9702_m16_qp_42
A paper of Physics, 9702
Questions:
13
Year:
2016
Paper:
4
Variant:
2
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1
State Newton’s law of gravitation. A satellite of mass m has a circular orbit of radius r about a planet of mass M. It may be assumed that the planet and the satellite are uniform spheres that are isolated in space. Show that the linear speed v of the satellite is given by the expression GM r v = where G is the gravitational constant. Explain your working. Two moons A and B have circular orbits about a planet, as illustrated in . B A planet vA vB rB rA (not to scale) Moon A has an orbital radius rA of 1.3 × 108 m, linear speed vA and orbital period TA. Moon B has an orbital radius rB of 2.2 × 1010 m, linear speed vB and orbital period TB. Determine the ratio 1. vA vB , ratio = 2. TA TB . ratio = The planet spins about its own axis with angular speed 1.7 × 10–4 rad s–1. Moon A is always above the same point on the planet’s surface. Determine the orbital period TB of moon B. TB = s
13. Gravitational fields  →  13.2. Gravitational force between point masses
13. Gravitational fields  →  13.3. Gravitational field of a point mass
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2
State what is meant by internal energy, the basic assumption of the kinetic theory of gases that leads to the conclusion that there is zero potential energy between the molecules of an ideal gas. The pressure p and volume V of an ideal gas are related by pV = 1 3 Nm 〈c2〉 where N is the number of molecules, m is the mass of a molecule and 〈c2〉 is the mean-square speed of the molecules. Use this equation to show that the mean kinetic energy 〈EK〉 of a molecule is given by 〈EK〉 = 3 2 kT where k is the Boltzmann constant and T is the thermodynamic temperature. A cylinder contains 17 g of oxygen gas at a temperature of 12 °C. The mass of 1.0 mol of oxygen gas is 32 g. It may be assumed that the oxygen behaves as an ideal gas. Calculate, for the oxygen gas in the cylinder, the mean kinetic energy of a molecule, mean kinetic energy = J the number of molecules, number = the total internal energy. internal energy = J
15. Ideal gases  →  15.3. Kinetic theory of gases
16. Thermodynamics  →  16.1. Internal energy
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3
Define specific heat capacity. A student carries out an experiment to determine the specific heat capacity of a liquid using the apparatus illustrated in . liquid in, temperature 19.5 °C liquid out, temperature 25.5 °C tube heating coil Liquid enters the tube at a constant temperature of 19.5 °C and leaves the tube at a temperature of 25.5 °C. The mass of liquid flowing through the tube per unit time is m. Electrical power P is dissipated in the heating coil. The student changes m and adjusts P until the final temperature of the liquid leaving the tube is 25.5 °C. The data shown in are obtained. m / g s–1 P/ W 1.11 33.3 1.58 44.9 Suggest why the student obtains data for two values of m, rather than for one value. Calculate the specific heat capacity of the liquid. Show your working. specific heat capacity = J kg–1 K–1 When the heating coil in dissipates 33.3 W of power, the potential difference V across the coil is given by the expression V = 27.0 sin (395t). The potential difference is measured in volts and the time t is measured in seconds. Determine the resistance of the coil. resistance = Ω
14. Temperature  →  14.3. Specific heat capacity and specific latent heat
14. Temperature  →  14.2. Temperature scales
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4
An object of mass 80 g oscillates with simple harmonic motion. The variation with time t of the displacement x of the object is shown in . 0 0 2.0 1.0 –2.0 –1.0 0.1 0.2 0.3 0.4 0.5 t / s x / cm Use to determine the amplitude and the period of the oscillations. amplitude = cm period = s Use and your answers in to calculate the kinetic energy of the object at time t = 0.19 s. kinetic energy = J
17. Oscillations  →  17.2. Energy in simple harmonic motion
17. Oscillations  →  17.1. Simple harmonic oscillations
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5
A digital signal is produced by sampling an analogue signal and passing the samples through an analogue-to-digital converter (ADC). State what is meant by a digital signal. State one change to the sampling or to the ADC that will improve the accuracy of reproduction of the original analogue signal. The least significant bit of the four-bit digital number 1100 represents a signal voltage of 2.5 mV. Determine the signal voltage, in mV, represented by this digital number. voltage = mV
24. Medical physics  →  24.2. Production and use of X-rays
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6
A parallel beam of ultrasound is incident normally on the surface of a layer of fat of thickness 1.1 cm, as shown in . I1 I2 I4 I3 1.1 cm muscle fat ultrasound beam For the ultrasound, I1 is the intensity just after entering the surface of the fat layer, I2 is the intensity incident on the fat-muscle boundary, I3 is the intensity reflected from the fat-muscle boundary, I4 is the intensity received back at the surface of the fat layer. Some data for the fat are given in . specific acoustic impedance Z 1.4 × 106 kg m–2 s–1 density ρ 940 kg m–3 absorption coefficient μ 48 m–1 Calculate the time interval between a short pulse of ultrasound initially entering the layer of fat and then returning back to the surface of the fat layer. time = s Calculate the ratio I2 I1 . ratio = Intensity I4 is 0.33% of intensity I1. Determine the ratio I3 I2 . ratio = The specific acoustic impedance of the muscle is greater than that of the fat. State the effect, if any, on the value of the ratio I3 I2 of an increase in the difference between the specific acoustic impedance of the muscle and that of the fat.
