Outline what is meant by gravitational field strength at a point.

Newton’s law of gravitation applies to point masses. Suggest why the law can be applied to a satellite orbiting Mars.

Mars has a mass of 6.4 × 10²³ kg. Show that, for Mars, k is about 9 × 10^–13s²m^–3.

The time taken for Mars to revolve on its axis is 8.9 × 10⁴ s. Calculate, in m s^–1, the orbital speed of the satellite.

Show that the intensity of solar radiation at the orbit of Mars is about 600 W m^–2.

Determine, in K, the mean surface temperature of Mars. Assume that Mars acts as a black body.

The atmosphere of Mars is composed mainly of carbon dioxide and has a pressure less than 1 % of that on the Earth. Outline why the mean temperature of Earth is strongly affected by gases in its atmosphere but that of Mars is not.

force per unit mass ✔

acting on a small/test/point mass «placed at the point in the field» ✔

Mars is spherical/a sphere «and of uniform density so behaves as a point mass» ✔

satellite has a much smaller mass/diameter/size than Mars «so approximates to a point mass» ✔

«$\frac{m{v}^2}{r}=\frac{GMm}{r^2}$ hence» $v=\sqrt{\frac{GM}{R}}$. Also $v=\frac{2\pi R}{T}$

OR

$m{\omega }^{2}r=\frac{GMm}{r^2}$ hence ${\omega }^2=\frac{GM}{R^3}$ ✔

uses either of the above to get $T^2=\frac{4{\pi }^2}{GM}{R}^3$

OR

uses $k=\frac{4{\pi }^2}{GM}$ ✔

k = 9.2 × 10⁻¹³ / 9.3 × 10⁻¹³

Unit not required

$R^3=\frac{T^2}{k}=\frac{{\left(8.9\times {10}^4\right)}^2}{9.25\times {10}^{-13}}$  R = 2.04 × 10⁷ «m» ✔

v = «$\omega r=\frac{2\pi \times 2.04\times {10}^7}{89000}=$» 1.4 × 10³ «m s^–1»

OR

v = «$\sqrt{\frac{GM}{R}}=\sqrt{\frac{6.67\times {10}^{-11}\times 6.4\times {10}^{23}}{2.04\times {10}^7}}=$» 1.4 × 10³ «m s^–1» ✔

use of $I\propto \frac{1}{r^2}$ «1.36 × 10³ × $\frac{1}{{1.5}^2}$» ✔

604 «W m^–2» ✔

use of $\frac{600}{4}$ for mean intensity ✔

temperature/K = «$\sqrt[4]{\frac{600}{4\times 5.67\times {10}^{-8}}}=$» 230 ✔

reference to greenhouse gas/effect ✔

recognize the link between molecular density/concentration and pressure ✔

low pressure means too few molecules to produce a significant heating effect

OR

low pressure means too little radiation re-radiated back to Mars ✔

The greenhouse effect can be described, it doesn’t have to be named

Identify the laws of conservation that are represented by Kirchhoff’s circuit laws.

State the emf of the cell.

Deduce the internal resistance of the cell.

Calculate the reading on the voltmeter.

Comment on the implications of your answer to (c)(i) for cell B.

Outline why electricity is a secondary energy source.

Some fuel sources are renewable. Outline what is meant by renewable.

A fully charged cell of emf 6.0 V delivers a constant current of 5.0 A for a time of 0.25 hour until it is completely discharged.

The cell is then re-charged by a rectangular solar panel of dimensions 0.40 m × 0.15 m at a place where the maximum intensity of sunlight is 380 W m⁻².

The overall efficiency of the re-charging process is 18 %.

Calculate the minimum time required to re-charge the cell fully.

Outline why research into solar cell technology is important to society.

« conservation of » charge ✓

« conservation of » energy ✓

Allow [1] max if they explicitly refer to Kirchhoff’ laws linking them to the conservation laws incorrectly.

12 V ✓

I = 2.0 A OR 12 = I (r + 4) OR 4 = Ir OR 8 = 4I ✓

«Correct working to get » r = 2.0 «Ω» ✓

Allow any valid method.

