One student complains that this is impossible because the car would not be able to stop before hitting the cab of the lorry.

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Lorraine Chandler
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1 Total 102 marks 1 hour and 45 minutes 31. Two students are watching an action film in which a car drives down a ramp onto the back of a moving lorry. Both are moving at high speed, the car slightly faster than the lorry. One student complains that this is impossible because the car would not be able to stop before hitting the cab of the lorry. The car has mass 1250 kg and is moving at a speed of 28.0 m s 1. The lorry has mass 3500 kg and a speed of 25.5 m s 1. The length of the flat back of the lorry allows a braking distance of 5.0 m. By considering both momentum and energy show that the stunt is possible, provided a minimum force of about 600 N slows the car down. You should support your explanations with calculations. Treat the situation as one in which two objects join together.

2 (Total 8 marks) 42. On one type of theme park ride, a boat swings freely along a circular path from successively higher starting positions. As the boat moves through the lowest point on its swing, the riders are travelling at high speeds, and feel quite big forces on them. With some rides, such as Rush at Thorpe Park, the highest starting point is with the supporting arm horizontal as shown. 18 m Rush boat at starting point Boat The length of the supporting arm of Rush is 18 m. The mass of a typical rider is 70 kg. (a) Calculate the maximum g-force felt by a typical rider on Rush. forcefromseat g-force = weight of rider

3 (5) (b) Two students in the queue are having a discussion. A says: If they made a new ride twice as big the g-force at the bottom would be amazing! B says: I think the g-force wouldn t be any different. With reference to your calculation, explain which student is correct. (1) (Total 6 marks) 171. Most types of microphone detect sound because the sound waves cause a diaphragm to vibrate. In one type of microphone this diaphragm forms one plate of a parallel plate

4 capacitor. As the diaphragm plate moves. the capacitance chances. Moving the plates closer together increases the capacitance. Moving the plates further apart reduces the capacitance. This effect is used to produce the electrical signal. The circuit shown below consists of a 3 V supply, an uncharged capacitor microphone C. a resistor R. and a switch S. The switch S is closed. Sketch a graph of the voltage across the capacitor microphone against time. Assume that the capacitor microphone is not detecting any sound. V/V RC t (3) Explain why movement of the diaphragm causes a potential difference (the signal) across R. (4)

5 (Total 7 marks) 172. The results of particle collisions are observed using particle detectors. Sometimes the products of these collisions are themselves unstable and decay to give further particles; the products of decay can be photons. gamma ray photons. The rest mass of the meson is 135 MeV/c2. two Calculate the wavelength of each photon. Wavelength =... (5) (Total 5 marks) 107. A student is learning about how capacitors work. He uses the circuit shown in Figure 1 to investigate the capacitor C. Letter X labels a connection which he can make to either of the

6 oints L or M. Each cell has an e.m.f. of 1.5 V. Figure 1 Figure k L M X I/ A A 1 A 2 10 C t/s Connection X to L made at t = 3 s He connects X to L. He sketches how the reading on ammeter 1 varies with time (Figure 2). Explain in terms of charge what has happened in the circuit. (3) Explain what he would have seen if he had watched ammeter 2.

7 Use his sketch graph (Figure 2) to estimate the charge which has passed through ammeter 1 between the times t = 3 s and t = 10 s. Charge =... Use the graph and your answer above to estimate the capacitance of the capacitor. Capacitance =... (3) State and explain what he would observe on each ammeter if he then continued the experiment by moving the connection X from L to M. (Total 12 marks) 74. Most smoke detectors contain an isotope of Americium (241Am), the nuclei of which decay by emitting an alpha particle. When a nucleus of Americium emits an alpha particle the principle of conservation of momentum and the principle of conservation of energy are obeyed.

8 Show that the ratio the origin of this energy. kineticenergy of kineticenergy of alpha particle resulting nucleus is about 60 and briefly discuss (Total 6 marks) 183. Fast modern passenger and car ferries are often twin-hull boats, propelled using water jets instead of conventional propellers. A pumping system throws water out backwards at speed. One such ferry is the Stena Lynx II, which sails between Fishguard in Wales and Rosslare in Ireland.

Some data about the Stena Lynx II: Resistive forces at cruising speed = 8.

9 Some data about the Stena Lynx II: Resistive forces at cruising speed = N Mass of water per second ejected by the jets = kg s 1 Show that water must be thrown backwards at about 13 m s 1 while the boat is maintaining cruising speed. (3) The pumping system converts energy which is expended in two main ways: working against resistive forces and giving kinetic energy to the water thrown backwards. ms 1. Calculate the power expended against the resistive forces at the cruising speed of 20 Power =

10 Calculate the rate at which the water in the jets gains kinetic energy. Rate = Hence show that the overall efficiency of the pumping system at cruising speed is about 40%. Data: Fuel consumption of pumping system at cruising speed = 1.6 litres/second 1 litre of fuel provides J of energy when burnt (3) (Total 10 marks) 127. In London the Earth s magnetic field has a magnetic flux density of T at 66 to the horizontal as shown in the diagram. Earth's magnetic field 66º Earth's surface

