>
<mi>π</mi>
<mfrac>
<mrow>
<msubsup>
<mi>A</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<msubsup>
<mi>A</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
<mo>−</mo>
<msubsup>
<mi>A</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
</math></span>» ⇒ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{A_1^2}}{{A_0^2}} = 1 - \frac{{2\pi }}{Q}">
<mfrac>
<mrow>
<msubsup>
<mi>A</mi>
<mn>1</mn>
<mn>2</mn>
</msubsup>
</mrow>
<mrow>
<msubsup>
<mi>A</mi>
<mn>0</mn>
<mn>2</mn>
</msubsup>
</mrow>
</mfrac>
<mo>=</mo>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mi>Q</mi>
</mfrac>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{A_1}}}{{{A_0}}} = ">
<mfrac>
<mrow>
<mrow>
<msub>
<mi>A</mi>
<mn>1</mn>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>A</mi>
<mn>0</mn>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span> «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\sqrt {1 - \frac{{2\pi }}{{22}}} ">
<msqrt>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mrow>
<mn>22</mn>
</mrow>
</mfrac>
</msqrt>
</math></span> =» <em>A</em><sub>1</sub> = 8.5 «cm»</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p>driver amplitude is constant ✔</p>
<p>so mass amplitude is unchanged at 10 cm ✔</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A pendulum bob is displaced until its centre is 30 mm above its rest position and then released. The motion of the pendulum is lightly damped.</span></p>
<p><span style="background-color: #ffffff;"><img style="margin-right: auto; margin-left: auto; display: block;" 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" width="243" height="244"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Describe what is meant by damped motion.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">After one complete oscillation, the height of the pendulum bob above the rest position has decreased to 28 mm. Calculate the <em>Q</em> factor.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">The point of suspension now vibrates horizontally with small amplitude and frequency 0.80 Hz, which is the natural frequency of the pendulum. The amount of damping is unchanged.</span></p>
<p><span style="background-color: #ffffff;"><img style="margin-right:auto;margin-left:auto;display: block;" src="data:image/png;base64,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" width="192" height="277"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">When the pendulum oscillates with a constant amplitude the energy stored in the system is 20 mJ. Calculate the average power, in W, delivered to the pendulum by the driving force.</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">a situation in which a resistive force opposes the motion<br><em><strong>OR</strong></em><br>amplitude/energy decreases with time ✔</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi><mo>=</mo><mn>2</mn><mi mathvariant="normal">π</mi><mo>×</mo><mfrac><mn>30</mn><mrow><mn>30</mn><mo>-</mo><mn>28</mn></mrow></mfrac><mo>=</mo><mn>94</mn><mo>.</mo><mn>25</mn><mo>≈</mo><mn>94</mn></math> ✔</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>94</mn><mo>=</mo><mn>2</mn><mi mathvariant="normal">π</mi><mo>×</mo><mn>0</mn><mo>.</mo><mn>80</mn><mo>×</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>020</mn></mrow><mrow><mi>power</mi><mo> </mo><mi>loss</mi></mrow></mfrac></math><span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</span></p>
<p>power added <span style="background-color: #ffffff;">= <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>1</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup></math> «W» ✔</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Gasoline of density 720 kg m<sup>–3</sup> flows in a pipe of constant diameter.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>one</strong> condition that must be satisfied for the Bernoulli equation</p>
<p style="text-align:center;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> <em>ρv</em><sup>2</sup> + <em>ρgz</em> + <em>ρ</em> = constant</p>
<p style="text-align:left;">to apply</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the speed of the gasoline at X is the same as that at Y.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the difference in pressure between X and Y.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The diameter at Y is made smaller than that at X. Explain why the pressure difference between X and Y will increase.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>flow must be laminar/steady/not turbulent ✔</p>
<p>fluid must be incompressible/have constant density ✔</p>
<p>fluid must be non viscous ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«continuity equation says» <em>Av</em> = constant «and the areas are the same» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Bernoulli: «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span> <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\rho v_x^2">