Allow ECF from (b)(i)

Loop equation showing EITHER correct voltages, i.e., 10 – 4 on one side or both emf’s positive on different sides of the equation OR correct resistances, i.e. I (1 + 2) ✓

10−4 = I (1 + 2) OR I = 2.0 «A» seen ✓

V = 8.0 «V» ✓

Allow any valid method

Charge is being driven through the 4.0 V cell OR it is being (re-)charged ✓

is generated from primary/other sources ✓

«a fuel » that can be replenished/replaced within a reasonable time span

OR

«a fuel» that can be replaced faster than the rate at which it is consumed

OR

renewables are limitless/never run out

OR

«a fuel» produced from renewable sources

OR

gives an example of a renewable (biofuel, hydrogen, wood, wind, solar, tidal, hydro etc..) ✓

OWTTE

ALTERNATIVE 1

«energy output of the panel =» Vlt OR 6 x 5 x 0.25 x 3600 OR 27000 «J» ✓

«available power =» 380 x 0.4 x 0.15 x 0.18 OR 4.1 «W» ✓

$t=$ «$\frac{27000}{4.1}$=» 6600 «s» ✓

ALTERNATIVE 2

«energy needed from Sun =» $\frac{vlt}{eff}$ OR $\frac{6\times 5\times 0.25\times 3600}{0.18}$ OR 150000 «J» ✓

« incident power=» 380 x 0.4 x 0.15 OR 22.8 «W» ✓

$t=$ «$\frac{150000}{22.8}$=» 6600 «s» ✓

Allow ECF for MP3

Accept final answer in minutes (110) or hours (1.8).

coherent reason ✓

e.g., to improve efficiency, is non-polluting, is renewable, does not produce greenhouse gases, reduce use of fossil fuels

Do not allow economic reasons

a) Most just stated Kirchhoff's laws rather than the underlying laws of conservation of energy and charge, basically describing the equations from the data booklet. When it came to guesses, energy and momentum were often the two, although even a baryon and lepton number conservation was found. It cannot be emphasised enough the importance of correctly identifying the command verb used to introduce the question. In this case, identify, with the specific reference to conservation laws, seem to have been explicit tips not picked up by some candidates.

bi) This was probably the easiest question on the paper and almost everybody got it right. 12V. Some calculations were seen, though, that contradict the command verb used. State a value somehow implies that the value is right in front to be read or interpreted suitably.

bii) In the end a lot of the answers here were correct. Some obtained 2 ohms and were able to provide an explanation that worked. A very few negative answers were found, suggesting that some candidates work mechanically without properly reflecting in the nature of the value obtained.

ci) A lot of candidates figured out they had to do some sort of loop here but most had large currents in the voltmeter. Currents of 2 A and 10 A simultaneously were common. Some very good and concise work was seen though, leading to correct steps to show a reading of 8V.

cii) This question was cancelled due to an internal reference error. The paper total was adjusted in grade award. This is corrected for publication and future teaching use.

di) The vast majority of candidates could explain why electricity was a secondary energy source.

dii) An ideal answer was that renewable fuels can be replenished faster than they are consumed. However, many imaginative alternatives were accepted.

ei) This question was often very difficult to mark. Working was often scattered all over the answer box. Full marks were not that common, most candidates achieved partial marks. The commonest problem was determining the energy required to charge the battery. It was also common to see a final calculation involving a power divided by a power to calculate the time.

eii) Almost everybody could give a valid reason why research into solar cells was important. Most answers stated that solar is renewable. There were very few that didn't get a mark due to discussing economic reasons.

State what is meant by binding energy of a nucleus.

Outline why quantities such as atomic mass and nuclear binding energy are often expressed in non-SI units.

Show that the energy released in the reaction is about $180 \mathrm{MeV}$.

Estimate, in $\mathrm{J} {\mathrm{kg}}^{-1}$, the specific energy of U-235.

The power station has a useful power output of $1.2 \mathrm{GW}$ and an efficiency of $36 \%$. Determine the mass of U-235 that undergoes fission in one day.

The specific energy of fossil fuel is typically $30 \text{MJ} {\text{kg}}^{–1}$. Suggest, with reference to your answer to (b)(i), one advantage of U-235 compared with fossil fuels in a power station.

Write down the proton number of nuclide X.

State the half-life of Sr-94.

Calculate the mass of Sr-94 remaining in the sample after $10$ minutes.

energy required to «completely» separate the nucleons
OR
energy released when a nucleus is formed from its constituent nucleons ✓

Allow protons AND neutrons.

the values «in SI units» would be very small ✓

$140\times 8.29+94\times 8.59-235\times 7.59$ OR $184 «\mathrm{MeV}»$ ✓

see $«\mathrm{energy}=» 180\times {10}^6\times 1.60\times {10}^{-19}$ AND $«\mathrm{mass}=» 235\times 1.66\times {10}^{-27}$ ✓

$7.4\times {10}^{13} «\mathrm{J} {\mathrm{kg}}^{-1}»$ ✓

energy produced in one day$=\frac{1.2\times {10}^9\times 24\times 3600}{0.36}=2.9\times {10}^{14} «\mathrm{J}»$ ✓

mass$=\frac{2.9\times {10}^{14}}{7.4\times {10}^{13}}=3.9 «\mathrm{kg}»$ ✓

«specific energy of uranium is much greater than that of coal, hence» more energy can be produced from the same mass of fuel / per $\text{kg}$
OR
less fuel can be used to create the same amount of energy ✓

$39$ ✓

Do not allow ${}_{39}{}^{94}\mathrm{X}$ unless the proton number is indicated.

