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nuclear and particles</a></li><li><a href="../446/energy-production.html"><i class="fa fa-fw fa-caret-right"></i> Energy production</a></li><li><a href="../848/options.html"><i class="fa fa-fw fa-caret-right"></i> Options</a></li><li><a href="../823/astrophysics.html"><i class="fa fa-fw fa-caret-right"></i> Astrophysics</a></li><li><a href="../849/engineering.html"><i class="fa fa-fw fa-caret-right"></i> Engineering</a></li></ul><div class="pull-right"><a class="sidenav-expand" title="Expand all" href="#"><i class="fa fa-plus-circle"></i></a> <a class="sidenav-compress" title="Compress all" href="#"><i class="fa fa-minus-circle"></i></a></div></h4><ul class="side-nav level-0"><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../1398/hl-practice-paper-1.html">HL practice paper 1</a></label></li><li class="expanded parent selected"><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="hl-practice-paper-2.html">HL practice paper 2</a></label></li></ul></div> <div class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> HL practice paper 2 <a href="#" class="mark-page-favorite pull-right" data-pid="1366" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../2885/exam-questions.html">Exam questions</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">HL practice paper 2</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 20 minutes"><i class="fa fa-clock-o"></i> 20'</span> </ol> <article id="main-article"> <div class="pinkBg"> <p>This is an original paper for you to try. It's equivalent to a Higher Level Paper 2:</p> <ul> <li>90 marks</li> <li>5 minutes reading time</li> <li>2 hours 15 minutes</li> <li>Print it off and have a go</li> <li>Use of a calculator and data booklet are permitted</li> <li>Then check out our complete walk-through below</li> </ul> <p>WARNING: Do not attempt this paper until the revision phase of your course. Make the most of the opportunity.</p> </div> <p><iframe frameborder="0" height="480" scrolling="no" src="../../practice-papers/hl-practice-paper.pdf" width="100%"></iframe></p> <div class="yellowBg"> <p style="text-align: center;">Are you finished?</p> <p style="text-align: center;"><img alt="" src="../../practice-papers/exam.jpg" style="width: 500px; height: 333px;"></p> <p style="text-align: center;">Are you really finished?</p> <p style="text-align: center;"><img alt="" src="../../practice-papers/exam-2-1.jpg" style="width: 500px; height: 294px;"></p> <p style="text-align: center;">Ok! We'll walk you through it.</p> </div> <h4>Question 1</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/391490347"></iframe></div> <p><a href="../264/circular-motion.html" target="_blank">Circular motion</a></p> <p>The <strong>centripetal force</strong> is the <em>resultant force </em>acting towards the centre that makes a body travel in a circle:</p> <p style="text-align: center;"><span class="math-tex">\(F=m \omega^2 r={mv^2 \over r}\)</span></p> <p><a href="../232/vectors.html" target="_blank">Vectors</a></p> <p>Vectors are usually drawn with an arrow in the correct direction, where the length of arrow represents the magnitude. A force is an example of a vector.</p> <p><a href="../236/balancing-forces.html" target="_blank">Balancing forces</a></p> <p>If the force vectors acting on a body add up to zero then we say they are balanced. To determine if this is the case, resolve the forces into two perpendicular directions (e.g. vertically and horizontally) and see if they cancel out in each.</p> <p><a href="../188/pythagoras-and-trigonometry.html" target="_blank">Trigonometry</a></p> <p style="text-align: center;">A trigonometric identity is an equation that applies for any value of angle. The identity that you must learn is: <span class="math-tex">\(\tan \theta={\sin \theta\over \cos\theta}\)</span></p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/391669458"></iframe></div> <p><a href="../220/work-and-energy.html" target="_blank">Energy transfers</a></p> <p><em>Kinetic</em> energy (E<sub>k</sub>) is due to movement, equal to the amount of work required to make a body move.