In your answer, you should use appropriate technical terms spelled correctly

Transcription

1 1. State Newton s second and third laws of motion. In your answer, you should use appropriate technical terms spelled correctly. (i) second law (ii) third law [Total 2 marks] 2. A golfer uses a golf club to hit a stationary golf ball off the ground. The figure below shows how the force F on the golf ball varies with time t when the club is in contact with the ball F / N t / ms 1

2 (i) Estimate the area under the graph. area =... Ns (ii) Name the physical quantity represented by the area under the graph in (i). In your answer, you should use appropriate technical terms spelled correctly.... (iii) Show that the speed of a golf ball, of mass kg, as it leaves the golf club is about 50 m s 1. speed =... m s 1 2

3 (iv) The ground is level. The ball leaves the ground at a velocity of 50 m s 1 at an angle of 42 to the horizontal. Determine the horizontal distance travelled by the ball before it hits the ground. State one assumption that you make in your calculations. distance =... m assumption [5] [Total 10 marks] 3. The figure below shows the London Eye. capsule It has 32 capsules equally spaced around the edge of a large vertical wheel of radius 60 m. The wheel rotates about a horizontal axis such that each capsule has a constant speed of 0.26 m s 1. 3

4 (i) Calculate the time taken for the wheel to make one complete rotation. time =... s (ii) Each capsule has a mass of kg. Calculate the centripetal force which must act on the capsule to make it rotate with the wheel. centripetal force =... N [Total 3 marks] 4. The figure below shows the drum of a spin-dryer as it rotates. A dry sock S is shown on the inside surface of the side of the rotating drum. A S B C spinning drum (i) Draw arrows on the figure above to show the direction of the centripetal force acting on S when it is at points A, B and C. 4

5 (ii) State and explain at which position, A, B or C the normal contact force between the sock and the drum will be 1 the greatest the least... [Total 4 marks] 5. The figure below represents the planet Jupiter. The centre of the planet is labelled as O. Jupiter O 5

6 (a) Draw gravitational field lines on the figure above to represent Jupiter s gravitational field. (b) Jupiter has a radius of m and the gravitational field strength at its surface is 24.9 N kg 1. (i) Show that the mass of Jupiter is about kg. [3] (ii) Calculate the average density of Jupiter. density =... kg m 3 [Total 7 marks] 6. The figure below shows a mass suspended from a spring. 6

7 (a) The mass is in equilibrium. By referring to the forces acting on the mass, explain what is meant by equilibrium (b) The mass in (a) is pulled down a vertical distance of 12 mm from its equilibrium position. It is then released and oscillates with simple harmonic motion. (i) Explain what is meant by simple harmonic motion..... (ii) The displacement x, in mm, at a time t seconds after release is given by x = 12 cos (7.85 t). Use this equation to show that the frequency of oscillation is 1.25 Hz. 7

8 (iii) Calculate the maximum speed V max of the mass. V max =... m s 1 (c) Fig. 1 shows how the displacement x of the mass varies with time t t / s Fig. 1 Sketch on Fig. 2 the graph of velocity against time for the oscillating mass. Put a suitable scale on the velocity axis. velocity / ms t / s Fig. 2 [3] [Total 11 marks] 8

9 7. State Newton s second law of motion [Total 2 marks] 8. Explain how the principle of conservation of momentum is a natural consequence of Newton s laws of motion [Total 3 marks] 9. Most cars are now fitted with safety airbags. During a sudden impact, a triggering mechanism fires an ammunition cartridge that rapidly releases nitrogen gas into the airbag. In a particular simulated accident, a car of mass 800 kg is travelling towards a wall. Just before impact, the speed of the car is 32 m s 1. It rebounds at two-thirds of its initial speed. The car takes 0.50 s for the car to come to rest. During the crash, the car s airbag fills up to a maximum volume of m 3 at a pressure of Pa. The temperature inside the airbag is 20 C. Calculate: (i) the change in the momentum of the car momentum change =... (ii) the magnitude and direction of the average force acting on the car during impact. 9

10 force =...N direction:... (iii) the mass of nitrogen inside the cartridge. Molar mass of nitrogen = kg mol 1 mass =...kg [3] [Total 8 marks] 10. Define gravitational field strength at a point in a gravitational field [Total 1 mark] 10