$75 «\mathrm{s}»$ ✓

ALTERNATIVE 1

$10 \min$$=8 t_{1/2}$ ✓

mass remaining$=1.0\times {\left(\frac{1}{2}\right)}^8=3.9\times {10}^{-3}«\mathrm{kg}»$ ✓

ALTERNATIVE 2

decay constant$=«\frac{\ln 2}{75}=»9.24\times {10}^{-3} «{\mathrm{s}}^{-1}»$ ✓

mass remaining$=1.0\times e^{-9.24\times {10}^{-3}\times 600}=3.9\times {10}^{-3} «\mathrm{kg}»$ ✓

Generally, well answered but candidates did miss the mark by discussing the constituents of a nucleus rather than the nucleons, or protons and neutrons. There seemed to be fewer comments than usual about 'the energy required to bind the nucleus together'. 

Well answered with some candidates describing the values as too large or small.

Well answered.

This caused problems for some with mass often correctly calculated but energy causing more difficulty with the eV conversion either being inaccurate or omitted. Candidates were allowed error carried forward for the second mark as long as they were dividing an energy by a mass.

Most candidates had the right idea, but common problems included forgetting the efficiency or not converting to days.

HL only. This was well answered.

Most candidates answered this correctly.

Most candidates answered this correctly.

This was answered well with most candidates (even at HL) going down the number of half-lives route rather than the exponential calculation route.

Outline the conditions necessary for simple harmonic motion (SHM) to occur.

A wave of amplitude 4.3 m and wavelength 35 m, moves with a speed of 3.4 m s^–1. Calculate the maximum vertical speed of the buoy.

Sketch a graph to show the variation with time of the generator output power. Label the time axis with a suitable scale.

Outline, with reference to energy changes, the operation of a pumped storage hydroelectric system.

The water in a particular pumped storage hydroelectric system falls a vertical distance of 270 m to the turbines. Calculate the speed at which water arrives at the turbines. Assume that there is no energy loss in the system.

The hydroelectric system has four 250 MW generators. Determine the maximum time for which the hydroelectric system can maintain full output when a mass of 1.5 x 10¹⁰ kg of water passes through the turbines.

Not all the stored energy can be retrieved because of energy losses in the system. Explain two such losses.

force/acceleration proportional to displacement «from equilibrium position»

and directed towards equilibrium position/point
OR
and directed in opposite direction to the displacement from equilibrium position/point

Do not award marks for stating the defining equation for SHM.
Award [1 max] for a ω–=²x with a and x defined.

frequency of buoy movement $=\frac{3.4}{35}$ or 0.097 «Hz»

OR

time period of buoy $=\frac{35}{3.4}$ or 10.3 «s» or 10 «s»

v = «$\frac{2\pi x_0}{T}$ or $2\pi f{x}_0$» $=\frac{2\times \pi \times 4.3}{10.3}$ or $2\times \pi \times 0.097\times 4.3$

2.6 «m s^–1»

peaks separated by gaps equal to width of each pulse «shape of peak roughly as shown»

one cycle taking 10 s shown on graph

Judge by eye.
Do not accept cos₂ or sin₂ graph
At least two peaks needed.
Do not allow square waves or asymmetrical shapes.
Allow ECF from (b)(i) value of period if calculated.

PE of water is converted to KE of moving water/turbine to electrical energy «in generator/turbine/dynamo»

idea of pumped storage, ie: pump water back during night/when energy cheap to buy/when energy not in demand/when there is a surplus of energy

specific energy available = «gh =» 9.81 x 270 «= 2650J kg^–1»

OR

mgh $=\frac{1}{2}$mv²

OR

v² = 2gh

v = 73 «ms^–1»

Do not allow 72 as round from 72.8

total energy = «mgh = 1.5 x 10¹⁰ x 9.81 x 270=» 4.0 x 10¹³ «J»

OR

total energy = «$\frac{1}{2}m{v}^2=\frac{1}{2}\times 1.5\times {10}^{10}\times$ (answer (c)(ii))² =» 4.0 x 10¹³ «J»

time = «$\frac{4.0\times {10}^{13}}{4\times 2.5\times {10}^8}$» 11.1h or 4.0 x 10⁴ s

Use of 3.97 x 10¹³ «J» gives 11 h.

