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Mechanics, Materials and Waves AQA GCE 2450 Physics A AS Unit 2 Exam Questions Physics A Unit2 Mechanics, Materials and Waves Mechanics 1. (a) Distinguish between a scalar quantity and a vector quantity. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (b) A car travels one complete lap around a circular track at an average speed of 100 km h–1. (i) If the lap takes 3.0 minutes, show that the length of the track is 5.0 km. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) What is the magnitude of displacement of the car after 1.5 minutes? ........................................................................................................................... (4) (Total 6 marks) 2. The diagram shows a straight, horizontal swimming bath spring board of length 4.00m and of weight 300 N. It is freely hinged at A and rests on a roller B, where AB is 1.60m. A boy of weight 400N stands at end C. 1.60m 4.0m A B C (a) On the diagram show the directions of the forces acting on the board at A and B. (2) (b) Calculate the magnitudes of the forces (i) at A ................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) at B ................................................................................................................... ........................................................................................................................... ........................................................................................................................... (4) (Total 6 marks) 3. A ball is dropped and rebounds vertically to less than the original height. For this first bounce only, sketch graphs of (a) the velocity of the ball plotted against time, velocity time (4) (b) the acceleration of the ball plotted against time. acceleration time (1) Q P (c) 50° The ball is then thrown at an angle to the horizontal and follows the trajectory shown in the diagram. Mark on the diagram the directions of (i) the acceleration vector at P, (ii) the acceleration vector at Q, (iii) the momentum vector at P, (iv) the momentum vector at Q. (4) (Total 9 marks) 4. A mass of 1500kg is attached to a cable and raised vertically by a crane. The graph shows how its velocity varies with time. 3.0 velocity/ms –1 2.0 1.0 A 0 (a) B C 1.0 D E 2.0 3.0 F 4.0 time/s 5.0 Determine (i) the initial uniform acceleration of the mass, ................................................... ........................................................................................................................... ........................................................................................................................... (ii) the distance travelled by the mass while it is accelerating upwards. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (b) (i) Calculate the tension in the cable in the intervals AB, ................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... CD. ................................................................................................................... ........................................................................................................................... (ii) State in which interval of the motion the tension in the cable is least. ........................................................................................................................... (4) (c) Calculate the power supplied by the crane during the interval CD. ..................................................................................................................................... ..................................................................................................................................... (2) (Total 9 marks) 5. The graph shows how the vertical speed of a parachutist changes with time during the first 20 s of his jump. To avoid air turbulence caused by the aircraft, he waits a short time after jumping before pulling the cord to release his parachute. 50 C vertical speed/ms –1 40 B 30 D 20 10 A 0 0 (a) 2 4 6 8 10 12 time/s 14 16 18 Regions A, B and C of the graph show the speed before the parachute has opened. With reference to the forces acting on the parachutist, explain why the graph has this shape in the region marked (i) A, ...................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) B, ....................................................................................................................... ........................................................................................................................... ........................................................................................................................... (iii) C. ...................................................................................................................... ........................................................................................................................... ........................................................................................................................... 20 ........................................................................................................................... (6) (b) Calculate the maximum deceleration of the parachutist in the region of the graph marked D, which shows how the speed changes just after the parachute has opened. Show your method clearly, ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (c) Use the graph to find the total vertical distance fallen by the parachutist in the first 10 s of the jump. Show your method clearly. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (4) (d) During his descent, the parachutist drifts sideways in the wind and hits the ground with a vertical speed of 5.0 m s–1 and a horizontal speed of 3.0 m s–1. Find (i) the resultant speed with which he hits the ground, ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) the angle his resultant velocity makes with the vertical. ........................................................................................................................... ........................................................................................................................... (2) (Total 14 marks) 6. (a) The diagram shows an object at rest at the top of a straight slope which makes a fixed angle with the horizontal. P Q (i) The object is released and slides down the slope from P to Q with negligible friction. Assume that the potential energy is zero at Q. Sketch a graph showing the potential energy at different distances measured along the slope, and label it A. On the same set of axes, sketch a second graph showing the kinetic energy of the object at different distances along the slope and label it B. energy 0 P Q distance along slope (ii) Using the same axes as in part (i), sketch a third graph, labelled C, showing the kinetic energy at different distances along the slope when there is a constant frictional force between the object and the surface. (iii) Use your knowledge of the principle of conservation of energy to explain the important features of the graphs you have drawn in part (i) and part (ii). ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (6) (b) In a theme park ride, a cage containing passengers falls freely a distance of 30 m from A to B and travels in a circular arc of radius 20m from B to C. Assume that friction is negligible between A and C. Brakes are applied at C after which the cage with its passengers travels 60m along an upward sloping ramp and comes to rest at D. The track, together with relevant distances, is shown in the diagram. CD makes an angle of 20° with the horizontal passenger cage A 30 m B 20 m radius 60 m C (i) D 20° Calculate the speed of the cage at C ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) Calculate the force required on a passenger of mass 80 kg for circular motion at C and state the direction of this force. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (iii) If the mass of the cage and passengers is 620 kg, determine the gain in gravitational potential energy in travelling from C to D. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (iv) Calculate the average resistive force exerted by the brakes between C and D ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (9) (Total 15 marks) 7. The diagram shows a uniform bar, AB, which is 1.6 m long and freely pivoted to a wall at B. The bar is maintained horizontal and in equilibrium by an angled string which passes over a pulley and which carries a mass of 2.0 kg at its free end. 1.6 m 30° A B 2.0 kg (a) The pulley is positioned as shown in the diagram, with the string at 30° to the vertical. (i) Calculate the tension, T, in the string. ......................................................................................................................... ......................................................................................................................... (ii) Show that the mass of the bar is approximately 3.5 kg. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (4) (b) A mass, M, is attached to the bar at a point 0.40 m from A. The pulley is moved horizontally to change the angle made by the string to the vertical, and to maintain the rod horizontal and in equilibrium. Determine the largest value of the mass, M, for which this equilibrium can be maintained. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. (4) (Total 8 marks) 8. An athlete is analysing his shot putting technique so as to improve his performance. He finds that the optimum performance is achieved when the angle which his leg makes with the ground is 57° immediately before releasing the shot. The maximum force he can exert on the ground is 650 N at an angle of 57° to the ground. 57° (a) Draw and label arrows on the diagram above to represent (i) T, the force the foot exerts on the ground, (ii) N, the normal reaction of the ground on the foot, (iii) F, the frictional force of the ground on the foot. (3) (b) Calculate the magnitude of (i) the frictional force F, ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) the normal reaction of the ground N. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (Total 5 marks) 9. A solid iron ball of mass 890 kg is used on a demolition site. It hangs from the jib of a crane suspended by a steel rope. The distance from the point of suspension to the centre of mass of the ball is 15 m. (a) Calculate the tension in the rope when the mass hangs vertically and stationary. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... (2) (b) The iron ball is pulled back by a horizontal chain so that the suspension rope makes an angle of 30° with the vertical. Calculate the new tension in the suspension rope. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (c) The ball is now released from rest and hits a brick wall just as it passes through the vertical position. It can be assumed that the ball is brought to rest by the impact with the wall in 0.2s. Calculate (i) the vertical height through which the ball falls, ........................................................................................................................... ........................................................................................................................... (ii) the speed of the ball just before impact, ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (iii) the average force exerted by the ball on the wall. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (5) (Total 9 marks) 10. F The diagram shows stationary kite. The the air exerts on the the forces acting on a force F is the force that kite. 30º tension, T, in string weight (a) Show on the diagram how force F can be resolved into horizontal and vertical components. (2) (b) The magnitude of the tension, T, is 25 N. Calculate (i) the horizontal component of the tension, ........................................................................................................................... (ii) the vertical component of the tension. ........................................................................................................................... (2) (c) (i) Calculate the magnitude of the vertical component of F when the weight of the kite is 2.5 N. ........................................................................................................................... (ii) State the magnitude of the horizontal component of F. ........................................................................................................................... (iii) Hence calculate the magnitude of F. ........................................................................................................................... ........................................................................................................................... (4) (Total 8 marks) 11. (a) A cricketer throws a ball vertically upwards so that the ball leaves his hands at a speed of 25 m s–1. If air resistance can be neglected, calculate (i) the maximum height reached by the ball, ........................................................................................................................... ........................................................................................................................... (ii) the time taken to reach maximum height, ........................................................................................................................... ........................................................................................................................... (iii) the speed of the ball when it is at 50% of the maximum height. ........................................................................................................................... ........................................................................................................................... (4) (b) When catching the ball, the cricketer moves his hands for a short distance in the direction of travel of the ball as it makes contact with his hands. Explain why this technique results in less force being exerted on the cricketer’s hands. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (Total 6 marks) 12. A heavy sledge is pulled across snowfields. The diagram shows the direction of the force F exerted on the sledge. Once the sledge is moving, the average horizontal force needed to keep it moving at a steady speed over level ground is 300 N. F 20º (a) Calculate the force F needed to produce a horizontal component of 300 N on the sledge. ..................................................................................................................................... ..................................................................................................................................... (1) (b) (i) Explain why the work done in pulling the sledge cannot be calculated by multiplying F by the distance the sledge is pulled. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) Calculate the work done in pulling the sledge a distance of 8.0 km over level ground. ........................................................................................................................... ........................................................................................................................... (iii) Calculate the average power used to pull the sledge 8.0 km in 5.0 hours. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (6) (c) The same average power is maintained when pulling the sledge uphill. Explain in terms of energy transformations why it would take longer than 5.0 hours to cover 8.0 km uphill. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (Total 10 marks) 13. (a) The torque of a couple is given by torque = Fs. (i) With the aid of a diagram explain what is meant by a couple. Label F and s on your diagram. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) State the unit for the torque of a couple. ........................................................................................................................... (4) (b) The see-saw shown in the diagram consists of a uniform beam freely pivoted at the centre of the beam. Two children sit opposite each other so that the see-saw is in equilibrium. Explain why (i) the see-saw is in equilibrium, ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) the weight of the beam does not affect equilibrium. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (c) The diagram shows the see-saw with three children of weights 400N, 250N and 200N sitting so that the see-saw is in equilibrium. d 1.0 m 400 N 0.50 m 200 N 250 N Calculate the distance, d. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (Total 9 marks) 14. The diagram shows a car travelling at a constant velocity along a horizontal road. (a) (i) Draw and label arrows on the diagram representing the forces acting on the car. (ii) Referring to Newton’s Laws of motion, explain why the car is travelling at constant velocity. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (5) (b) The car has an effective power output of 18 kW and is travelling at a constant velocity of 10 m s–1. Show that the total resistive force acting is 1800 N. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (1) (c) The total resistive force consists of two components. One of these is a constant frictional force of 250 N and the other is the force of air resistance, which is proportional to the square of the car’s speed. Calculate (i) the force of air resistance when the car is travelling at 10 m s–1, ........................................................................................................................... ........................................................................................................................... (ii) the force of air resistance when the car is travelling at 20 m s–1, ........................................................................................................................... ........................................................................................................................... (iii) the effective output power of the car required to maintain a constant speed of 20 m s–1 in a horizontal road. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (4) (Total 10 marks) 15. A public house sign is fixed to a vertical wall as shown in the diagram. 40° wall wire hinge metal bar sign A uniform metal bar 0.75 m long is fixed to the wall by a hinged joint that allows free movement in the vertical plane only. The wire is fixed to the wall directly above the hinge and to the free end of the horizontal metal bar. The wire makes an angle of 40° with the wall. A single support holds the sign and is mounted at the mid point of the metal bar so that the weight of the sign acts through that point. (a) (i) Draw on the diagram three arrows showing the forces acting on the metal bar, given that the system is in equilibrium. Label the arrows A, B and C. (ii) State the origin of the forces. A ....................................................................................................................... B ....................................................................................................................... C ....................................................................................................................... (b) The combined mass of the metal bar and sign is 12 kg and the mass of the wire is negligible. By taking moments about the hinged end of the bar, or otherwise, calculate the tension in the wire. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (4) (Total 9 marks) 16. A student carried out an experiment to determine the terminal speed of various ball bearings as they fell through a viscous liquid. She did this by timing their fall between two marks, P and Q, which were 850 mm apart on a vertical glass tube. ball bearing P 850 mm Q You may be awarded marks for the quality of written communication in your answer. (a) (i) Describe the motion of a ball bearing after being released from rest at the surface. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) In terms of the forces acting, explain why a ball bearing reaches a terminal speed under these conditions. (5) ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (5) (b) The student’s results are shown in columns A and B. Complete column C. column A column B column C column D column E radius of ball bearing r / mm time of fall / s (through 850 mm) terminal speed / mm s–1 log10(r / mm) log10( / mm s– 1 ) 1.62 32.0 0.210 1.98 21.4 0.297 2.21 17.2 0.344 2.73 11.3 0.436 3.40 7.2 0.531 4.12 4.9 0.615 (2) (c) The relationship between and r is known to be of the form = krn, where n and k are constants. (i) Enter the corresponding values for log10( / mm s–1) in column E of the table in part (b). (ii) Plot a graph of log10( / mm s–1) on the y-axis, against log10(r / mm) on the xaxis. (Allow one sheet of graph paper) (4) (d) Use your graph to determine (i) the constant n, ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) the constant k. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (5) (Total 16 marks) 17. A fairground ride ends with the car moving up a ramp at a slope of 30° to the horizontal as shown in the figure below. ramp 30° (a) The car and its passengers have a total weight of 7.2 × 103 N. Show that the component of the weight parallel to the ramp is 3.6 × 103 N. ..................................................................................................................................... ..................................................................................................................................... (b) (1) Calculate the deceleration of the car assuming the only force causing the car to decelerate is that calculated in part (a). ..................................................................................................................................... ..................................................................................................................................... (c) The car enters at the bottom of the ramp at 18 m s–1. Calculate the minimum length of the ramp for the car to stop before it reaches the end. The length of the car should be neglected. ..................................................................................................................................... ..................................................................................................................................... (2) ..................................................................................................................................... ..................................................................................................................................... (d) (2) Explain why the stopping distance is, in practice, shorter than the value calculated in part (c). ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (Total 7 marks) 18. (a) Define the moment of a force. ................................................................................................................................