11 11. A satellite of mass 1500 kg is launched from the surface of the Earth into a circular orbit around the Earth at a height of 6800 km above the Earth s surface. At this height the satellite has an orbital period of s. The radius of the Earth is 6400 km. (i) A student uses the equation gain in potential energy = mgh to determine the increase in the potential energy of the satellite. Suggest why this equation cannot be used and state whether the student s answer would be less than, equal to, or greater than the actual value (ii) Calculate the kinetic energy of the satellite. kinetic energy =... J [3] 11

12 (iii) State a benefit of having a satellite in a geostationary orbit round the Earth. Explain whether or not a satellite orbiting at a height of 6800 km above the Earth s surface is in a geostationary orbit. In your answer, you should use appropriate technical terms, spelled correctly [3] [Total 8 marks] 12. The graph below shows how the gravitational field strength g varies with distance r from the centre of a planet of radius m. 15 g / Nkg r / 10 m The gravitational field strength on the surface of the planet is 40 N kg 1. 12

13 (i) Use the graph above to write down the value for g at a height of m above the surface of the planet. g =...N kg 1 (ii) Calculate the mass M of the planet. Assume that the planet can be treated as a point mass of magnitude M situated at its centre. M =.... kg (iii) Astronomers investigating the planet believe that the planet s interior has a uniform density. Show that within the interior of the planet, its gravitational field strength g is proportional to the distance r from the centre.... [Total 6 marks] 13

14 13. Define simple harmonic motion. In your answer, you should use appropriate technical terms, spelled correctly [Total 2 marks] 14. The figure below shows a trolley attached to the end of a helical spring. The trolley executes simple harmonic motion on the smooth table. spring trolley smooth table (i) Describe how, for this oscillating trolley, you can determine the following quantities using a stopwatch and a ruler. 1 the frequency oscillation 2 the maximum speed of the trolley 14

15 (ii) The amplitude of the trolley is doubled. The trolley still moves in simple harmonic motion. State with a reason the change, if any, in the maximum speed of the trolley (iii) Using your knowledge of Hooke s law and Newton s second law, determine the period T of the trolley in terms of the force constant k of the spring and the mass m of the trolley [3] [Total 9 marks] 15. This question is about an alpha particle making a head on collision with a gold nucleus. (a) (i) When the alpha particle is at a large distance from the gold nucleus it has a kinetic energy of J. Show that its speed is about m s 1. mass of alpha particle = kg 15

16 (ii) As the alpha particle approaches the gold nucleus, it slows down and the gold nucleus starts to move, Fig. 1. gold nucleus alpha particle Fig.1 Explain this and explain how it is possible to calculate the speed of the gold nucleus. [3] (iii) Fig.2 shows the alpha particle and the gold nucleus at the distance of closest approach. At this instant the gold nucleus is moving with speed V and the alpha particle is stationary. V gold nucleus alpha particle Fig. 2 Calculate the speed V of the gold nucleus. mass of gold nucleus = kg V =...m s 1 16

17 (iv) The alpha particle bounces back. Its final speed approximately equals its initial speed of approach. Assume that the mean force on the nucleus is 9.0 N during the interaction. Estimate the time of the collision. time =. s (b) F / N r / 10 m Fig. 3 17

18 (i) Fig. 3 shows two points on the graph of the electrostatic repulsive force F between the alpha particle and nucleus against their separation r. The particle and the nucleus are being treated as point charges. Use data from the graph to calculate the values of the force at distances r = m and m. F at m =.N F at m =.N [3] (ii) Plot the two points on the graph and draw the curve. [Total 13 marks] 16. The electric motor in a washing machine rotates the drum containing the clothes by means of a rubber belt stretched around two pulleys, one on the motor shaft and the other on the drum shaft, as shown in Fig. 1. X motor machine casing belt drum Fig. 1 18

19 (a) The motor pulley of radius 15 mm rotates at 50 revolutions per second. Calculate (i) the speed of the belt speed =... m s 1 (ii) the centripetal acceleration of the belt at point X. acceleration =... m s 2 (iii) When the motor speed is increased, the belt can start to slip on the motor pulley. Explain why the belt slips. 19