<mi>ρ</mi>
<msubsup>
<mi>v</mi>
<mi>x</mi>
<mn>2</mn>
</msubsup>
</math></span></span> + 0 + <em>P<span style="font-size:11.6667px;"><sub>x</sub></span></em> =<em> </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span><em> </em><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\rho v_y^2">
<mi>ρ</mi>
<msubsup>
<mi>v</mi>
<mi>y</mi>
<mn>2</mn>
</msubsup>
</math></span></span> +<em> pgH + P<sub>y</sub> » gives P<sub>x</sub> − P<sub>y</sub> = pgH </em>✔</p>
<p><em>P</em><sub>x</sub> − <em>P</em><sub>y </sub>= 720 × 9.81 × 1.2 = 8.5 «kPa» ✔</p>
<p><em>Award <strong>[2]</strong> for bald correct answer.</em></p>
<p><em>Watch for POT mistakes.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the fluid speed at Y will be greater «than that at X» ✔</p>
<p>reducing the pressure at Y<br><em><strong>OR</strong></em><br>the formula used to show that the difference is increased ✔</p>
<div class="question_part_label">b.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Gasoline in a pipe. In a), most of the candidates well noted that for the Bernoulli equation, the fluid must be” non-viscous”, some noted, “laminar” and a few, “incompressible”. Some students stated vaguer and less concrete responses such as “the fluid must be ideal”.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In b) most candidates well noted and understood the application of the continuity equation.</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>In b) most candidates well noted and understood the application of the continuity equation and successfully went on to correctly calculate the pressure difference.</p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Sub-question iii) well discriminated between the better and weaker candidates. As weaker candidates often wrote that “lower diameter means higher pressure” without a direct reference to the greater speed at Y implying reduced pressure.</p>
<div class="question_part_label">b.iii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A solid sphere is released from rest <strong>below</strong> the surface of a fluid and begins to fall.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Draw and label the forces acting on the sphere at the <strong>instant</strong> when it is released.</span></p>
<p><span style="background-color:#ffffff;"><img src="data:image/png;base64,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"></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Explain why the sphere will reach a terminal speed.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">The weight of the sphere is 6.16 mN and the radius is 5.00 × 10<sup>-3</sup> m. For a fluid of density 8.50 × 10<sup>2</sup> kg m<sup>-3</sup>, the terminal speed is found to be 0.280 m s<sup>-1</sup>. Calculate the viscosity of the fluid.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img 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" width="303" height="124"></p>
<p><em><span style="background-color:#ffffff;">Both forces must be suitably labeled. </span></em></p>
<p><em><span style="background-color:#ffffff;">Do not accept just ‘gravity’ </span></em></p>
<p><em><span style="background-color:#ffffff;">Award <strong>[0]</strong> if a third force is shown.</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">«as the ball falls» there is a drag force ✔<br></span></p>
<p><span style="background-color:#ffffff;">when drag force+buoyant force/upthrust =«-» weight<br></span></p>
<p><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p><span style="background-color:#ffffff;">When net/resultant force =0 ✔<br></span></p>
<p><span style="background-color:#ffffff;">«terminal speed occurs»</span></p>
<p><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">OWTTE<br></span></span></em></p>
<p><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Terminal speed is mentioned in the question, so no additional marks for reference to it.</span></span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color:#ffffff;">any evidence (numerical or algebraic) of a realisation that</span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="6\pi \eta rv + \rho gV = W">
<mn>6</mn>
<mi>π</mi>
<mi>η</mi>
<mi>r</mi>
<mi>v</mi>
<mo>+</mo>
<mi>ρ</mi>
<mi>g</mi>
<mi>V</mi>
<mo>=</mo>
<mi>W</mi>
</math></span> ✔</span></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\eta = \frac{{6.16 \times {{10}^{ - 3}} - 4.366 \times {{10}^{ - 3}}}}{{6\pi \times 0.005 \times 0.280}}">
<mi>η</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mn>6.16</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
<mo>−</mo>
<mn>4.366</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>3</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>6</mn>
<mi>π</mi>
<mo>×</mo>
<mn>0.005</mn>
<mo>×</mo>
<mn>0.280</mn>
</mrow>
</mfrac>
