9702_s16_qp_43
A paper of Physics, 9702
Questions:
13
Year:
2016
Paper:
4
Variant:
3
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1
By reference to the definition of gravitational potential, explain why gravitational potential is a negative quantity. Two stars A and B have their surfaces separated by a distance of 1.4 × 1012 m, as illustrated in . star A star B 1.4 = 1012 m P x Point P lies on the line joining the centres of the two stars. The distance x of point P from the surface of star A may be varied. The variation with distance x of the gravitational potential φ at point P is shown in . –2 –4 –6 –8 –10 –12 –14 –16 0.2 0.4 0.6 0.8 1.0 1.2 1.4 x / 1012 m / 108 J kg–1 q A rock of mass 180 kg moves along the line joining the centres of the two stars, from star A towards star B. Use data from to calculate the change in kinetic energy of the rock when it moves from the point where x = 0.1 × 1012 m to the point where x = 1.2 × 1012 m. State whether this change is an increase or a decrease. change = J At a point where x = 0.1 × 1012 m, the speed of the rock is v. Determine the minimum speed v such that the rock reaches the point where x = 1.2 × 1012 m. minimum speed = m s−1
13. Gravitational fields  →  13.4. Gravitational potential
5. Work, energy and power  →  5.2. Gravitational potential energy and kinetic energy
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2
An ideal gas is assumed to consist of atoms or molecules that behave as hard, identical spheres that are in continuous motion and undergo elastic collisions. State two further assumptions of the kinetic theory of gases. 1. 2. Helium-4 (4 2He) may be assumed to be an ideal gas. Show that the mass of one atom of helium-4 is 6.6 × 10−24 g. The mean kinetic energy EK of an atom of an ideal gas is given by the expression EK = 3 2 kT. Calculate the root-mean-square (r.m.s.) speed of a helium-4 atom at a temperature of 27 °C. r.m.s. speed = m s−1
15. Ideal gases  →  15.3. Kinetic theory of gases
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3
State, by reference to displacement, what is meant by simple harmonic motion. A mass is undergoing oscillations in a vertical plane. The variation with displacement x of the acceleration a of the mass is shown in . a x State two reasons why the motion of the mass is not simple harmonic. 1. 2. A block of wood is floating in a liquid, as shown in . oscillation of block liquid block The block is displaced vertically and then released. The variation with time t of the displacement y of the block from its equilibrium position is shown in . 0.4 0.8 1.2 1.6 2.0 2.4 2.0 1.5 1.0 0.5 –0.5 –1.0 –1.5 –2.0 t / s y / cm Use data from to determine the angular frequency ω of the oscillations, ω = rad s−1 the maximum vertical acceleration of the block. maximum acceleration = m s−2 The block has mass 120 g. The oscillations of the block are damped. Calculate the loss in energy of the oscillations of the block during the first three complete periods of its oscillations. energy loss = J
17. Oscillations  →  17.1. Simple harmonic oscillations
17. Oscillations  →  17.2. Energy in simple harmonic motion
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4
State what is meant by the specific acoustic impedance of a medium. The intensity reflection coefficient α is given by the expression α = (Z2 − Z1)2 (Z2 + Z1)2 . Explain the meanings of the symbols in this expression. α : Z2 and Z1: A parallel beam of ultrasound has intensity I0 as it enters a muscle. The beam passes through a thickness of 3.4 cm of muscle before being incident on the boundary with a bone, as shown in . muscle bone intensity I0 entering muscle intensity IT entering bone 3.4 cm The intensity of the ultrasound beam as it passes into the bone is IT.
24. Medical physics  →  24.1. Production and use of ultrasound
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5
The variation with time t of the voltage level of part of an analogue signal is shown in . 0.25 0.50 0.75 1.00 1.25 1.50 time t / ms voltage level The signal is sampled at 0.25 ms intervals. Each sample is converted into a four-bit digital number. lists various times t at which the voltage level is sampled. The digital number for time t = 0 is shown. time t / ms 0.25 0.50 0.75 1.00 1.25 1.50 digital number On , underline the most significant bit (MSB) for the digital number at time t = 0. Complete for the times shown. After transmission of the digital numbers, the signal is passed through a digital-to-analogue converter (DAC). On , plot the transmitted analogue signal from the DAC. 0.25 0.50 0.75 1.00 1.25 1.50 time t / ms voltage level The transmitted signal in has less detail than the original signal in . Suggest and explain two means by which the level of detail in the transmitted signal could be increased. 1. 2.