20 (b) When the drum is rotated at one particular speed, a metal side panel of the machine casing vibrates loudly. Explain why this happens (c) A fault develops in the motor, causing the coil to stop rotating. Magnetic flux from the electromagnet of the motor still links with the now stationary coil. Fig. 2 shows how the flux linkage of the coil varies with time. 3 flux linkage / Wb turns time/ms 30 3 Fig. 2 (i) Using Fig. 2 state a time at which the e.m.f. induced across the ends of the coil is 1 zero... ms 2 a maximum.... ms 20

21 (ii) Use the graph of Fig. 2 to calculate the peak value of the e.m.f. across the ends of the coil. peak e.m.f. =... V [Total 12 marks] 17. The student next designs a loop-the-loop stunt shown in the diagram below. The cyclist must enter the circular runway at the same 15 m s 1 speed in order to exit from it smoothly. T B A 15 m s 1 E 21

22 In order to calculate the maximum diameter of loop in which the cyclist can safely execute the manoeuvre, the student makes the following assumptions the cyclist stops pedalling once he enters the loop at E the normal reaction of the runway on the tyre just becomes zero at the top of the loop T therefore the centripetal force at the top T is provided by the force of gravity only air resistance and runway friction can be ignored. As a result, the student calculates the diameter of the track to be 9.17 m. (i) Show that the speed of the cyclist at the top T of the loop should be 6.7 m s 1. [3] (ii) The total mass of the cyclist and bike is 86 kg. Calculate 1 the kinetic energy of the cyclist at the top T kinetic energy =... J 22

23 2 the gravitational potential energy of the cyclist at the top T. Take the gravitational potential energy at E to be zero. potential energy =... J (iii) Show that the sum of the kinetic and potential energies at the top T of the loop is equal to the kinetic energy of the cyclist as he enters the loop at E. (iv) The cyclist suggests that removing the top half or semicircle of the loop from A to B would allow him to fly in a semi-circular arc through the air and thus make a more spectacular stunt. How should the student should respond to this suggestion? Explain your reasoning [Total 11 marks] 23

24 18. This question gives a statement which can lead to misconceptions in physics. The statement is correct. When an astronaut is in the International Space Station, the gravitational force acting on him is 90% of the force acting on him when he is on the Earth s surface. Why does the astronaut imagine himself to be weightless? [Total 4 marks] 19. This question is about a simple model of a hydrogen iodide molecule. Fig. 1 shows a simple representation of the hydrogen iodide molecule. It consists of two ions, 1 H and 53 I, held together by electric forces. H + I Fig. 1 (a) (i) Draw on Fig. 1 lines to represent the resultant electric field between the two ions. 24

25 (ii) Calculate the electrical force F of attraction between the ions. Treat the ions as point charges a distance m apart. Each ion has a charge of magnitude C. F =... N [4] (b) The electrical attraction is balanced by a repulsive force so that the two ions are in equilibrium. When disturbed the ions oscillate in simple harmonic motion. Fig. 2 shows a simple mechanical model of the molecule consisting of two unequal masses connected by a spring of negligible mass. m H m I Fig. 2 25

26 Use Newton s laws of motion and the definition of simple harmonic motion to explain why the amplitude of oscillation of the hydrogen ion is 127 times the amplitude of oscillation of the iodine ion [4] (c) The natural frequency of oscillation of the hydrogen ion is Hz. Take the amplitude of oscillation to be m. (i) Sketch on Fig. 3 a displacement against time graph for the hydrogen ion displacement 12 / 10 m time / s Fig.3 [3] 26

27 (ii) It is found that infra-red radiation of frequency close to Hz, incident on the molecules, can cause this oscillation, but other frequencies of infra-red do not. Suggest how this result can be explained. [Total 15 marks] 20. In a distant galaxy, the planet Odyssey is orbited by two small moons Scylla and Charybdis, labelled O, S, C respectively in the diagram below. The distances of the moons from the centre of the planet are 5R and 4R, where R is the radius of the planet. 4R O C 5R R S 27