</math></span>»</span></span></p>
<p><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\eta = 0.0680">
<mi>η</mi>
<mo>=</mo>
<mn>0.0680</mn>
</math></span>«Pas»<span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></span></span></p>
<p> </p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The question was generally well answered but many candidates did not realise that the drag force would only be present when the ball starts moving.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates could explain correctly that the drag force would increase as the speed increases and that the weight would be balanced by the buoyant force and the drag force.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>When the condition for forces in equilibrium was correctly formed, many candidates managed to obtain the correct answer. The working was often poorly presented making it difficult to mark or award marks for the process.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The graph shows the variation with time<em> t</em> of the total energy <em>E</em> of a damped oscillating system.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Q factor for the system is 25. Determine the period of oscillation for this system.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Another system has the same initial total energy and period as that in (a) but its <em>Q</em> factor is greater than 25. Without any calculations, draw on the graph, the variation with time of the total energy of this system.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><span style="background-color:#ffffff;">«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Q = 2\pi \frac{{{E_0}}}{{{E_0} - {E_1}}} » \Rightarrow {E_1} = \left( {1 - \frac{{2\pi }}{Q}} \right){E_0}">
<mi>Q</mi>
<mo>=</mo>
<mn>2</mn>
<mi>π</mi>
<mfrac>
<mrow>
<mrow>
<msub>
<mi>E</mi>
<mn>0</mn>
</msub>
</mrow>
</mrow>
<mrow>
<mrow>
<msub>
<mi>E</mi>
<mn>0</mn>
</msub>
</mrow>
<mo>−</mo>
<mrow>
<msub>
<mi>E</mi>
<mn>1</mn>
</msub>
</mrow>
</mrow>
</mfrac>
<mrow>
<mo>»</mo>
</mrow>
<mo stretchy="false">⇒</mo>
<mrow>
<msub>
<mi>E</mi>
<mn>1</mn>
</msub>
</mrow>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mi>Q</mi>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<msub>
<mi>E</mi>
<mn>0</mn>
</msub>
</mrow>
</math></span> <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{E_1} «= \left( {1 - \frac{{2\pi }}{{25}}} \right) \times 12» = 9.0">
<mrow>
<msub>
<mi>E</mi>
<mn>1</mn>
</msub>
</mrow>
<mrow>
<mo>«</mo>
</mrow>
<mo>=</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mn>2</mn>
<mi>π</mi>
</mrow>
<mrow>
<mn>25</mn>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>×</mo>
<mn>12</mn>
<mrow>
<mo>»</mo>
</mrow>
<mo>=</mo>
<mn>9.0</mn>
</math></span>«mJ» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span></p>
<p>reading off the graph, period is 0.48 «s» ✔</p>
<p><em>Allow correct use of any value of E<sub>0</sub>, not only at the time = 0.</em></p>
<p><em>Allow answer from interval 0.42−0.55 s</em></p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p>use of <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="Q = 2\pi f\frac{{{\text{energy stored}}}}{{{\text{power loss}}}}">
<mi>Q</mi>
<mo>=</mo>
<mn>2</mn>
<mi>π</mi>
<mi>f</mi>
<mfrac>
<mrow>
<mrow>
<mtext>energy stored</mtext>
</mrow>
</mrow>
<mrow>
<mrow>
<mtext>power loss</mtext>
</mrow>
</mrow>
</mfrac>
</math></span></span> ✔</p>
<p>energy stored = 12 «mJ» <em><strong>AND</strong></em> power loss = 5.6 «mJ/s»✔</p>
<p>«<em>f</em> = 1.86 s so» period is 0.54 «s» ✔</p>
<p>Allow answer from interval 0.42−0.55 s.</p>
<p><em>Award <strong>[3]</strong> for bald correct answer.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>similar shape graph starting at 12 mJ and above the original ✔</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Q factor. Most of the candidates attempted to find the period of the damped system by using the correct formula.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many thus went on to establish the correct period within the range given. Some candidates made POT errors not recognizing or identifying the unit used in this question.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A horizontal pipe is inserted into the cylindrical tube so that its centre is at a depth of 5.0 m from the surface of the water. The diameter D of the pipe is half that of the tube.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>When the pipe is opened, water exits the pipe with speed <em>u</em> and the surface of the water in the tube moves downwards with speed <em>v</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An ice cube floats in water that is contained in a tube.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The ice cube melts.</p>