24. Medical physics  →  24.1. Production and use of ultrasound
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7
Define capacitance. Three capacitors of capacitances C1, C2 and C3 are initially uncharged. They are then connected in series to a battery, as shown in . C1 C2 V C3 The battery applies a potential difference V across the three capacitors. Show that the combined capacitance C of the capacitors is given by C = 1 C1 + 1 C2 + 1 C3 . A battery of e.m.f. 12 V and negligible internal resistance is connected to a network of two capacitors and a resistor, as shown in . A B 600 +F 200 +F 12 V The capacitors have capacitances of 200 μF and 600 μF. The switch has two positions, A and B. The switch is moved to position A. Calculate 1. the combined capacitance of the two capacitors, combined capacitance = μF 2. the charge on the 600 μF capacitor, charge = C 3. the potential difference across the 600 μF capacitor. potential difference = V The switch is now moved from position A to position B. Calculate the potential difference across the 600 μF capacitor when it has discharged 50% of its initial energy. potential difference = V
19. Capacitance  →  19.1. Capacitors and capacitance
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8
State two effects of negative feedback on the gain of an amplifier incorporating an operational amplifier (op-amp). 1. 2. An incomplete diagram of an amplifier circuit incorporating an ideal operational amplifier is shown in . – + VIN VOUT +8.0 V 7.2 k1 –8.0 V The amplifier has a voltage gain of +5.0. Complete the circuit diagram of . Calculate the resistance of any additional resistor you have drawn on . resistance = kΩ shows the variation with time of the input potential VIN. time / ms potential / V VIN On , draw the variation with time of the output potential VOUT.
10. D.C. circuits  →  10.1. Practical circuits
19. Capacitance  →  19.3. Discharging a capacitor
7. Waves  →  7.1. Progressive waves
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9
A particle of charge +q and mass m is travelling with a constant speed of 1.6 × 105 m s–1 in a vacuum. The particle enters a uniform magnetic field of flux density 9.7 × 10–2 T, as shown in . particle charge +q mass m speed 1.6 × 105 m s–1 uniform magnetic field out of the plane of the paper flux density 9.7 × 10–2 T path of particle The magnetic field direction is perpendicular to the initial velocity of the particle and perpendicular to, and out of, the plane of the paper. A uniform electric field is applied in the same region as the magnetic field so that the particle passes undeviated through the fields. State and explain the direction of the electric field. Calculate the magnitude of the electric field strength. Explain your working. electric field strength = V m–1 The electric field is now removed so that the positively-charged particle follows a curved path in the magnetic field. This path is an arc of a circle of radius 4.0 cm. Calculate, for the particle, the ratio q m. ratio = C kg–1 The particle has a charge of 3e where e is the elementary charge. Use your answer in to determine the mass, in u, of the particle. mass = u The particle is the nucleus of an atom. State the number of protons and the number of neutrons in this nucleus. number of protons = number of neutrons =
20. Magnetic fields  →  20.3. Force on a moving charge
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10
A small coil of wire is situated in a non-uniform magnetic field, as shown in . constant velocity coil, 40 turns non-uniform magnetic field x P The coil consists of 40 turns of wire and moves with a constant speed in a straight line. The coil has displacement x from a fixed point P. The variation with x of the magnetic flux Φ in the coil is shown in . x / cm / 10–6 Wb \ The coil is moved at constant speed between point P and the point where x = 3.0 cm. Calculate the change in magnetic flux linkage of the coil. change in flux linkage = Wb The e.m.f. induced in the coil is 5.0 × 10–4 V. Determine the speed of the coil. speed = m s–1 On , sketch the variation with x of the e.m.f. E induced in the coil for values of x from x = 0 to x = 6.0 cm. x / cm E
20. Magnetic fields  →  20.4. Magnetic fields due to currents
20. Magnetic fields  →  20.5. Electromagnetic induction
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11
With reference to the photoelectric effect, state what is meant by the threshold frequency. Electromagnetic radiation of wavelength λ is incident on a metal surface. Electrons of maximum kinetic energy EMAX are emitted. On , sketch the variation with 1/λ of EMAX. EMAX 1 /h State an equation relating the gradient of the graph drawn on to the Planck constant h. Explain any symbols you use. Explain why, for any particular wavelength of electromagnetic radiation, most of the electrons are emitted with kinetic energies less than the maximum value EMAX. Light of a particular wavelength is incident on a metal surface and gives rise to a photoelectric current. The wavelength is reduced. The intensity of the light is kept constant. State and explain the effect, if any, on the photoelectric current.
22. Quantum physics  →  22.2. Photoelectric effect
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13
Beryllium-7 (7 4 Be) is produced in the upper atmosphere and then sinks down onto the Earth’s surface. Nuclei of beryllium-7 decay with a half-life of 53.3 days to form stable nuclei. The activity of a sample of beryllium-7 on a tree leaf is 39 mBq. Show that the decay constant of beryllium-7 is 1.5 × 10–7 s–1. Determine the mass of the beryllium-7 on the leaf. mass = kg The leaf is covered so that no further beryllium-7 is added to the existing sample from the atmosphere. Calculate the time that must elapse before the activity of the sample is reduced to 2.0 mBq. time = s
23. Nuclear physics  →  23.2. Radioactive decay
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