28 (a) Draw a gravitational field line of the planet passing through moon S. (b) The radius R of the planet is m. The gravitational field strength g at its surface is 40 N kg 1. (i) Write down a formula for the gravitational field strength g at the surface of the planet of mass M. (ii) Use the data above to show that the gravitational field strength at S is 1.6 N kg 1. (iii) Show that the gravitational field strength at C is 2.5 N kg 1. 28

29 (iv) Using an average value of g, estimate the increase E in gravitational potential energy of a small space vehicle of mass kg when it moves from the orbit of C to the orbit of S. E =... J [3] (c) Calculate the orbital period of S. Assume that the gravitational effects of the two moons on each other are negligible in comparison to the gravitational force of O. gravitational field strength at S = 1.6 N kg 1 radius of orbit = m period =... s [4] [Total 12 marks] 29

30 21. In this question, two marks are available for the quality of written communication. Faraday invented the concept of a field of force. Starting from the definitions of electric, gravitational and magnetic field strengths, discuss the similarities and differences between the three force fields. [7] Quality of Written Communication [Total 9 marks] 22. A cricketer throws a cricket ball of mass 0.16 kg. (a) The figure below shows how the force on the ball from the cricketer s hand varies with time. The ball starts from rest and is thrown horizontally. force / N time / s (i) Estimate the area under the graph. area =... Ns (ii) The area under the graph represents a change in a physical quantity for the ball. State the name of this quantity. 30

31 (iii) Calculate the speed of the ball, mass 0.16 kg, when it is released. speed =... m s 1 (iv) Calculate the maximum horizontal acceleration of the ball. acceleration =... m s 2 (b) The ball bounces several times on a hard surface. The maximum height to which it rises after each bounce is given in the table below. bounce number, n maximum height, h/ m The data given in the table fit a relationship for the variation in maximum height with bounce number of the form where k is a constant. h = 1.5 e kn (i) State the name of this form of relationship. 31

32 (ii) Calculate the value of k. k =... (iii) What is the height from which the ball was thrown? height =... m (iv) Show that the loss of kinetic energy of the ball at the second bounce is about 0.6 J. Assume that the horizontal speed of the ball is unchanged. [Total 12 marks] 32

33 23. Fig. 1 shows two protons A and B in contact and at equilibrium inside a nucleus. A B Fig. 1 Proton A exerts three forces on proton B. These are an electrostatic force F E, a gravitational force F G and a strong force F S. (a) On Fig. 1, mark and label the three forces acting on proton B. Assume that every force acts at the centre of the proton. (b) Write an equation relating F E, F G and F S. (c) The radius of a proton is m. Calculate the values of (i) F E F E =... N 33

34 (ii) F G F G =... N (iii) F S. F S =... N (d) Comment on the relative magnitudes of F E and F G

35 (e) Fig. 2 shows two neutrons in contact and at equilibrium inside a nucleus. Fig. 2 Without further calculation, state the values of F E, F G and F S for these neutrons. (i) (ii) (iii) F E =... N F G =... N F S =... N [Total 12 marks] 35

36 24. State what is meant by kinetic energy and momentum. This should not be answered just in terms of the equations E k = ¹ ₂ mv 2 and p = mv [Total 4 marks] 25. This question is about pressing a red hot bar of steel into a sheet in a rolling mill. (a) A bar of steel of mass 500 kg is moved on a conveyor belt at 0.60 m s 1. Calculate the momentum of the bar giving a suitable unit for your answer. momentum =... unit... 36

37 (b) From the conveyor belt, the bar is passed between two rollers, shown in the figure below. The bar enters the rollers at 0.60 m s 1. The rollers flatten the bar into a sheet with the result that the sheet leaves the rollers at 1.8 m s 1. steel bar roller conveyor belt v = 0.60 ms 1 conveyor belt v = 1.8 ms 1 (i) Explain why there is a resultant horizontal force on the bar at the point immediately between the rollers. (ii) Draw an arrow on the figure at this point to show the direction of the force. (iii) The original length of the bar is 3.0 m. Calculate the time it takes for the bar to pass between the rollers. time =... s 37