11 Calculate the magnitude of the horizontal component of the Earth s magnetic field in London. Horizontal component =... For a conductor of length I moving at a speed i) perpendicular to a field of flux density B, the induced voltage V between the ends of the conductor is given by V = A metal scaffolding pole falls from rest off a high building. The pole is aligned horizontally in an east-west direction. The Earth s magnetic field lines at this point lie in a north-south direction. 2.5 m Direction of fall Calculate the induced voltage across the pole 2.0 s after it started to fall. Induced voltage =... (3)

12 What would be the induced voltage after 2.0 s if the pole were aligned in a northsouth direction? explain your answer. (Total 7 marks) 131. To restore a regular heart rhythm to a patient in an emergency, paramedics can use a machine called a defibrillator. The defibrillator uses a capacitor to store energy at a voltage of several thousand volts. Conducting paddles are placed on either side of the patient s chest, and a short pulse of current flows between them when the capacitor is discharged. The graph below shows voltage against charge for the capacitor used in a defibrillator Voltage /V Charge /C formula W = With reference to the graph, show that the energy stored in a capacitor is given by the 1 2 QV.

13 Calculate the energy stored by the capacitor when charged to 5000 V. Energy =... (1) The graph below shows how voltage varies with time as the capacitor s discharged across a test circuit that has a resistance equivalent to that of the patient s chest Voltage /V Time /ms Use the graph to find the time constant for the circuit. Time constant =... The total resistance of the circuit, including the paddles and chest, is the capacitance of the capacitor.

14 Capacitance =... The energy delivered to the patient s chest is selected by the operator from these settings: 50 J, 180 J, 380 J. This is achieved inside the machine electronically, by allowing the discharge to proceed for an appropriate length of time. On one particular setting, the discharge lasts for 2.0 ms. Calculate the energy left in the capacitor at this time. Some energy loss occurs and roughly 60% of the energy leaving the capacitor during the discharge actually goes into the patient. Find which setting the operator has selected. Energy setting =... (Total 11 marks) 150. One practical arrangement for verifying Coulomb s law is to use a lightweight, negatively-charged, freely-suspended ball. It is repelled by the negative charge on a larger sphere that is held near it, on an insulated support. The small angle of deflection is then measured.

15 Thread Charged sphere r Charged suspended ball Draw a free-body force diagram for the suspended ball. (3)

16 The weight of the ball is W. Show that the force of repulsion F on the suspended ball is given by F = W tan A student takes several sets of readings by moving the larger sphere towards the suspended ball in order to increase the mutual force of repulsion between them. He measures the angle of deflection and the separation distance r in each case. He then calculates the magnitude of the force F. Here are some of his results. Force F/10 3 N Distance r/10 3 m Calculate the values that you would expect the student to have obtained for the missing forces, assuming that Coulomb s law was obeyed. (4) Write your answers in the table.

17 Suggest why, in practice, it was necessary for the student to take measurements quickly using this arrangement. (1) (Total 10 marks) 157. A tennis ball connected to a long piece of string is swung around in a horizontal circle above the head of a pupil. The pupil feels that there is a tension in the string and argues that for equilibrium there must be an outward centrifugal force acting on the ball. Criticise his argument and explain why there is a tension in the string. (5) The pupil lets go of the string. Draw a free-body force diagram for the ball at the instant after release.

18 (1) (Total 6 marks) 23. A capacitor C1 is connected to a supply. When a potential difference of 4.0 V is applied across the capacitor, it stores a charge of 0.80 nc. C V (a) (i) Calculate the electrical work done by the supply as it transfers this charge Work done =... (ii) Mark on the diagram above the magnitudes and polarities of the charges stored on the plates of the capacitor. (1) Total: 3 radius of atom 34. (a) The ratio radius of nucleus for a given atom is about 105. Use this value to calculate the ratio density of nucleus. State the assumption you have made. density of atom

19 Assumption... (4) (b) What observation is made in the alpha particle scattering experiment that supports your assumption? (1) (Total 5 marks) 90. A student wants to test Coulomb s law, which is about the force between two charged objects. She plans to hang two balloons on insulated threads, charge them both with equal positive charges, and measure the angles at which they hang away from each other. The dimensions she plans to use in her experiment are shown on the diagram. 0.5 m 1.8 m 0.5 m

20 She thinks she can make accurate measurements if the balloons hang at an angle of 1.5 or more from the vertical. Add to the diagram to show all the forces acting on one of the balloons. Hence show that the minimum charge Q she needs on each balloon must be about [Assume that each balloon behaves as though the charge were concentrated at its centre.] The mass of each balloon = kg (Total 6 marks)

Figure 1. (a) An alternating current power supply provides a current that keeps switching direction.

Figure 1. (a) An alternating current power supply provides a current that keeps switching direction. 1 Figure 1 shows the output from the terminals of a power supply labelled d.c. (direct current). Voltage / V 6 4 2 0 2 0 5 10 15 20 25 Time/ms 30 35 40 45 50 Figure 1 (a) An alternating current power supply