21. Alternating currents  →  21.2. Rectification and smoothing
19. Capacitance  →  19.3. Discharging a capacitor
17. Oscillations  →  17.1. Simple harmonic oscillations
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6
A solid metal sphere of radius R is isolated in space. The sphere is positively charged so that the electric potential at its surface is VS. The electric field strength at the surface is ES. On the axes of , show the variation of the electric potential with distance x from the centre of the sphere for values of x from x = 0 to x = 3R. 1.0 Vs 0.8 Vs 0.6 Vs 0.4 Vs 0.2 Vs R 2R 3R distance x potential On the axes of , show the variation of the electric field strength with distance x from the centre of the sphere for values of x from x = 0 to x = 3R. 1.0 Es 0.8 Es 0.6 Es 0.4 Es 0.2 Es R 2R 3R distance x field strength
18. Electric fields  →  18.5. Electric potential
18. Electric fields  →  18.3. Electric force between point charges
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7
A student sets up the circuit shown in to measure the charge on a capacitor C for different values of potential difference across the capacitor. V C meter to measure charge The variation with potential difference V of the charge Q stored on the capacitor is shown in . V / V Q / mC State and explain how indicates that there is a systematic error in the readings of one of the meters. Use to determine the capacitance, in μF, of capacitor C. capacitance = μF Use your answer in to determine the additional energy stored in the capacitor C when the potential difference across it is increased from 6.0 V to 9.0 V. energy = J
19. Capacitance  →  19.2. Energy stored in a capacitor
19. Capacitance  →  19.3. Discharging a capacitor
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8
The circuit of an inverting amplifier incorporating an ideal operational amplifier (op-amp) is shown in . V IN R2 R1 V OUT +V –V + – P Explain why point P is known as a virtual earth. Derive an expression, in terms of the resistances R1 and R2, for the gain of the amplifier circuit. Explain your working. A relay and the output terminals of the amplifier circuit are shown in . V OUT On , show how the relay may be connected to the amplifier output so that the relay operates only when VOUT is positive.
10. D.C. circuits  →  10.1. Practical circuits
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9
A thin rectangular slice of aluminium has sides of length 65 mm, 50 mm and 0.10 mm, as shown in . current direction of magnetic field 3.8 A 0.10 mm 50 mm 65 mm P Q Z Y X R S (not to scale) Some of the corners of the slice are labelled. A current I of 3.8 A is normal to face RSXY of the slice. In aluminium, the number of free electrons per unit volume is 6.0 × 1028 m−3. A uniform magnetic field of magnetic flux density B equal to 0.13 T is normal to face QRYZ of the aluminium slice in the direction from Q to P. A Hall voltage VH is developed across the slice and is given by the expression VH = BI ntq . Use to state the magnitude of the distance t. t = mm Calculate the magnitude of the Hall voltage VH. VH = V
20. Magnetic fields  →  20.3. Force on a moving charge
20. Magnetic fields  →  20.4. Magnetic fields due to currents
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10
A coil of insulated wire is wound on a copper core, as illustrated in . insulated wire copper core An alternating current is passed through the coil. The heating effect of the current in the coil is negligible. Explain why the temperature of the core rises. Two hollow tubes of equal length hang vertically as shown in . magnet A plastic tube magnet B aluminium tube One tube is made of plastic and the other of aluminium. Two small similar bar magnets A and B are held above the tubes and then released simultaneously.
20. Magnetic fields  →  20.4. Magnetic fields due to currents
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11
The variation with time t of the sinusoidal current I in a resistor of resistance 450 Ω is shown in . 1.0 0.5 –0.5 –1.0 I / A t / ms Use data from to determine, for the time t = 0 to t = 30 ms, the frequency of the current, frequency = Hz the mean current, mean current = A the root-mean-square (r.m.s.) current, r.m.s. current = A the energy dissipated by the resistor. energy = J
21. Alternating currents  →  21.1. Characteristics of alternating currents
19. Capacitance  →  19.3. Discharging a capacitor
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12
Some of the electron energy bands in a solid are illustrated in . conduction band (partially filled) forbidden band valence band In isolated atoms, electron energy levels have discrete values. Suggest why, in a solid, there are energy bands, rather than discrete energy levels. A light-dependent resistor (LDR) consists of an intrinsic semiconductor. Use band theory to explain the dependence on light intensity of the resistance of the LDR when it is at constant temperature.
9. Electricity  →  9.3. Resistance and resistivity
22. Quantum physics  →  22.4. Energy levels in atoms and line spectra
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13
Copper-66 is a radioactive isotope. When a nucleus of copper-66 decays, the emissions include a β− particle and a γ-ray photon. The count rate produced from a sample of the isotope copper-66 is measured using a detector and counter, as illustrated in . to counter detector radioactive sample shielding State three reasons why the activity of the sample of copper-66 is not equal to the measured count rate. 1. 2. 3. In a time of 42.0 minutes, the count rate from the sample of copper-66 is found to decrease from 3.62 × 104 Bq to 1.21 × 102 Bq. Calculate the half-life of copper-66. half-life = minutes The γ-ray photons emitted from radioactive nuclei have specific energies, dependent on the nucleus emitting the photons. By comparison with emission line spectra, suggest what can be deduced about energy levels in nuclei.
23. Nuclear physics  →  23.2. Radioactive decay
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