38 (iv) Calculate the magnitude of the resultant force on the bar during the pressing process. force =... N [3] (c) To monitor the thickness of the sheet leaving the rollers, a radioactive source is placed below the sheet and a detector is placed above the sheet facing the source. State, with a reason, which radioactive emission would be suitable for this task. Assume that the thickness of the sheet is about 20 mm [Total 11 marks] 26. (a) The figure below shows a graph of the variation of the gravitational field strength g of the Earth with distance r from its centre R r /10 6 m g / N kg

39 (i) Define gravitational field strength at a point. (ii) Write down an algebraic expression for the gravitational field strength g at the surface of the Earth in terms of its mass M, its radius R and the universal gravitational constant G. (iii) Use data from the figure above and the value of G to show that the mass of the Earth is kg. (iv) State which feature of the graph in the figure above indicates that the gravitational field strength at a point below the surface of the Earth, assumed to be of uniform density, is proportional to the distance from the centre of the Earth. 39

40 (v) Calculate the two distances from the centre of the Earth at which g = N kg 1. Explain how you arrived at your answers. distance 1... distance 2... (b) A spacecraft on a journey from the Earth to the Moon feels no resultant gravitational pull from the Earth and the Moon when it has travelled to a point 0.9 of the distance between their centres. Calculate the mass of the Moon, using the value for the mass of the Earth in a(iii). mass =... kg [3] [Total 12 marks] 40

41 27. The external wing mirror of a large vehicle is often connected to the body of the vehicle by a long metal arm. See Fig. 1. The wing mirror assembly sometimes behaves like a mass on a spring, with the mirror oscillating up and down in simple harmonic motion about its equilibrium position. The graph of Fig. 2 shows a typical oscillation. body of vehicle motion of mirror Fig. 1 displacement / mm time/s Fig.2 (a) (i) Define simple harmonic motion. 41

42 (ii) Calculate the frequency of oscillation of the wing mirror. frequency =... Hz (iii) Calculate the maximum acceleration of the wing mirror. acceleration =... m s 2 [3] (b) With the vehicle at rest and the engine running slowly at a particular number of revolutions per second, the wing mirror oscillates significantly, whereas at other engine speeds the mirror hardly moves. (i) Explain how this phenomenon is an example of resonance. [3] 42

43 (ii) Suggest, giving a reason, one change to the motion of the mirror 1 for a mirror of greater mass 2 for a metal arm of greater stiffness. [Total 14 marks] 28. This question is about nuclear fission. 235 When a uranium-235 ( 92 U) nucleus absorbs a neutron, it becomes uranium ( 92 U) which may undergo fission. (a) In order to increase the probability of neutron-induced fission, neutrons from a 235 fission reaction are slowed down before they collide with another 92 U nucleus. This is achieved by causing the neutrons to collide elastically with other nuclei. Explain why these other nuclei should have a mass which is similar to the neutron mass

44 236 (b) The fission of 92 U can produce many different pairs of nuclei. The table below shows 3 possible pairs of product nuclei and their relative yields. nucleus 1 nucleus 2 relative yield zirconium-100 ( Zr ) tellurium-135 ( 52 Te ) 6.4% selenium-83 ( 34 Se ) cerium-152 ( 58 Ce ) 0.40% rhodium-110 ( Rh ) silver-121 ( 47 Ag ) 0.020% Write an equation to show the fission reaction which produces 110 Rh and Ag [Total 4 marks] 44

45 29. The figure below shows a diagram of the Earth and the path of a geostationary satellite around it. For the satellite to be in a geostationary orbit, three conditions must be satisfied regarding the period, the plane of the orbit and the direction of rotation. State and explain why each of these conditions is necessary. period plane direction [Total 5 marks] 30. Data can be displayed in graphical form in many different ways. Sometimes it is necessary to change from one way of displaying data to another. Four graphs are drawn below. velocity / ms graph A distance / m time / s time / s 45

46 current I / A 1 I /A graph B resistance / resistance / graph C g / ms 2 lg ( g / ms 2) x10 10x10 15x10 20x10 r / m lg (r / m) (a) (i) Calculate the total distance travelled from the velocity-time graph A. distance =... m [3] (ii) Using graph A, draw the corresponding distance-time graph. 46

47 [3] (b) Graph B shows how the current I in a circuit varies with the total circuit resistance R when the e.m.f. of the supply is kept constant. (i) Draw the corresponding graph of 1/I against R. (ii) What is the e.m.f. of the supply? e.m.f. =... V (iii) How is the gradient of the graph you have drawn related to your answer to (b)(ii)? 47