For MP2 the unit must be present.

friction/resistive losses in pipe/fluid resistance/turbulence/turbine or generator «bearings»
OR
sound energy losses from turbine/water in pipe 

thermal energy/heat losses in wires/components

water requires kinetic energy to leave system so not all can be transferred

Must see “seat of friction” to award the mark.

Do not allow “friction” bald.

Show that the intensity of the solar radiation at the location of Titan is 16 W m⁻².

Titan has an atmosphere of nitrogen. The albedo of the atmosphere is 0.22. The surface of Titan may be assumed to be a black body. Explain why the average intensity of solar radiation absorbed by the whole surface of Titan is 3.1 W m⁻².

Show that the equilibrium surface temperature of Titan is about 90 K.

The mass of Titan is 0.025 times the mass of the Earth and its radius is 0.404 times the radius of the Earth. The escape speed from Earth is 11.2 km s⁻¹. Show that the escape speed from Titan is 2.8 km s⁻¹.

The orbital radius of Titan around Saturn is $R$ and the period of revolution is $T$.

Show that $T^2=\frac{4{\mathrm{\pi }}^2{R}^{ 3}}{GM}$ where $M$ is the mass of Saturn.

The orbital radius of Titan around Saturn is 1.2 × 10⁹m and the orbital period is 15.9 days. Estimate the mass of Saturn.

Show that the mass of a nitrogen molecule is 4.7 × 10⁻²⁶ kg.

Estimate the root mean square speed of nitrogen molecules in the Titan atmosphere. Assume an atmosphere temperature of 90 K.

Discuss, by reference to the answer in (b), whether it is likely that Titan will lose its atmosphere of nitrogen.

incident intensity $\frac{1360}{9.3^2}$ OR $15.7\approx 16$ «W m⁻²» ✓

Allow the use of 1400 for the solar constant.

exposed surface is ¼ of the total surface ✓

absorbed intensity = (1−0.22) × incident intensity ✓

0.78 × 0.25 × 15.7  OR  3.07 «W m⁻²» ✓

Allow 3.06 from rounding and 3.12 if they use 16 W m⁻².

σT ⁴ = 3.07

OR

T = 86 «K» ✓

$v=«\sqrt{\frac{2GM}{R}}=»\sqrt{\frac{0.025}{0.404}}\times 11.2$

OR

$2.79$ «km s⁻¹» ✓

correct equating of gravitational force / acceleration to centripetal force / acceleration ✓

correct rearrangement to reach the expression given ✓

Allow use of $\sqrt{\frac{GM}{R}}=\frac{2\mathrm{\pi }R}{T}$ for MP1.

$T=15.9\times 24\times 3600$ «s» ✓

$M=\frac{4{\mathrm{\pi }}^2{\left(1.2\times {10}^9\right)}^3}{6.67\times {10}^{-11}\times {\left(15.9\times 24\times 3600\right)}^2}=5.4\times {10}^{26}$«kg» ✓

Award [2] marks for a bald correct answer.

Allow ECF from MP1.

$m=\frac{28\times {10}^{-3}}{6.02\times {10}^{23}}$

OR

$4.65\times {10}^{-26}$ «kg» ✓

$«\frac{1}{2}m{v}^2=\frac{3}{2}kT\Rightarrow »v=\sqrt{\frac{3kT}{m}}$ ✓

$v=«\sqrt{\frac{3\times 1.38\times {10}^{-23}\times 90}{4.651\times {10}^{-26}}}=»283\approx 300$ «ms⁻¹» ✓

Award [2] marks for a bald correct answer.

Allow 282 from a rounded mass.

no, molecular speeds much less than escape speed ✓

Allow ECF from incorrect (d)(ii).

Identify the missing information for this decay.

On the graph, sketch how the number of boron nuclei in the sample varies with time.

After 4.3 × 10⁶ years,

$$\frac{\text{number of produced boron nuclei}}{\text{number of remaining beryllium nuclei}}=7.$$

Show that the half-life of beryllium-10 is 1.4 × 10⁶ years.

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 10¹¹ atoms of beryllium-10. The present activity of the sample is 8.0 × 10⁻³ Bq.

Determine, in years, the age of the sample.

State what is meant by thermal radiation.