</p> <p style="text-align: center;"><span class="math-tex">\(E_k={1\over 2} mv^2\)</span></p> <p><em>Potential</em> energy (E<sub>p</sub>) is positional, equal to the amount of work done in taking a body from a place of zero potential energy to the place in question.</p> <p style="text-align: center;"><span class="math-tex">\(E_p=mgh\)</span></p> <p><a href="../244/collisions.html" target="_blank">Inelastic collisions</a></p> <p>When bodies stick together, E<sub>k</sub> isn't conserved. Energy is lost. However, momentum is conserved.</p> </section> <h4>Question 2</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/391766431"></iframe></div> <p><a href="../263/ideal-gas-equation.html" target="_blank">Ideal gases</a></p> <p>The ideal gas equation relates pressure, temperature, volume and the amount of gas:</p> <p style="text-align: center;"><span class="math-tex">\(pV=nRT\)</span></p> <p>To calculate the internal energy, <em>U</em>, of a gas we assume that potential energy is zero: </p> <p style="text-align: center;"><span class="math-tex">\(U=\sum E_p+\sum E_k=\sum E_k\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Rightarrow U=N{3\over 2} kT\)</span></p> <p><a href="../258/modelling-gases.html" target="_blank">Gas laws</a></p> <p><strong>Boyle's law:</strong> The pressure of a fixed mass of gas at constant temperature is inversely proportional to its volume.</p> <p style="text-align: center;"><span class="math-tex">\(p\propto{1\over V}\)</span></p> <p>Pressure - <a href="../235/examples-of-forces.html" target="_blank">at a surface</a> and <a href="../262/pressure-law.html" target="_blank">due to movement of particles</a></p> <p>Pressure is the ratio of force acting to the surface area. The pressure of the hot gas is greater than the cold because the molecules hit the walls harder and more often due to their increased kinetic energy.</p> </section> <h4>Question 3</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/391769837"></iframe></div> <p><a href="../278/waves.html" target="_blank">Standing waves</a></p> <p>Standing waves (or stationary waves) form when the following occurs:</p> <ul> <li>Two waves</li> <li>With the same freqency and amplitude</li> <li>Travelling in opposite directions</li> <li>Interfere with each other</li> </ul> <p>The most regular occurence of this is a single wave reflecting back onto itself.</p> <p><strong>Node:</strong> Point that has zero amplitude</p> <p><strong>Wavelength (<em>λ</em>): </strong>The distance between two equivalent points on consecutive waves (e.g. peak to peak)</p> <p><a href="../280/graphical-representation-of-waves.html" target="_blank">Displacement-position graphs</a></p> <p style="text-align: center;"><span class="math-tex">\(v=f\lambda\)</span></p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/391773417"></iframe></div> <p><a href="../278/waves.html" target="_blank">Refraction</a></p> <p><strong>Critical angle: </strong>When light travels from glass to air, it refracts away from the normal. If the angle of incidence is large enough then the angle of refraction will be 90°. The angle at which this happens is called the <em>critical angle</em>.</p> <p>NB: Sound not <a href="../284/light.html" target="_blank">light</a>. The angle of refraction can be calculated by Snell's law, where <em>n</em> is the refractive index (ratio of the speed of light to its speed in the material).</p> <p style="text-align: center;"><span class="math-tex">\({\sin i \over \sin r}={n_2 \over n_1}={v_1\over v_2}\)</span></p> <p><a href="../279/introduction-to-waves.html" target="_blank">Wavefronts</a></p> </section> <h4>Question 4</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/393108849"></iframe></div> <p><a href="../181/electric-circuits.html" target="_blank">Electric circuits</a></p> <p><strong>Potential divider:</strong> Any circuit that splits the terminal potential difference of the battery using two or more resistors. </p> <p><strong>Electromotive force or EMF (ε):</strong> The amount of work done per unit charge taking a small positive charge from one side of the battery to the other, when no current is being drawn.