<p>Suggest what happens to the level of the water in the tube.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why <em>u</em> = 4<em>v</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The density of water is 1000 kg m<sup>–3</sup>. Calculate <em>u</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>ice displaces its own weight of water / OWTTE</p>
<p><em><strong>OR</strong></em></p>
<p>melted ice volume equals original volume displaced / OWTTE ✔</p>
<p> </p>
<p>no change will take place ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>continuity equation says <em>v</em> × <em>A</em><sub>1</sub> = <em>u</em> × <em>A</em><sub>2</sub> ✔</p>
<p>«and» <em>A</em><sub>1</sub> = 4<em>A</em><sub>2</sub> ✔</p>
<p>«giving result»</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>Bernoulli:</em></p>
<p>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}\rho {v^2} + \rho gH + {P_{{\text{atm}}}} = \frac{1}{2}\rho {u^2} + 0 + {P_{{\text{atm}}}}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>ρ</mi>
<mrow>
<msup>
<mi>v</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mi>ρ</mi>
<mi>g</mi>
<mi>H</mi>
<mo>+</mo>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mrow>
<mtext>atm</mtext>
</mrow>
</mrow>
</msub>
</mrow>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mi>ρ</mi>
<mrow>
<msup>
<mi>u</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>+</mo>
<mn>0</mn>
<mo>+</mo>
<mrow>
<msub>
<mi>P</mi>
<mrow>
<mrow>
<mtext>atm</mtext>
</mrow>
</mrow>
</msub>
</mrow>
</math></span>» gives <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2} \times 1000 \times \frac{{{u^2}}}{{16}} + 1000 \times 9.8 \times 5.0 = \frac{1}{2} \times 1000 \times {u^2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>1000</mn>
<mo>×</mo>
<mfrac>
<mrow>
<mrow>
<msup>
<mi>u</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>16</mn>
</mrow>
</mfrac>
<mo>+</mo>
<mn>1000</mn>
<mo>×</mo>
<mn>9.8</mn>
<mo>×</mo>
<mn>5.0</mn>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
<mo>×</mo>
<mn>1000</mn>
<mo>×</mo>
<mrow>
<msup>
<mi>u</mi>
<mn>2</mn>
</msup>
</mrow>
</math></span> ✔</p>
<p><em>u</em> = 10.2 «m s<sup>–1</sup>» ✔</p>
<p> </p>
<p><em>Accept solving directly via conservation of energy.</em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A farmer is driving a vehicle across an uneven field in which there are undulations every 3.0 m.</p>
<p style="text-align: center;"><img 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sJC037+hMMJ4hkGX2cCdhwgfwgYmM1jWQLLDtJI0TJvuCWGYaCMD00E6qDcuWCZhu9rn0Cd69evX6/9anANmIDnEsC++tEjR1VqQO8+feiL2K8qPc/KyqLsrCzh+z8sLIysGfZVSuTAg6iISLq5S5Rm40AUlZuTQzd17kTLP6z+bYwONE13SfCb+Do2lmBcyoEJ1CQBNgysSdpcli4JTHvwoUrtwjLA24sWVnqOBxj48eln9a3rHrZq1YpKr1xxSAho0rQp/XfLFnHaIZ806Lo+scwJBpjrv4oVh0rB1wSWlZi3JSW+r04CvBxQnXQ5b90TwPatvLw8s3ZiGQCqfwz0nhpwrkBwk6a05H11J8p5ajtro94Y6LGFc2j0IHp1/gLqN6A/7T90kOBrggWA2ugRY5fJywHG7n9uvUYC+A9cutX19q5LkydNorKyMrNcOnXuTJvjfjR7przBLoL4+D0Uvzuerl2/TseOJNOFoiJlFLPr3n37UWBQAN0RE0PjJ6g3Hhw8MJqCmjSlRn5+ZvmpvblYXEy5mRm098B+tUk4nh0C+N2s+nglfb1+Pd0+fDiN/9sE3oZphxe/qhkCvBxQM5y5FA8mgPXa9bHrKe7HODqanESdIiLJ19eXjh9JJl8/P2GUpWzeOxbLAMpB//c98dTp5gjqdNPN1C96EPn4+ND4/72bQoKDlVmYrksuXRKnFJ7KzaVFCxdTYmISzZ2nzhkR1vXD2rQ15aX1AsJD6eXL7DNAKziL+OtjY+mTj1cKGxAM/DAS9WQtkUXz+NbDCbAmwMM7kKtfvQQwc1u8aBH1HRhNkV2iqKvF4Tu/791LG76OpatXrojtge3btaMhQ4dSYdEFSkpKpL179ohjeyOjulL7Dh2pS5cu5NuwoeZKZ2Vn0/f/2UjHkxIJDoVuH347jR471qb6GBqLXt260y0DBmouS5ngTH4+hQQ3pnVffqF87DbX0sjSskLVZWxpWY6te9Trk5UrxXo/BvwHHpyqSYtjK19+zgRcTYCFAFcT5fx0Q2DxwkW0auUqevK5ORQWGmq3XYcTEgizdWVo266d2BLoyKAv88Hg//nqf1Naygm6Vl4uHxMOBmrRogV9/+MPZoIAVM4QAGBstmnTJmrSrLlI49eoEXl5ewu3wPAKqDZcvXqV/tj7u1izdvV6NTQkMsjBHHUvKiyi/Px8ggBSWlpq+pw5c0ZGN33jrAU/38rLHThPITQ0jH7a5rjzJlMhGi4sDf2mPDiV4LOBAxNwVwIsBLhrz3C9XEZADjD2MrSMk5WZRT/GxdFTz/2jSgHAXr6Ovjt+4gRtjfuRkg4dpCt23P9iF8KS5ctow7cb6KetW6mhnx8FNg6mps2aiWWKy5cviyWHgjNnqPxaOeWfOkUNfX2pUUAABQY1psaNG1dZxYSDf9D0GTNo5uOPWY2rtJNISkqi9LR0IbCgbDmYIw4GdOVA7uvnK/IrKTb3r2C1EAceNmvenHbt+VPQcCALVUmE0HVD5Y8EctbvaqFJVWU4EhPQSIBtAjQC4+g1Q8ByYNkjjOiuUVBgkMkwT84Si0tKqLyszKaHPBzIg48MMp28t/Yd0rQZjbhzTI0LABj8v/16PaWnnKDmrUKpThWzdszuH5oylXr27UfjJ91LwTZsC5RtLCgooOysTDp4YL+pnGYtWtg8Yrh+/QaUnpYmuGOQ/2P/Adq7d6/QfEivhBjwlKcZKsuzda128EfeZeVlZBm/SZMmwiYjIz2d/jJihLDTwEmO/gEBhLMTsCRQncHS0O/FeXPZ0K86gXPe1UKANQHVgpUzdYbAB++9T+8uXiQGbsv/+J3JV0tav0b+9Orrbzi0fq+lHBkXtgWb/7ORCs7kU4tWodQ4JEQMyufOnaOTJ44LIUfGxTe28GFJoOPNETRw0GBq1KiR8rXqawgE+37/jY4lJQqho2WrVmZpL126RMkJh0X5EKQgQDkSUF8sLViG0NBQYfgonw8eMoQ6dOwgljigRlfOprHEAct6BH9/f3ph3lz6xzPPErQh0JYsWbGcYpw8eEnWw963paHfA1OnsqGfPWD8zq0JsBDg1t1jzMoN7Nef8k6frrXG+zRsSK1ah4vB5fKlS6Ie9Rs0IHgA7Nuvv8sEA1j+/7YnXgz+KAeW/NbU80eTEqm4uFgMxBhMEVq3a084Trh5i5Yu4XT6VC5t/+UXOpufZ7IjKCkuFkJJAx8fsUtAS0EQUCZOmkQ9elWciggNwv8teMWUxYm0k6ZruKSVAf4VbHnN69m1m0nbA8c6cXFxwmBz9JixtOT99wiWDt9v/l5m5dJvNvRzKU7OzI0I8HKAG3UGV6WCwJfrY4VbXckDDlWSk5PFLfZXR3apMLTCur2cGeIlBhAZ7L3DjDI7O1sYyvn5+lL5tWuEAa+Rvz9h779/YCBdKS0lDH5YY0eAUR5m6vg8NP1R6tSxoyxK8zeM/f67dQvt2xNPPj4Nxe4B5YzXMsP2nToL2wCvevVcPvjLsiBM/G3iJIIwkJqaKh7DMO9C4XnVAoB33Yr/Ture+N6zZw8dPHiQBkZHU/MWFQaKsjyt3zC4k0sPSDv8jhjR99hxAcNLnKZ3JOGw1myrjG9p6Lfmi3Vs6FclNY7gSQRYCPCk3jJIXbGlSrmPGvYBMkAAkDNFWJebCwF/+l23fHfXhAmEZ199+RWdzssTs/zA4GBq1MiffGAop8KhDgZqqOcXv/k63TvlQRrQv7+sVpXfmPVjQNzyw2bKy82hJs2bU0RU1ypd+kIdj4EZx/v+ZdSdLpv526qw1Cz88P1/6FJJiVUVvkwLIQnCEdT8MDYMCg6mgMAgIVzJODhV8ftNm+j82bMEIQHxHTmuZMuPcTJLsRQwPCaG+vbvTx8teZ9+792HDu7bS4+7yO++NUM/9uZnws8XOiPAQoDOOlQvzZHW+vgPGbN2GTDDl1vLoGJWBvkcz+Q1DOewJW7YoMHCDW5gUBBFde9R5eCrzFd5DXW9T5co+nzVx2Id3tJvgDIuBv7ExET6LX43Hdq/T5Qf3KQJ9ehzizKazWu0HVsD+w8aTD179bYZz1UvIGyAW+bJCk2Acg0fHOt6e1PZjW2KQY2DhVEetCZVCVAQnsJahxM8EGanp4mljbWfr6FJ996juuqYkcsAAQBh2YrlFPtVLCUlJdOkSXfTBA3eFGVeym829FPS4GujEGCbAKP0tIe0E0ZX7y5cZDbwO1J1aSwG//cYeAMCA21avzuSPzQCmWkn6V9vLzTZCEDNj+fJSYmUlHCYcrOyTAO/1vJzsrPF+vxf//a/1Tr7h0FdRnoa7dy+jWCXUHb1qmn2j5m7V506YrkEgz4EKHykXYIj3JAGwk1Gagp17NiR3lu6RAhoMi9rNgEQAGZMe0RGoaUrlrvUCh+/OSwRQQiARz829DOh5gsDEGBNgAE62VOaiFnonGeedaq6GPwxW23WshXhJDxnByxblYFGAHvvn5s9yzRoQmVf94ZNQVBwiJj92kpv7zkEAKjMJ0950GGrf3v54x1m/UeOHBG2BrD6x3n0MvwpQDWh4JAmZhb6Mo4z39AMRHTrTrnZWfSX4TFi+UDpCMkyb2tLAZZxtN5D04Sje+ERkj36aaXH8fVEgIUAPfWmh7dFqfLV2hQMXAjh7Tu4fNZvqy5tO3QQa9EY0KpSidvKw/L56dOnhQAwbvwEYbdg+d6Ze2wHPHb0CB1JTBCzfljw42wAfBAgMOEZBCh7fgOcqYNMiyUaLBFAWEo5kkzl0DhYHMQk4yp/F3IpQL7T+g1BEwP/1i1bCDsMln24Quyy0JoPx2cCeiHAQoBeelIH7UhK/HONv2+/fuI/aMwalVvIPl+31vSf9rIlSwiufWHdj4HLco97dSPBQNYyNIxyMjKoc0SE08VhzRxGg9AASKHG2UwvXrwo1P2HDhwQywv16jegkuKLZtnKwR8ClLUtimaRXXwD4SmqZy/KO3WKcrIyaeOG76ik5BL17tNb9DMGbctdAVqrYGnoB5U/G/pppcjx9UqAhQC99qyHt6v/gP521dD/2biRFi9aTEEhIdS6TVuXrvdrQQfBA2ptDODOagMK8vNpyG3/45IlgBPHj1HKiROUfPiQcDx07uxZ0SylsR9m/fBIWNsMhTDVqkL7UHzxIv3wYxxhnf5cQQE1b/7n1kI4CNKiCZCGftAkwPEQe/TT8svmuEYhwEKAUXpaJ+0sLi6hmdNn0E8//UTYPw9NQW0HaANO5+RQo06dHK4KtBnnzxWIkwodzQSz/oTDh+jA778JfwdlV6+IrKQAIPOFwR9sDuBlMLRNW6eFF5mvs98QBtCfFX3aSmh4oCHAzgQILMNuvVVVEZaGfhs3bzLbcqoqE47EBAxCgIUAg3S0Xpo594UX6GJJCXXt2avWZv+WLLF+vn9PPIW3beuwISL8AeCsAEcCjPwO/vGHMPLDoUBY48dyAgQLuZcfgygMJrHND/4R4A+goQNHGjtSP0fTKDUEaSkpYvsiVPvWBD9rhn7QGliL62h9OB0T0CMBFgL02Ks6ahPWhGXA2jUO043oEiUfucU3BitsRSw8f17sSKipSmF73+5dO8XgHxrehnr1628SjLA8AYt7qNfhBrle/frUoH59h4WUmmqTtXLAt0OnTpR2MpXG3jmaft6+zRSNDf1MKPiCCThEgIUAh7BxopomAAEAa9dt27Wv6aJVlde0eXPKTEtzWAjArDz50EFVZSESLP2//Hy1WO+35nlQ2ifoaSaMvj9x9AjNn/cyhbcJp08+Xil4saGf6p8NR2QClQiwEFAJCT9wJwI4JAdHw8K1r7sKAOCFwba09LLwGQCBRWvAbFdtkAJAG2yHdAObCLX1djYelky8vOvS6k8/pe49erChn7NAOT0TICIWAvhn4NYEXvjn83SdyK0FAAkQ6/E1sSSw8Zv1BPW/UQQALG1gG+bFixeE/4KQps3olr59Ne0UkH3E30yACZgTYCHAnAffuQkBGIBhvRcHBHXp1t1NamW/GnBPDC+C8FRYXQFaAJx42LHzTdVVhFP5Ygti6ZUrdOGGB0L53cCnAeEwobKrZeIgIV8/P/Jr1EgYJ1alOYFtQ9MWLahD4E3C5gFCQexXX9E/nv+nU3XlxEyACbAmgH8DbkQA7lt/27NH1AiOg+J3x1NYeBunjNmgQr58+bLwkFdeXkYlF4tNLa7v04AaNPAR9zgIB+vyWtTypoxuXGDL3YkjycKIzfKdmntY9GObH/KxFa5eKaWAoCBbr2v8OQZ91BnCz4WiQvL29qa2bdtSr57dxTf25ys1Fjj0adVHH1P+qVzKu37d7EAinEsgBQNlQ5Tp8Rz2DlevXBG+/pE/BybABBwnwJoAx9lxShcTiOgSSbR+vcgVwgAG5agePTWXgkN85KDk5+dHHTt1osj+/cTA0b5jB1N+6WnpdOFCkfBQl5mRQfsPHSTE9/X3d8hnPma02JLnqOOgkGbNqPjiBbtCQE5ODvkHBJraUBsX2HqIswZO5WTTxaIi6tO3L901biwNHjJYVAdaHMsghQHYeEyZOpWwpe+l51+gXbt2UnlZORWcyaeLRYViWyN8GIQ0bWq3D9BHG77dIJwAWZbF90yACagnwKcIqmfFMauZADy8jR45SpSCwbR123aq3dhiYIJjmdO5OdSiRQuadM89YgYKYSI+Pp7yTp8m77o4DrculZaWmlri6+cr7jEQtW/fntp3qDC2Q7rTeXkUFBxMoWGtVWsjsI0N2gVHXBhnpqfTrbffbvfUwAP799Gp3Fyz2bWpMdV8gVk/fBKcycujDh060KR7JokSt27ZSn8cOCDc++IwIgQlY8zkIRhA09GmbVsaO24sDR02TAzg6POnZj9JqakpQhiQTYBDIwRoZqy5M0Z+da6V0382b5JJ+JsJMAEHCLAQ4AA0TlJ9BIZGDzIdI6zc926vxDP5+ZSVkU6dOnWiadMfoe82bKAd238VXvGUbnLt5aF8B2HBt6Ev3XrbbXSx+CL9tPW/Yk1ajWw5D4gAAB4qSURBVDAgtRDY1641pJ44QTEjRridEAABC66RcTTy/wwfTqPHjKbVn/6b9u3dK9T/WOvXGrBsgGWPp555mkaPHUsbN2yg/3vlVYLvA8sADQu8BrbvfJPJuyHqBAdNJ9JOWkbneybABDQQUL8vSUOmHJUJOEoAp7q1bNlSON+pan0e6/3JiQlUdqWU3nz7LQoJCaHZj88SgzYGE0cEANQbWgEcWgNhAgLAiFEjqUf37pR46CDl5uTYbZqPj49Q6duNZOOlbyM/OnvDx7+NKDX+GELN4QP7qU1YGC167106mZJCTz0xWwgAqIwjAoBMV1hYSAvmz6f+fW4hLHPE7/2dIiIiyMtiuyT6EZ+jiQkm/vhtBAQGCuPRGofCBTIBHRFgIUBHnamHpmDt+JZ+fQnW4/YCBuNjyUn06KOP0shRI8Xg/+v27faSOPxu8/ebaNvPP9OsJ2ZBQhCCB2ai1gLsGOC219Z7a2nkM19fPzM1unxeG9+of8rx43Tm9Cn6YOlSata8OT39JNT2qXTNRtsdqScELghsH634kG4dPESc7vfwI9OEhkGZH3YI4HM6J1t4DsQ7P39/+m7Dd8pofM0EmIBGAiwEaATG0aufwLGjxwjW+taCHJwwGH+6ejV98/XXYgCxFteVzzBQLXz7Hep8803Ut+8tYnYMTYS1AH8Btt5Ziy+fwcWvOwShYTl8iCJuvomWLl9OT8+eLbQiGLCrK0CjAM2AtAl5f+kSq3YY0AicP3tWaAQCAoMoLi6uuqrE+dYCAfwGcHT4m6+/rqn03t170OMzZ2pKA+H+/smTTWkSDh8WZS9fusz0zAgXLAQYoZc9rI34j8DaUgAEAMz+AwP86c133hF/wMePHXNYJa0VC2bA237+hZITk+i5OXPoaFKi1cEean25P15LGfDxn5+XZzcJjtMtKjxvN44zLyEAoF2Pz5pFMXfE0N/vvVcsjTiTp9a0Hy5fQV99+SV9veFbm4JATlamsBO4XFLCSwJaAXN8QWDTpu8p4XCCiUZU167CxuSRGdNNz4xwwUKAEXrZw9oIVT/U6pYh5ehR6t6tG737/nticLJmRGaZxtX3mLHm5ubSyo8+MgkClqp/H5+GwoWw1rJxyI/Sqt5aeggBV0orG89Zi6v1mRQA5s6bR35+vrTg5fkO21VoLVsZXwpbC995RwgCynfK65yMdApp1pxemb9A+ZivmQAT0ECAhQANsDhq7RHIysyggAB/emzWLLpr7LhaGZyUrZeCAPbGQzuhFARwzsGVy39uQ1Smq+pajTFj/Qb1q8pG83theJeUSBAAsG0SAoCjRn+aC7eSAGVD6wJB4JnnnhXbO5XRYB8AJ0VYNkq5ccyw8j1fVw8BqMqhrofqXBnGjR5D+CBAzY44iAt1O67xwTX8cSjDujVrCap8vMc37pVBTXnK+PIa5WB5QJZtWT7qinrK5QeUY205AM+Ubbh1yFDRLlmOlrbKNO72zUKAu/UI14eCGpuvqcP5ztn8fFq6YjlNf/jhWhcAZBdBEMjNzqHw1q0pMz1NPhZajMLz50z3ai+g/chITakyeqmDAoa9jNNTU2j0mDHUo2cP+sezz9WqACDrKQWBtJNp1LlTZ/nY9A1BACcvwntgaFiY6TlfuAeBFcuW0YiRo4SK/duN31FGRiY9PvMxU+Uw8L74/PM0bfp0U5zNm1zj9+Hvk+8TDq2whRQfHD9dWFhkKh/1wa6fwMBAm0sAECTun3yfqO++g3+IeBMnTRL2Cqi7MlTVVmVcd7tmIcDdeoTrI3zvK2fWp7IyafaTT9K8F18Skrs7ITp27Bj169dP2ABIT3nSnkHZBjV1lunsxW3eoqXwrmcvjtZ32AZIderQi3NfogenTHUbIQvtgCAA489HHp1RSRuArYSDBg+iX3b8SnA5zcG9CGCQnXjDoRTW26MHRYvZNmbfCOvWrhXP5Bp86/BwemS68+vx0CZgAH92zhwTEORtWb7ppY2LN24YJ777wQdCWEA01BXtwqAv24HnVbXVRhFu8ZiFALfoBq6EkkCbNm0IBl8I0ALAjWzzFs3pwP79ymhucY1BatXKlcKQTjmLd3SHgDw/oCYbl52eRu9/8D699sqrdPbsmZosWlVZYAwXw02a/HkwE5wNzX15Hn2yejULAKoo1nyk1q3DzQrFrFsGqNkxUA+MHiQfiW85Ozd7qPEGgod0IoVdBvhApW85e68q2107dlJU1yiTACDjR0cPEgIAlgJksNdWGcddv1kIcNeeMXC9evfuLY6NBYIzeafprgnj6Z/PzXFqfzrcEOMIWsuAQRfPYZnvTPj2m2+ES1wxq76REdTVWkNwk6aqnA1p1TLYqgfqi1MPoU7HyXzObAPEvn24WbYMjQICrLK3jGfvHs6bgm/kLQWAe++rUNXaS8fvjEkAgz7W/Xfu2CkAQNiQGgc1RDDLxwcOqSyDFGaUmgDLOJ50zwcIeVJvGaSuMLb74L33RGvPFxRQ0XkcLKN9QEUGmJFjfT566DCK7BJFrVq1ohDFQHW2oEA4wNmzexcdP5JMdevVE4fiaEWdcuIEwcnN55+vocaNGwuDNez7tzwBr6p8YaCHAQ9qf1sBvvRhyY/T9JwNZ/NO01NPP01Pz37S4awwyJeXlVG/gdGCMc4V8FUIVVnZ2XQyNZW2/LCZiosvUtnVq+JUR60F4pwBuBD+ZPW/CQcRcWAC1ghgxo/B/70PPhBqehkH9gdqAwZ6fHBQlmWQg394uLmmwzKep9yzEOApPWWgesJrIP6zxywVp/rBfa8jM1TM8iO6dqUxY8eZDfxKlBAI8LmlTx86fuIEfbM+lrzq1LH6x69MZ3mNbW1bfowTAoQaC3/L9PK+SbNmVe7Lr3vjcB2ZxtFvaBPOFRRQz9696OV5czVnI7UnQ279HxoeE2M28CszCwsNJXwGDx5MhxMS6Is1nzksbI0cNYoFACXcWrqGkZ0yQLWPdXe1ATYCiA9DQOUMHYO3HGSVeWkpLyGhYufCwEHRyizMfAKYvbBxg/RYEkB95OwfUXfu3CFSYKlA6WfARjZu/5iXA9y+i4xZwdtuv51yMjMJ++KxJuxI+PtD02jKlKk2BQDLPDt17EjPzfkH9ek/QBwJbPm+qvv0jHTq0LGjaeuaIw6DrpSWihP37JVVp04d4ULXXhw17zDLuTkigt556y3NQhYEAC8vb3rsyadp7NixNgUAy3p0jYqi51+aR1Hde1hVtVrGt7x3lfW4Zb58r44AjOsQ1q1dY0oA1bu1gdsUwcYFjABhGyDX6iFIWHoKdKS8qKiuokQY78mA7YIoC0HO7uXAjrqjbMsAh2AIs2bONLUPdYUtAIwOtQg9lnm70z0LAe7UG1wXE4EpU6dQSfFF4VdeqxCAAeqhRx8Ts3tThhou7r57Io3+63jy9WukIVXFwUPQYFy24U5YTWbwMVB43r5HwLDWrckVLoaxTDLstlvFiYtq6ibjSAHg6X/8kyA4aQ1YKoBwFtmtO2EpQUvAb2F9bKyWJBzXhQQwg3/1tdfEDFjuwcd6O55rDTDgQ17YJYC8sAd/xMiKbXsyL0fKg2YBHwzYso4Y8OVuATl7x3Y/rPkL/wRrzf0ToHwM8p9+tlpURfoyQF2Rj1J7Ievqqd98lLCn9pwB6j1s0GDKP3NGHMijtrkwTLv9jhE0fPhwtUlsxlu1aiUdSUwg2CWoDQ19famhrx+Ft21LyQmHqVvPXmqTinhYSkC6GbNm20x3YP8+ys7KItgeOBNSTxyn6TOm079ee02TJgBGlo8/9YxDAoCyviWXLtH77y6mrPQ0TX08eMgQWvXvT5VZ8TUTYAIOEmBNgIPgOFn1E7h/ygOalgIwQ4WlvysEALTu7omTNA1OSHOppEQYyUEjgNMEtQa16WAh72yAA6aTKamaBADwhZGlIxoAy/pCI/DX8RMIyxtawp74eC3ROa4TBLKysggfDvolwEKAfvvW41uWnZ0tLMnVNgRr1CNG3ak2epXxMEiNGvtXsrbtzVZiDM716tez9VrV85ZhYXT6VK7NuK44REgaL8bv3m2zHGsvzubn0e3DY6y9cugZhImbIrtossHAThEemBzCrSkRll1GjxhJ2JXBQb8EWAjQb996fMv27NY248PpfTA8c2Xo1bu3puUArFkXX7ggqgC1ObbyaQ3Ypnj27FmbyVxxiFDplSvUvkMHTYMp2tN/8BDVhpY2G2DxYvDQYYRlFC0ByyEcqo/AqwsW0KvzF9Abb78ldn5UX0mcc20TYCGgtnuAy7dJQLrhtRlB8QLbAbv16Kl44ppLbB9s17GTpszkwI/TBB1x6uPt5U35+fmaynQksh8OOrqi/kRCDNRRXbs5UpTdNBDctNhdYLsoLwnYRerwS/zNTX94GkEAX/PFOhYAHCbpOQlZCPCcvjJcTbEcoDb4BwZRq1ahaqNriteuQwdN8Z2N3NDPj06eOO5sNnbT49AdzOy1BAgBQUFBWpKojgsHSFqCFgFRS75Gjgu1/713TxQIPv9iHcFfBwf9E2AhQP99bIgWlpZephYtbXvZcwZCcHCI025vpXZATT3gCRAzYxyVW10B2xgDg4I0eTTMzcqi0NDqEbS07nQosnBWU12cjJLvlrg4uufuiTT8jhha9uEKTb8LozDSazvZY6Bee5bbVesEcNY9HAbh/IP8U6dM9cEuhgYNfAg2DN7edcmvUSPy8vYWRxDLkwRbt2tHx48dpZ69epvSyYvSUvUqfJnGVd9Kd8CuypPzqV0C7y5aRKs+Xsnr/7XbDbVWOgsBtYaeC3YlAbjSPZWb65Kta5b1KikpIVjFOxKgocBWvP2HDgor62eeeZaiBw+l2LWfU/cePYi8iFKPnyCUUXD2rFDR16tfX+yKyMvNFd4DmzZtSiEhIabzBHDSX6CTPgLQlqCgxlV6J1S2GYcbwbWyK7YHKvPFdWlpqeUju/cBgdqcDNnNzKAvsaTy3NPPCJ8TWP9n9b8xfwgsBBiz3z2i1VA9q7ULKCsrowINTn20ADh6JFlLdLO4JcXF1KVLF6FeTUpKohatQgke/2JG3UlJCQmUl5sjjAcbNfInbA2EZgAB2gG0Kf/0aTqVky28EJ67ISQ0aNCAvOvWFYKBWWEablAvPz9tFvnYz3++Cm+GGqpgFvXIDX/vZg/t3Gg9mMlOVoZ8hfV/CAA4PRLr/8zTkD8D0WgWAozb927fcl8Np+RdLCqi3/fsFn7sXdkweLVLOXpEU5bY4pebkyOWAnC6nnQ9eqGoyPSfbXFxsVgmaNeps+mZmkKwvx9pM06mUnJCAvkHBpBfI3+C9qBhw4YklxOs5YW0sDPIzkinJk2a0OynnqR1a9ao3iFw8UIRJRw+5LA7Zmt1wjMcKgRfDGp3CHjX9eZDhGzBVPEc6/8QAKY8OJVmzbbtmVJFVhxFBwRYCNBBJ+q1CX1wst+xY6qbB299rlZX79yxQxgFqlkOgLc/zJYHRA+kVqGhVHi+iJo2DbE6yOPAkrA2ba2+s9dglAEhA2H+K/MpOSmZEg4dovSMDErOyRHP4UfAz9/fLJtTOTkEWwT4Yn94wXwaP2GCeB8WFiaOUjaLbOMGHhDjf90uPCm60jYgKTFBaD1sFGv1MWawHLQTWLVyJb27cBG9OG+u6TegPRdOoScCLAToqTd11pYhw4bSl19+odqt7ZXLl+nHzZuo0+OzXEICWoBN320QBxmpyRAzbcxS57/yCmFwtRbk1rZevfvQ999+TfUiIgm7AbSEa+XldP3aNRo7bpz4WKaFqleWI99hvdeayheMU1NTZbQqv+E2GDNJnBzoipCVnU27tm/TdOgS/CjY4uuKOukxD/we4PwH/hV4/V+PPex4m3iLoOPsOGU1E+jXv79qAQBVgeOblGPH6Ndff3VJzTZ+t4G8vLX9iTTya2RzgEJ7zpw+LerWtl07GjXuLspMO0mH/zgglg8uFherci5UcPYMBYc0sdlGDPgoS/mxJgAgA8SB4KI2QCPyU9wPQuOiNo29eGs+W23SbNiLp3wXERGhvOXrKgjAxTL2/+N74+ZNbABYBS+jvWZNgNF63IPai4GrZcuWlJtr24++ZXNw/PBnqz4WPgOcsWL/fe9e2rntF82HAA0dNsyySqZ7DLiXL1+iuB82U9NmzcTzgYOHEDQIp06dEjYC58+eFfcyERz0QI1/rfya2FJYcrGYsOPg409WyShOfQ+PiSHMrMupXFM+SxYvIhwlHOaE34AvvlgnjB6lm2U1FcDZDPfcN1lNVI5DJGb+8AA4/m8T6MW5c5kJE6hEgI8SroSEH7gTgc9Xr6YF8+dr0ghg0MRhQvfc/4BDRmxbtmyh/3z7tSYVNZhhgPp243d2Z1qYjX2xbh1dvVomMOfk5Iitjbi5cvVqJfRw6lNefo3q1vUif/8AiomJof+deLdV1X6lxCofTHvoIfpp639Vxq6IFhjUWAgrjggCWGaBlmVv/G4qKizUVC5sIvbs2+vS9muqgAdF5vV/D+qsWqwqCwG1CJ+LrpoA1jL79e5jNjuuOlVFDLjFxbG3o8eMJTWGbGcLCuiLtWvo+JEjqu0AlHWB1uLX3buUjzziGjYE48aM0SRooWHgC2PBCZPupehBg1QxhuHmN+tjhd8FtbsBlBD/MmIEvb90ifIRX1sQUK7/w/sf7/+3AMS3ZgRYCDDDwTfuSAAnmn2y0jH1NwzZsEQwYPAQiuwSVemUQbEFMCWF9v7+m7B8h1W9FvW05IV19df+9S+PtbgWR8YmO+YPAYyxM2PY7cOpd58+lZYIIFzB+HDP7l10NDGB6nh5aV5mkZx/2fGrTZsLGcfI39A0zXh4GvkHBLD7XyP/EDS0nYUADbA4au0QwMymf59bVO9nt1ZLDO5QJWP2iXV2bM87nlxxTjoGMeyBx6zW0dC+fXuK+0mbSt3RsqojHazG/z55smZtgLIuWCIov1ZO8NkA74Lw85CVniaigHHxxQual1iU+bMWQEmj8jX6EOv/sPPAEcAcmIAaAiwEqKHEcWqdwLIlS+idt96ma9eu1XpdLCsALcC339m3BbBM4473Tz0xm77bsMEdq0Y4Kjp+7+9sC2Cjd9bHxtKcZ56l199602O1UTaaxo+rmQALAdUMmLN3HQFnVNauq4V5TjAG/Otdd9G/3nzD/IUH3kHjMjR6EF24cMGtag/GmNnCLwKHygTg/Q++G3j/f2U2/KRqAiwEVM2oVmJAtYcgv61VAut+kTecwBjB+McVywLWODrzDE5rsE6tlwAjwdEjR7lNcyAADL11GK346CO3qVNtVARr/dlZWYTzJ+B+WoY1n30uLrEFEGdKwJMifpPyW8bjbyZgiwALAbbI1PBzSPJbfowTJ80lJycTHKJgkO8/oL/NmmRlZgkHIPjPAQft9O3XT5wHjjVBvXpUwyB119hxDu0WsAnSwRdBjRvTT9t+0Z2KWmzLfHk+lZdr8x3gIEa7yfB3AAc3RgsY9PF/wp7d8aaJAAR9/F2Htf7TGyX+D7C8R1r8nSDAN8XwO2KEnYAth1FGY8vtNSfAQoA5jxq9w8z2k5UrxVne+AOFNC+9vGmtCPKC1gCCBP7zwH8YyE/6iNeanzvHdwdBwMfHh776er1ut1+5gyCALZff//iD7oQse39b+Bte9fFK2rplC90+fLgYwPF/giNCPYQB+X8C8rtr/Hia9eRsh/KyV2d+59kEWAiopf6TjjwwWD/x5Gwx+LuyKjAUwkEhUAtWR/6urKsjedWmIIDBae1XX+r+P1MIAvNeqnkvc1gC6Ny5s6GOuMWALX3743S/B6ZOdanwg/y/jo0VAgY0hThAiDUDjvzPo780LATUcJ9CMscfOwL+ECHlV2d4d9Ei8YcPrQCODdXTHz4EgWkPPkR5eXk1orr28vKinr160YcrP9YVR3u/P/xep/z9fqe2Z9rL3/KdngwtLdtm674m/0aVwga0AlOmTrVVLX5uEAIsBNRQR0Ndj8EfqvqaPsdb+YevtyNEwfW1V16l2K++qtaehI8BaFSmP/potZbjjpmD8cNTH6QD+/dX6xZNHIEMD3fVLRi7C+OanhAo242ysatAr5pCZVv52j4BFgLs83H6raUarjbX5CCASC0E6qEnewFoBZ6a/SSlnDjh8oFq8JAh9Mpr/6d79X9VP3YMHDNnPEoXLhQ55VTIshwIWPfeN1l3mirLdsp7cFy8cJEw3qvN2TiEO2mThCUCaZMk68nfxiDAQkA19DMGpPj4eGHZKw1yMPt3l218sBf45OOVYmcB/vhhPSwtj6sBR41mif9gly1ZSr9u3y6OyC0v027hDpU0VP+Dhw6huS+/bPjB37ID8ftZvmSpcAVs+U7tPRws+Tb0FQOP3papLBlgsMXvEh8Y7iJgwHX1ur9luWrvpTCw/qtYkUTuJsD/CXpaPlTLw2jxakUIkH8QeoEdv7tiTz/272J7X2hoaIWV/4D+Lt2a07FtOzqRdtJl2KClgHZAbk2EkxhsM0Sw3Ir07qLFLiuXM2ICeiMwa/YTpibJ/w/wABMC+XeF7b4Qul05GXD1/wlCUImLo6TEJPptzx7CEo2sLwSCyC6RpnZ68gWWQfSkCXWmL2pFCMAfBgYfvQS5hok/EvkHUx1tc/UfvGUdMSNA3yBAQID/ARlc/Z+XzLemvq21TTnTkX1YU/XRYznK34x0aiO5VvffRm3ylDNpWQfZZtwrf2PyvSu/q/v/BGWfKv+GXNmG2sgL/YL/0zgQ1YoQwOAdI1Ddf/CO1YpTMQEmUFsE+P+E2iKvn3K99NMUbgkTYAJMgAkwASaghQALAVpocVwmwASYABNgAjoiwEKAjjqTm8IEmAATYAJMQAsBFgK00OK4TIAJMAEmwAR0RICFAB11JjeFCTABJsAEmIAWAiwEaKHFcZkAE2ACTIAJ6IhAXR21xRBNwZYgDkyACTABJsAEXEGAhQBXUKzBPFzpMbAGq81FMQEmUA0EeFJQDVANliUvBxisw7m5TIAJMAEmwAQkARYCJAn+ZgJMgAkwASZgMAIsBBisw7m5TIAJMAEmwAQkARYCJAn+ZgJMgAkwASZgMAIsBBisw7m5TIAJMAEmwAQkARYCJAn+ZgJMgAkwASZgMAIsBBisw7m5TIAJMAEmwAQkARYCJAn+ZgJMgAkwASZgMAJ1rl+/ft1gbebmMgEmwASYABNgAkTEmgD+GTABJsAEmAATMCgBFgIM2vHcbCbABJgAE2ACLATwb4AJMAEmwASYgEEJsBBg0I7nZjMBJsAEmAATYCGAfwNMoJoJrFuzlm4dMpRw4hs+j8+cSYWFhVWWunzpMurdvYcp3f2TJ9Pm7zdVmY4jMAEmwATUEmAhQC0pjscEHCAAAeDF55+niZMmEY6B3nfwD8rMyKT7J99nNzcM9m++/jpNvKcinTxCGgJEZkaG3bT8kgkwASaglgALAWpJcTwm4ACBdWvXUvSgaHpkxnSROjAwUAgECYcP253V79y5g1qHh9Ozc+aYSn31tdfE9c4dO03P+IIJMAEm4AwBFgKcocdpmUAVBL7d+B19+tlnVcSq/BoDfVTXKLMXEArwgYBgLUBLMG70GMIyglx6wDIEtArKJQksMeCeAxNgAkyAhQD+DTCBGiQADcDyZcsoqmtXGjFqpNWSYS8AlX94eHil99AkYDnBVkD+u3buEEsPWEJAfAgH0Ej8+7PV4vnAQdFiiYKXFWxR5OdMwDgEWAgwTl9zS2uRAAZ2zM4xUy8qLBRLAo5Wp6rBWy4bIP8RIysEDSwrQIuAMHHSPeKblxUEBv6HCRiaQF1Dt54bzwRqiABm5NK4D+p6GAtCMJC2Aq6qBsqRg70yz8DAANOtvFazQ8GUiC+YABPQJQHWBOiyW7lR7kwAAz8GaqjoHQnWBnlH8uE0TIAJMAEWAvg3wARqgQBm7FgWsBbkbD7DylZAzN5bh7e2loyfMQEmwAQ0E2AhQDMyTsAE1BOAJT4M8yxDxWBe2fBPxsO2woTDCfJWfMMWAJ+oqK5mz/mGCTABJuAoARYCHCXH6ZiACgLTpk+nXTt2Eqz2ZYBNAAZzpQ8A+U5+R0cPEnFgOyADrqElgAMhDkyACTABVxBgw0BXUOQ8mIANAtLw7/GZj4lBHdEwy4f/AGwTlAG7BiAowKMgBnpsH3w2Yw6tWLbMtKcf8WH5j/ccmAATYAKuIFDn+vXr112REefBBJgAE2ACTIAJeBYBXg7wrP7i2jIBJsAEmAATcBkBFgJchpIzYgJMgAkwASbgWQRYCPCs/uLaMgEmwASYABNwGQEWAlyGkjNiAkyACTABJuBZBP4/nHtm6PHMoYgAAAAASUVORK5CYII="></p>
<p>The farmer’s seat is mounted on a spring. The system, consisting of the mass of the farmer and the spring, has a natural frequency of vibration of 1.9 Hz.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain why it would be uncomfortable for the farmer to drive the vehicle at a speed of 5.6 m s<sup>–1</sup>.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline what change would be required to the value of <em>Q</em> for the mass–spring system in order for the drive to be more comfortable.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>the time between undulations is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{3}{{5.6}}">
<mfrac>
<mn>3</mn>
<mrow>
<mn>5.6</mn>
</mrow>
</mfrac>
</math></span> = 0.536 «s»</p>
<p><em>f</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{0.536}}">