Discuss how the frequency of the radiation emitted by a black body can be used to estimate the temperature of the body.

Calculate the peak wavelength in the intensity of the radiation emitted by the ice sample.

The temperature in the laboratory is higher than the temperature of the ice sample. Describe one other energy transfer that occurs between the ice sample and the laboratory.

${}_4^{10}\text{Be}{\to }_5^{10}\text{B}{+}_{-1}^0\text{e}+{\overline{\text{V}}}_{\text{e}}$

antineutrino AND charge AND mass number of electron ${}_{-1}^0\text{e}$, $\overline{\text{V}}$

conservation of mass number AND charge ${}_5^{10}\text{B}$, ${}_4^{10}\text{Be}$

Do not accept V.

Accept $\overline{V}$ without subscript e.

[2 marks]

correct shape ie increasing from 0 to about 0.80 N₀

crosses given line at 0.50 N₀

[2 marks]

ALTERNATIVE 1

fraction of Be = $\frac{1}{8}$, 12.5%, or 0.125

therefore 3 half lives have elapsed

$t_{\frac{1}{2}}=\frac{4.3\times {10}^6}{3}=1.43\times {10}^6$ «≈ 1.4 × 10⁶» «y»

ALTERNATIVE 2

fraction of Be = $\frac{1}{8}$, 12.5%, or 0.125

$\frac{1}{8}={\text{e}}^{-\lambda }(4.3\times {10}^6)$ leading to λ = 4.836 × 10^–7 «y»^–1

$\frac{\ln 2}{\lambda }$ = 1.43 × 10⁶ «y»

Must see at least one extra sig fig in final answer.

[3 marks]

λ «= $\frac{\ln 2}{1.4\times {10}^6}$» = 4.95 × 10^–7 «y^–1»

rearranging of A = λN₀e^–λt to give –λt = ln $\frac{8.0\times {10}^{-3}\times 365\times 24\times 60\times 60}{4.95\times {10}^{-7}\times 7.6\times {10}^{11}}$ «= –0.400»

t = $\frac{-0.400}{-4.95\times {10}^{-7}}=8.1\times {10}^5$ «y»

Allow ECF from MP1

[3 marks]

emission of (infrared) electromagnetic/infrared energy/waves/radiation.

[1 mark]

the (peak) wavelength of emitted em waves depends on temperature of emitter/reference to Wein’s Law

so frequency/color depends on temperature

[2 marks]

$\lambda =\frac{2.90\times {10}^{-3}}{253}$

= 1.1 × 10^–5 «m»

Allow ECF from MP1 (incorrect temperature).

[2 marks]

from the laboratory to the sample

conduction – contact between ice and lab surface.

OR

convection – movement of air currents

Must clearly see direction of energy transfer for MP1.

Must see more than just words “conduction” or “convection” for MP2.

[2 marks]

Show that the intensity radiated by the oceans is about 400 W m^-2.

Explain why some of this radiation is returned to the oceans from the atmosphere.

Calculate the additional intensity that must be lost by the oceans so that the water temperature remains constant.

Suggest a mechanism by which the additional intensity can be lost.

5.67 × 10⁻⁸ × 289⁴

OR

= 396«W m⁻²» ✔

«≈ 400 W m⁻²»

«most of the radiation emitted by the oceans is in the» infrared ✔

«this radiation is» absorbed by greenhouse gases/named greenhouse gas in the atmosphere ✔

«the gases» reradiate/re-emit ✔

partly back towards oceans/in all directions/awareness that radiation in other directions is also present ✔

water loses 396 − 330/66 «W m ⁻²» ✔

extra intensity that must be lost is «170 − 66» = 104 ≈ 100 «W m⁻²» ✔

OR

absorbed by water 330 + 170/500 «W m⁻²»✔

extra intensity that must be lost is «500 − 396» = 104 ≈ 100 «W m⁻²» ✔

conduction to the air above

OR

«mainly» evaporation

OR

melting ice at the poles

OR

reflection of sunlight off the surface of the ocean ✔

Do not accept convection or radiation.

This was well answered with candidates scoring the mark for either a correct substitution or an answer given to at least one more sf than the show that value. Some candidates used 298 rather than 289.

For many this was a well-rehearsed answer which succinctly scored full marks. For others too many vague terms were used. There was much talk about energy being trapped or reflected and the ozone layer was often included. The word ‘albedo’ was often written down with no indication of what it means and ‘the albedo effect also featured.

This was well-answered, a very straightforward 2 marks.

Many candidates didn’t understand this question and thought that the answer needed to be some form of human activity that would reduce global temperature rise.