HL Paper 2
There is a proposal to place a satellite in orbit around planet Mars.
The satellite is to have an orbital time T equal to the length of a day on Mars. It can be shown that
T2 = kR3
where R is the orbital radius of the satellite and k is a constant.
The ratio = 1.5.
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 × 10–13 s2 m–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.
A cell is connected to an ideal voltmeter, a switch S and a resistor R. The resistance of R is 4.0 Ω.
When S is open the reading on the voltmeter is 12 V. When S is closed the voltmeter reads 8.0 V.
Electricity can be generated using renewable resources.
The voltmeter is used in another circuit that contains two secondary cells.
Cell A has an emf of 10 V and an internal resistance of 1.0 Ω. Cell B has an emf of 4.0 V and an internal resistance of 2.0 Ω.
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.
One possible fission reaction of uranium-235 (U-235) is
Mass of one atom of U-235
Binding energy per nucleon for U-235
Binding energy per nucleon for Xe-140
Binding energy per nucleon for Sr-94
A nuclear power station uses U-235 as fuel. Assume that every fission reaction of U-235 gives rise to of energy.
A sample of waste produced by the reactor contains of strontium-94 (Sr-94). Sr-94 is radioactive and undergoes beta-minus () decay into a daughter nuclide X. The reaction for this decay is
.
The graph shows the variation with time of the mass of Sr-94 remaining in the sample.
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 .
Estimate, in , the specific energy of U-235.
The power station has a useful power output of and an efficiency of . Determine the mass of U-235 that undergoes fission in one day.
The specific energy of fossil fuel is typically . 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 minutes.
A buoy, floating in a vertical tube, generates energy from the movement of water waves on the surface of the sea. When the buoy moves up, a cable turns a generator on the sea bed producing power. When the buoy moves down, the cable is wound in by a mechanism in the generator and no power is produced.
The motion of the buoy can be assumed to be simple harmonic.
Water can be used in other ways to generate energy.
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.
Titan is a moon of Saturn. The Titan-Sun distance is 9.3 times greater than the Earth-Sun distance.
The molar mass of nitrogen is 28 g mol−1.
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 and the period of revolution is .
Show that where is the mass of Saturn.
The orbital radius of Titan around Saturn is 1.2 × 109 m 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.
The radioactive nuclide beryllium-10 (Be-10) undergoes beta minus (β–) decay to form a stable boron (B) nuclide.
The initial number of nuclei in a pure sample of beryllium-10 is N0. The graph shows how the number of remaining beryllium nuclei in the sample varies with time.
An ice sample is moved to a laboratory for analysis. The temperature of the sample is –20 °C.
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,
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.
The average temperature of ocean surface water is 289 K. Oceans behave as black bodies.
The intensity in (b) returned to the oceans is 330 W m-2. The intensity of the solar radiation incident on the oceans is 170 W m-2.
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.