</p> <p><strong>Kirchhoff's second law:</strong> The sum of EMF around a closed loop = the sum of the potential difference</p> <p style="text-align: center;"><span class="math-tex">\(\sum \varepsilon = \sum V\)</span></p> <p>This is a consequence of conservation of energy.</p> <p><strong>Resistance (<em>R</em>):</strong> The ratio of the potential difference across an electrical conductor to the current flowing through it</p> <p style="text-align: center;"><span class="math-tex">\(R={V\over I}\)</span></p> <p>Resistance is measured in Ohms (Ω).</p> </section> <h4>Question 5</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/393116472"></iframe></div> <p><a href="../207/areas-and-volumes.html" target="_blank">Volume</a></p> <p>Volume will always be calculated by multiplying three lengths, sometimes with a numerical factor. This means it always has the unit m<sup>3</sup>.</p> <p style="text-align: center;"><img alt="" src="../../images/volumes.png"></p> <p><a href="../1241/density.html">Density</a></p> <p>Density is defined as the ratio of the mass of a body to its volume:</p> <p style="text-align: center;"><span class="math-tex">\(\rho={m\over V}\)</span></p> <p><a href="../220/work-and-energy.html" target="_blank">Energy and power</a></p> <p><em>Potential</em> energy (E<sub>p</sub>) is positional, equal to the amount of work done in taking a body from a place of zero potential energy to the place in question.</p> <p style="text-align: center;"><span class="math-tex">\(E_p=mgh\)</span></p> <p>Power is defined as the rate at which work is done. It is a scalar quantity.</p> <p style="text-align: center;"><span class="math-tex">\(P={W\over t}\)</span></p> </section> <h4>Question 6</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/393120123"></iframe></div> <p><a href="../364/atomic-model.html" target="_blank">Atomic model</a></p> <p>The Rutherford model of the atom had the following key ideas:</p> <ul> <li>A small, densely positive nucleus</li> <li>Surrounded by negative electrons</li> <li>Neutral overall</li> </ul> <p style="text-align: center;"> <img alt="" src="../../images/rutherfordatom.png"></p> <p><a href="../368/nuclear-physics.html" target="_blank">Nuclear physics</a></p> <p>Beta particles consist of an electron. Electrons are not normally found in the nucleus, but are released during the process of beta decay, when when a neutron changes into a proton plus an electron. This reduces the ratio of neutrons to protons.</p> <p><em>Binding energy</em> is the amount of energy required to pull a nucleus apart into separate nucleons. It is equal to the energy released when the separate nucleons combine to form the overall nucleus. </p> <p>Beta decay example:<img align="middle" alt="C presubscript 6 presuperscript 14 space rightwards arrow N presubscript 7 presuperscript 14 plus e to the power of minus plus nu with bar on top" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mmultiscripts»«mi»C«/mi»«mprescripts/»«mn»6«/mn»«mn»14«/mn»«/mmultiscripts»«mo»§#160;«/mo»«mo»§#8594;«/mo»«mmultiscripts»«mi»N«/mi»«mprescripts/»«mn»7«/mn»«mn»14«/mn»«/mmultiscripts»«mo»+«/mo»«msup»«mi»e«/mi»«mo»-«/mo»«/msup»«mo»+«/mo»«mover»«mi»§#957;«/mi»«mo»§#175;«/mo»«/mover»«/math»" src="../../../ckeditor/plugins/wiris/integration/showimage-41.php?formula=28c909f7a652d2b74ec2292d78f6ffdd.png"></p> <p style="text-align: center;"><img alt="" src="../../../ib/physics/activities/beta1.png"></p> <p>The <span class="math-tex">\(\bar{\nu}\)</span> symbol represents an anti-electron neutrino. The beta energy spectrum provides evidence of the <em>neutrino</em>, which takes some of the kinetic energy:</p> <ul> <li>Mass - almost nothing</li> <li>Charge - zero</li> <li>Spin - <span class="math-tex">\(1\over 2\)</span></li> </ul> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/393262292"></iframe></div> <p> <a href="../1132/ahl-quantum.html" target="_blank">Bohr model</a></p> <p>The Bohr model predicts the energy of an electron in an energy level as being discrete:</p> <p style="text-align: center;"><span class="math-tex">\(E=-{13.6\over n^2}\)</span></p> <ul> <li><span class="math-tex">\(E\)</span> is the energy associated with the <span class="math-tex">\(n^{th}\)</span> energy level (eV)</li> <li><span