48 (c) Graph C shows how g, the acceleration due to gravity, varies with r, the distance from the centre of the Earth. A log-log graph showing the same data has been drawn on new axes. (i) Calculate the gradient of the log-log graph. gradient =... (ii) What can be deduced from the value of the gradient? [Total 14 marks] 31. A mass oscillates on the end of a spring in simple harmonic motion. The graph of the acceleration a of the mass against its displacement x from its equilibrium position is shown in Fig a / m s x/mm Fig. 1 48

49 (a) (i) Define simple harmonic motion. (ii) Explain how the graph shows that the object is oscillating in simple harmonic motion. (b) Use data from the graph (i) to find the amplitude of the motion amplitude =... m (ii) to show that the period of oscillation is 0.4 s. [3] 49

50 (c) (i) The mass is released at time t = 0 at displacement x = m. Draw a graph on the axes of Fig. 2 of the displacement of the mass until t = 1.0 s. Add scales to both axes. x / m 0 0 t / s Fig. 2 [3] (ii) State a displacement and time at which the system has maximum kinetic energy. displacement... m time... s [Total 13 marks] 32. (a) (i) State the equation that represents Newton s law of gravitation, defining all symbols. 50

51 (ii) Why did Newton believe that the Universe must be infinitely large? (b) The period and average orbital radius of two Earth-orbiting research satellites are given in the table below. satellite period /h orbital radius /km A B (i) Satellite B has the larger orbital radius. Using Newton s law of gravitation, explain why the satellites have such different periods. (ii) Using data from the table, calculate the average orbital radius for a satellite with a period of 57.2 hours. radius =...km [3] 51

52 (c) Suggest three advantages that land based telescopes have over those which are on satellites orbiting the Earth [3] [Total 10 marks] 33. (a) The table of Fig. 1 shows four particles and three classes of particle. hadron baryon lepton neutron proton electron neutrino Fig. 1 Indicate using ticks, the class or classes to which each particle belongs. (b) The neutron can decay, producing particles which include a proton and an electron. (i) State the approximate half-life of this process. (ii) Name the force which is responsible for it. 52

53 (iii) Write a quark equation for this reaction. (iv) Write number equations which show that charge and baryon number are conserved in this quark reaction. charge... baryon number... (c) Fig. 2 illustrates the paths of the neutron, proton and electron only in a decay process of the kind described in (b). neutron proton electron Fig. 2 53

54 Fig. 3 represents the momenta of the neutron, p n, the proton, p p and the electron, p e on a vector diagram. p e p p Fig. 3 p n (i) Draw and label a line on Fig. 3 which represents the resultant p r of vectors p p and p e. (ii) According to the law of momentum, the total momentum of an isolated system remains constant. Explain in as much detail as you can, why the momentum p r is not the same as p n. [3] [Total 12 marks] 54

55 34. This question is about kicking a football. (a) The diagram below shows how the force F applied to a ball varies with time t whilst it is being kicked horizontally. The ball is initially at rest. 60 F / N t / s (i) Use the graph to find 1 the maximum force applied to the ball 2 the time the boot is in contact with the ball. maximum force = N time =...s 55

56 (ii) The mean force multiplied by the time of contact is called the impulse delivered to the ball. Use the graph to estimate the impulse delivered to the ball. impulse =... N s (b) The mass of the ball is 0.50 kg. Use your answers to (a) to calculate (i) the maximum acceleration of the ball acceleration =...m s 2 (ii) the final speed of the ball speed =...m s 1 (iii) the kinetic energy of the ball after the kick. kinetic energy =...J 56

57 (c) The ball hits a wall with a speed of 14 m s 1. It rebounds from the wall along its initial path with a speed of 8.0 m s 1. The impact lasts for 0.18 s. Calculate the mean force exerted by the ball on the wall. force =..N [3] [Total 12 marks] 35. (a) Define gravitational field strength at a point in a gravitational field (b) The gravitational field strength at the surface of a planet of uniform density is 40 N kg 1. A satellite of mass 1500 kg is launched from the surface into a circular orbit around the planet at a height of m with an orbital period of s. The radius of the planet is m. (i) Estimate the increase in potential energy of the satellite. potential energy = J 57