<mfrac>
<mn>1</mn>
<mrow>
<mn>0.536</mn>
</mrow>
</mfrac>
</math></span> = 1.87 «Hz»</p>
<p>«frequencies match» resonance occurs so amplitude of vibration becomes greater</p>
<p><em>Must see mention of “resonance” for MP3</em></p>
<p><em><strong>ALTERNATIVE 2</strong></em></p>
<p><em>f</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{v}{\lambda } = \frac{{5.6}}{3}">
<mfrac>
<mi>v</mi>
<mi>λ</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>5.6</mn>
</mrow>
<mn>3</mn>
</mfrac>
</math></span></p>
<p><em>f</em> = 1.87 «Hz»</p>
<p>«frequencies match» resonance occurs so amplitude of vibration becomes greater</p>
<p><em>Must see mention of “resonance” for MP3</em></p>
<p> </p>
<p> </p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«to increase damping» reduce <em>Q</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A Pitot tube shown in the diagram is used to determine the speed of air flowing steadily in a horizontal wind tunnel. The narrow tube between points A and B is filled with a liquid. At point B the speed of the air is zero.</span></p>
<p><span style="background-color: #ffffff;"><img style="margin-right: auto; margin-left: auto; display: block;" 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" width="550" height="242"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Explain why the levels of the liquid are at different heights.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">The density of the liquid in the tube is 8.7 × 10<sup>2 </sup>kg m<sup>–3</sup> and the density of air is 1.2 kg m<sup>–3</sup>. The difference in the level of the liquid is 6.0 cm. Determine the speed of air at A.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">air speed at A greater than at B/speed at B is zero<br><em><strong>OR</strong></em><br>total/stagnation pressure «<em>P</em><sub>B</sub>» – static pressure «<em>P</em><sub>A</sub>» = dynamic pressure ✔</span></p>
<p><span style="background-color: #ffffff;">so <em style="color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">P</em><sub style="color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 11.6px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">A</sub> is less than at <em style="color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">P</em><sub style="color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 11.6px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">B</sub> (or <em>vice versa</em>) «by Bernoulli effect» ✔</span></p>
<p><span style="background-color: #ffffff;">height of the liquid column is related to «dynamic» pressure difference «hence lower height in arm B» ✔</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">«<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ρ</mi><mi>liquid</mi></msub><mo> </mo><mi>g</mi><mi>h</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>×</mo><msub><mi>ρ</mi><mi>air</mi></msub><mo> </mo><msup><mi>v</mi><mn>2</mn></msup></math>»<br></span></p>
<p><span style="background-color: #ffffff;">difference in pressure <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>P</mi><mi mathvariant="normal">B</mi></msub><mo>-</mo><msub><mi>P</mi><mi mathvariant="normal">A</mi></msub><mo>=</mo><mn>8</mn><mo>.</mo><mn>7</mn><mo>×</mo><msup><mn>10</mn><mn>2</mn></msup><mo>×</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>06</mn><mo>=</mo><mn>510</mn></math> «Pa» ✔<br></span></p>
<p><span style="background-color: #ffffff;">correct substitution into the Bernoulli equation,<em> eg</em>: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>×</mo><mn>1</mn><mo>.</mo><mn>2</mn><msup><mi>v</mi><mn>2</mn></msup><mo>=</mo><mn>510</mn></math> ✔<br></span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>29</mn></math> «ms<sup>–1</sup>» ✔</span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The natural frequency of a driven oscillating system is 6 kHz. The frequency of the driver for the system is varied from zero to 20 kHz.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a graph to show the variation of amplitude of oscillation of the system with frequency.</p>
<p><img src="data:image/png;base64,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"></p>
<div class="marks">[3]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The <em>Q </em>factor for the system is reduced significantly. Describe how the graph you drew in (a) changes.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>general shape as shown</p>
<p>peak at 6 kHz</p>
<p>graph does not touch the <em>f </em>axis</p>
<p> </p>
<p><img src="images/Schermafbeelding_2018-08-14_om_10.21.57.png" alt="M18/4/PHYSI/HP3/ENG/TZ2/11.a/M"></p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>peak broadens</p>
<p>reduced maximum amplitude / graph shifted down</p>
<p>resonant frequency decreases / graph shifted to the left</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br>