class="math-tex">\(n\)</span> is the number of the energy level</li> </ul> <p>Angular momentum is also quantised:</p> <p style="text-align: center;"><span class="math-tex">\(mvr={nh\over 2\pi}\)</span></p> <ul> <li><span class="math-tex">\(mvr\)</span> is angular momentum (kgm<sup>2</sup>s<sup>-2</sup>)</li> <li><span class="math-tex">\(n\)</span> is an integer equal to 1 minus the quantum number</li> <li><span class="math-tex">\(h\)</span> is Planck's constant (Js)</li> </ul> <p><a href="../264/circular-motion.html" target="_blank">Circular motion</a> and <a href="../180/electric-fields.html">electric forces</a></p> <p>The <strong>centripetal force</strong> is the <em>resultant force </em>acting towards the centre that makes a body travel in a circle.</p> <p style="text-align: center;"><span class="math-tex">\(F=m \omega^2 r={mv^2 \over r}\)</span></p> <p>The force experienced by two point charges is directly proportional to the product of their charges and inversely proportional to their separation squared:</p> <h4 style="text-align: center;"><span class="math-tex">\(F_E \propto {{q_1 q_2}\over r^2}\)</span></h4> <p>The proportional sign can be replaced with an equals sign by multiplying by a constant:</p> <h4 style="text-align: center;"><span class="math-tex">\(F_E=k{{q_1 q_2}\over r^2}\)</span></h4> <p><em>k</em> is known as Coulomb's constant or the electric force constant. Its value is 8.99×10<sup>9</sup> N m<sup>2</sup> C<sup>−2</sup>.</p> <p><a href="../1134/wave-particle-duality.html" target="_blank">Heisenberg's uncertainty principle</a></p> <p>The Heisenberg uncertainty principle describes the inherent impossibility of measuring both momentum and position with certainty as an equation:</p> <p style="text-align: center;"><span class="math-tex">\(\Delta p \Delta x \geq{h\over 4\pi}\)</span></p> <ul> <li><span class="math-tex">\(\Delta p\)</span> is uncertainty in momentum (kgms<sup>-1</sup>)</li> <li><span class="math-tex">\(\Delta x\)</span> is uncertainty in position (m)</li> <li><span class="math-tex">\(h\)</span> is Planck's constant (Js)</li> </ul> </section> <h4>Question 7</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/393262681"></iframe></div> <p><a href="../1136/capacitors.html">Capacitance</a></p> <p>A capacitor contains a uniform electric field. The value of the capacitance of a capacitor is set according to three variables:</p> <p style="text-align: center;"><span class="math-tex">\(C=\varepsilon{A\over d}\)</span></p> <ul> <li><span class="math-tex">\(C\)</span> is capacitance (F)</li> <li><span class="math-tex">\(\varepsilon\)</span> is an electric constant (Fm<sup>−1</sup>)</li> <li><span class="math-tex">\(A\)</span> is the area of overlap of the two plates (m<sup>2</sup>)</li> <li><span class="math-tex">\(d\)</span> is the separation between the plates (m)</li> </ul> <p>The electric constant is the product of the permittivity of free space and the relative permittivity of the dielectric:</p> <p style="text-align: center;"><span class="math-tex">\(\varepsilon=\varepsilon_0k\)</span></p> <ul> <li><span class="math-tex">\(\varepsilon_0\)</span> is the permittivity of space (8.854 x 10<sup>-12</sup> Fm<sup>-1</sup>)</li> <li><span class="math-tex">\(k\)</span> is the permittivity of the dielectric (~1 for air and >1 for all media)</li> </ul> <p>The energy stored when a capacitor is charged can be calculated by adding the infinitesimal stages of work done when each new quantity of charge is added. This is equal to the area under the graph. Since charge stored is proportional to the potential difference across the capacitor:</p> <p style="text-align: center;"><span class="math-tex">\(E={1\over 2}qV\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Rightarrow E={1\over 2}CV^2\)</span></p> <ul> <li><span class="math-tex">\(E\)</span> is the energy stored on the capacitor or the work done that was required to store the charges (J)</li> </ul> <p>Expressions for the variation of charge, current and potential difference with time can be derived:</p> <p style="text-align: center;"><span class="math-tex">\(q=q_0e^{-t\over \tau}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(I=I_0e^{-t\over \tau}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(V=V_0e^{-t\over \tau}\)</span></p> <p>These equations are exponential decay relationships and have the following characteristic shape when plotted against time:</p> <p style="text-align: center;"><img alt="" src="../../em-induction/discharge.png" style="height: 113px; width: 200px;"></p> <p>Time constant also has a real-world meaning. It is the product of the capacitance and load resistance (for the circuit diagram shown above):</p> <p style="text-align: center;"><span class="math-tex">\(\tau=RC\)</span></p> <ul> <li><span class="math-tex">\(\tau\)</span> is time constant (s)</li> <li><span class="math-tex">\(R\)</span> is load resistance (<span class="math-tex">\(\Omega\)</span>)</li> <li><span class="math-tex">\(C\)</span> is capacitance (F)</li> </ul> <p><a href="../181/electric-circuits.html" target="_blank">Resistivity</a></p> <p><strong>Resistivity (<em>ρ</em>):</strong> The resistance of a material with cross-sectional area of 1 m<sup>2</sup> and length 1 m.</p> <p style="text-align: center;"><span class="math-tex">\(\rho ={RA\over l}\)</span></p> <p>Resistivity has the unit Ωm (which you can work out from the dimensions of the equation).</p> </section> <h4>Question 8</h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/393263111"></iframe></div> <p><a href="../1127/single-slit-diffraction.html" target="_blank">Single-slit diffraction</a></p> <p>We can determine the position of the first minimum using the approximation equation:</p> <p style="text-align: center;"><span class="math-tex">\(\theta = {\lambda \over a}\)</span></p> <ul> <li><span class="math-tex">\(\theta\)</span> is the angle subtended at the slit by the first minimum and the centre (rad)</li> <li><span class="math-tex">\(\lambda\)</span> is the wavelength of the light (m)</li> <li><span class="math-tex">\(a\)</span> is the width of the slit (m)</li> </ul> <p style="text-align: center;"><img alt="" src="../../waves/path-difference.png" style="height: 114px; width: 200px;"></p> <p>Since the angle is small, we can also state that it is approximately equal to the ratio of the distance to the minimum and the distance from the slit to the screen:</p> <p style="text-align: center;"><span class="math-tex">\(\theta = {y\over D}\)</span></p> <ul> <li><span class="math-tex">\(y\)</span> is the distance between the centre and the first minimum (on either side since symmetrical) (m)</li> <li><span class="math-tex">\(D\)</span> is the distance from the slit to the screen (m)</li> </ul> <p><a href="../1126/1805/multiple-slit-interference.html" target="_blank">Multiple-slit interference</a></p> <p>The phenonoma discussed rely on coherent light. Coherent light beams have constant phase difference (and therefore the same frequency). They should also have the same amplitude.</p> <p>The fringe spacing can be calculated as follows:</p> <p style="text-align: center;"><span class="math-tex">\(s={D\lambda\over d}\)</span></p> <ul> <li><span class="math-tex">\(s\)</span> is the distance between consecutive maxima (m)</li> <li><span class="math-tex">\(D\)</span> is the distance from the slits to the screen (m)</li> <li><span class="math-tex">\(\lambda\)</span> is the wavelength of light (m)</li> <li><span class="math-tex">\(d\)</span> is the distance separating the centres of the two slits (m)</li> </ul> <p>The result is a pattern of evenly spaced bright fringes separated by dark fringes. It is caused by the interference of the light from the two slits as the two paths to each point on the screen vary in distance. The central maximum is most intense.</p> <p style="text-align: center;"><img alt="" src="../../waves/double-6.png"></p> <p style="text-align: center;"><img alt="" src="../../waves/double-5.png"></p> <p>The two-slit <strong>interference</strong> pattern is modulated by the one-slit <strong>diffraction</strong> effect.</p> <p>This affects the distribution of intensity against distance on the screen from the centre by capping the double slit pattern within the intensity of the diffraction pattern.