58 (ii) Suggest with a reason whether your estimate in (i) is likely to be larger or smaller than the true value. (iii) Calculate the kinetic energy of the satellite in orbit. kinetic energy =. J [4] [Total 8 marks] 58

59 36. The diagram below shows how the gravitational field strength g varies with distance r from the centre of the planet of radius m. 15 g / Nkg r / 10 m (i) Use the diagram above to write down the value of g at a height of m above the surface. g =..N kg 1 (ii) Write down an algebraic expression for g at a distance r from the centre of the planet. The planet can be treated as a point mass of magnitude M situated at its centre

60 (iii) The value of g at the surface is 40 N kg 1. Use this information and your answer to (ii) to check, by a suitable calculation, your answer to (i). [Total 4 marks] 37. (a) The equation of state of an ideal gas is pv = nrt. Explain why the temperature must be measured in kelvin

61 (b) A meteorological balloon rises through the atmosphere until it expands to a volume of m 3, where the pressure is Pa. The temperature also falls from 17 C to 43 C. The pressure of the atmosphere at the Earth s surface = Pa. Show that the volume of the balloon at take off is about m 3. [3] (c) The balloon is filled with helium gas of molar mass kg mol 1 at 17 C at a pressure of Pa. Calculate (i) the number of moles of gas in the balloon number of moles =.. (ii) the mass of gas in the balloon. mass =...kg 61

62 (d) The internal energy of the helium gas is equal to the random kinetic energy of all of its molecules. When the balloon is filled at ground level at a temperature of 17 C the internal energy is 1900MJ. Estimate the internal energy of the helium when the balloon has risen to a height where the temperature is 43 C. internal energy =...MJ (e) The upward force on the filled balloon at the Earth s surface is N. The initial acceleration of the balloon as it is released is 27 m s 2. The total mass of the filled balloon and its load is M. (i) On the diagram below draw and label suitable arrows to represent the forces acting on the balloon immediately after lift off. 62

63 (ii) Calculate the value of M. M =...kg [3] [Total 15 marks] 38. (a) Define magnetic flux density

64 (b) The figure below shows an evacuated circular tube in which charged particles can be accelerated. A uniform magnetic field of flux density B acts in a direction perpendicular to the plane of the tube. Protons move with a speed v along a circular path within the tube. evacuated tube P path of proton (i) On the figure above draw an arrow at P to indicate the direction of the force on the protons for them to move in a circle within the tube. (ii) State the direction of the magnetic field. Explain how you arrived at your answer. (iii) Write down an algebraic expression for the force F on a proton in terms of the magnetic field at point P. 64

65 (iv) Calculate the value of the flux density B needed to contain protons of speed m s 1 within a tube of radius 60 m. Give a suitable unit for your answer. B = unit [5] (v) State and explain what action must be taken to contain protons, injected at twice the speed (2v), within the tube. [Total 13 marks] 65

66 39. (a) Fig. 1 shows a toy consisting of a light plastic aeroplane suspended from a long spring. Fig. 1 (i) The aeroplane is pulled down 0.040m and released. It undergoes a vertical harmonic oscillation with a period of 1.0 s. The oscillations are lightly damped. Sketch on the axes of Fig. 2 the displacement y of the aeroplane against time t from the moment of release y / m t / s Fig. 2 [3] 66

67 (ii) The aeroplane is replaced by a heavier model made of the same plastic having the same fuselage but larger wings. State and explain two changes which this substitution will make to the displacement against time graph that you have drawn on Fig. 2. [4] (b) The top end of the spring in Fig. 1 is then vibrated vertically with a small constant amplitude. The motion of the aeroplane changes as the frequency of oscillation of the top end of the spring is increased slowly from zero through resonance to 2.0 Hz. Explain the conditions for resonance to occur and describe the changes in the motion of the aeroplane as the frequency changes from zero to 2.0 Hz [5] [Total 12 marks] 67

68 40. Explain the physics of why the tension in the string of an oscillating simple pendulum is not equal to the weight of the pendulum bob when the string is vertical [Total 3 marks] 68