</p> <p><a href="../278/1808/waves.html">Intensity</a></p> <p><strong>Brightness:</strong> directly related to the <em>intensity</em> (power per unit area), brightness is proportional to the square of the amplitude.</p> </section> <h4>Question 9 </h4> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/393263483"></iframe></div> <p><a href="../268/gravitation.html" target="_blank">Gravitation</a></p> <p>Every particle of mass attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to their separation squared.</p> <p style="text-align: center;"><span class="math-tex">\(F=G{Mm \over r^2}\)</span></p> <p>In this equation, <span class="math-tex">\(G\)</span> is the universal gravitational constant, 6.67 × 10<sup>-11</sup> m<sup>3</sup>kg<sup>-1</sup>s<sup>-2</sup>.</p> <p><a href="../219/forces.html">Balanced forces</a></p> <p>Forces are said to be <em>balanced</em> if the resultant force is zero. The body is then in <em>equilibrium</em>.</p> <p><em>Equal</em> forces are balanced only if they act in opposite directions.</p> <p><a href="../264/circular-motion.html" target="_blank">Circular motion</a> and <a href="../266/examples-of-circular-motion.html" target="_blank">vertical circles</a></p> <p>The <strong>centripetal force</strong> is the <em>resultant force </em>acting towards the centre that makes a body travel in a circle.</p> <p style="text-align: center;"><span class="math-tex">\(F=m \omega^2 r={mv^2 \over r}\)</span></p> <p>In a 'cyclist on an igloo' problem, the rider is travelling in a vertical circle but on the <em>outside</em>.</p> <p>The centripetal force is therefore: <span class="math-tex">\(mg-N={mv^2\over r}\)</span></p> <p style="text-align: center;"><img alt="" src="../../circular-motion/igloo.png" style="height: 144px; width: 200px;"></p> <p><a href="../219/forces.html" target="_blank">Friction</a></p> <p><em>Friction</em> is a force that opposes the motion of a body in contact with a surface.</p> <p>Friction acts parallel to and along the contact surface. However, it is proportional to the normal force between the surfaces:</p> <p style="text-align: center;"><span class="math-tex">\(F=\mu N\)</span></p> <p>The constant of proportionality, <span class="math-tex">\(\mu\)</span> = the coefficient of friction, and varies depending on whether the body is stationary (static friction, <span class="math-tex">\(\mu_s\)</span>) or moving (dynamic friction, <span class="math-tex">\(\mu_d\)</span>).</p> <p><a href="../220/work-and-energy.html" target="_blank">Energy transfers</a> in a <a href="../1148/ahl-gravitational-fields.html">radial gravitational field</a></p> <p><em>Kinetic</em> energy (E<sub>k</sub>) is due to movement, equal to the amount of work required to make a body move.</p> <p style="text-align: center;"><span class="math-tex">\(E_k={1\over 2} mv^2\)</span></p> <p>When a mass moves parallel to a field line, its potential energy changes. Potential energy is the product of potential and the mass placed in the field:</p> <p style="text-align: center;"><span class="math-tex">\(E_p=mV_g=-G{Mm\over r}\)</span></p> <p>Change in potential energy can be calculated as follows:</p> <p style="text-align: center;"><span class="math-tex">\(\Delta E_p=m\Delta V_g=m\times GM({1\over r_f}-{1\over r_i})\)</span></p> <p><a href="../1148/ahl-gravitational-fields.html" target="_blank">Escape velocity</a></p> <p>A mass in orbit in a gravitational field possesses two types of energy:</p> <ul> <li>Kinetic energy due to its motion, <span class="math-tex">\(E_k={1\over 2}mv^2\)</span></li> <li>Gravitational potential energy due to its position in the field, <span class="math-tex">\(E_p=-G{Mm\over r}\)</span></li> </ul> <p>Total energy, <span class="math-tex">\(E_T=E_k+E_p\)</span>:</p> <p style="text-align: center;"><span class="math-tex">\(E_T={1\over 2}mv^2-G{Mm\over r}\)</span></p> <p>The escape speed is the speed that would just be enough to escape the field.</p> <p style="text-align: center;"><span class="math-tex">\(E_k+E_p=0\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Rightarrow v_\text{esc}=\sqrt{2G{M\over r}}\)</span></p> </section> <div class="greenBg"> <p>By now you will have a feel for the number of marks you have obtained overall. 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