… ................................................................................................................................… (2) (b) The diagram shows a uniform diving board of weight, W, that is fixed at A. The diving board is supported by a cylinder at C, that exerts an upward force, P, on the board. P A B C W (i) By considering moments about A, explain why the force P must be greater than the weight of the board, W. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) State and explain what would be the effect on the force P of a girl walking along the board from A to B. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (4) (Total 6 marks) 19. While investigating projectile motion, a student used stroboscopic photography to determine the position of a steel ball at regular intervals as it fell under gravity. With the stroboscope flashing 20 times per second, the ball was released from rest at the top of an inclined track, and left the foot of the track at P, as shown in the diagram below. straight ramp P curved path y x ball at time t after passing P For each of the images on the photograph, the student calculated the horizontal distance, x, and the vertical distance, y, covered by the ball at time t after passing P. Both distances were measured from point P. He recorded his results for the distances x and y in the table. (a) image x/cm y/cm t/s 1 11.6 9.3 0.05 2 22.0 21.0 0.10 3 32.4 35.0 0.15 4 44.2 51.8 0.20 5 54.8 71.0 0.25 6 66.0 92.2 0.30 (y/t)/cm s–1 Using two sets of measurements from the table, calculate the horizontal component of velocity of the ball. Give a reason for your choice of measurements. ................................................................................................................................. ................................................................................................................................. ................................................................................................................................. (2) (b) The student worked out that the variables y and t in the experiment could be represented by y = u + kt t where u and k are constants. (i) Complete the table above. (ii) Use the data in the table to plot a suitable graph to confirm the equation. (Allow one sheet of graph paper) (iii) Use your graph to find the values of u and k. ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... ....................................................................................................................... (9) (c) State the physical significance of u .............................................................................................................................. ................................................................................................................................. k .............................................................................................................................. ................................................................................................................................. (2) (d) Calculate the magnitude of the velocity of the ball at point P. ................................................................................................................................. ................................................................................................................................. ................................................................................................................................. ................................................................................................................................. (2) (Total 15 marks) 20. (a) What do you understand by the principle of conservation of energy? ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (b) (i) Explain how the principle of conservation of energy applies to a man sliding from rest down a vertical pole, if there is a constant resistive force opposing the motion. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) The man starts sliding at time t = 0 and reaches the ground at time t. Consider each form of energy that varies with time and sketch graphs on the axes to show these variations. Include a graph of the total energy involved and indicate the effect of the resistive force. Name each energy graph drawn and point out important features. energy time (5) (c) A domestic kettle is marked 250V, 2.3 kW and the manufacturer claims that it will heat a pint of cold water to boiling point in 94s. specific heat capacity of water = 4.2 × 103 J kg–1 K–1 specific latent heat of vaporisation of water = 2.3 × 106 J kg–1 K–1 density of water = 1000 kg m–3 1 pint = 5.7 × 10–4 m3 (i) Test this claim by calculation and state any simplifying assumptions that you make. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) If the kettle is left switched on after it boils, how long will it take to boil away half a pint of water, measured from when it first boils? ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (5) (Total 12 marks) Waves 21. The diagram shows two identical loudspeakers, A and B, placed 0.75 m apart. Each loudspeaker emits sound of frequency 2000 Hz. not to scale A E 0.75m C D B 5.0m Point C is on a line midway between the speakers and 5.0 m away from the line joining the speakers. A listener at C hears a maximum intensity of sound. If the listener then moves from C to E or D, the sound intensity heard decreases to a minimum. Further movement in the same direction results in the repeated increase and decrease in the sound intensity. speed of sound in air = 330 m s–1 (a) Explain why the sound intensity (i) is a maximum at C, ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) is a minimum at D or E. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (4) (b) Calculate (i) the wavelength of the sound, ........................................................................................................................... ........................................................................................................................... (ii) the distance CE. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (4) (Total 8 marks) 22. Stationary waves in air can be demonstrated using a long horizontal tube which contains fine powder. With a loudspeaker connected to a signal generator positioned at one end of the tube, stationary waves are formed by reflection of waves from the ends of the tube. The diagram shows part of the tube in such an arrangement. The powder forms heaps at nodes. Speed of sound waves in air = 340 m s–1 P Q 0.27 m (a) Determine (i) the wavelength of the waves, ........................................................................................................................... (ii) the frequency of vibration of the loudspeaker. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (2) (b) Distinguish between longitudinal waves and transverse waves and state which type of wave is being generated in the tube. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (c) P and Q are two points in the tube. Compare the motion of air particles at P with the motion of air particles at Q with reference to (i) frequency, ........................................................................................................................... ........................................................................................................................... (ii) amplitude, ........................................................................................................................... ........................................................................................................................... (iii) phase. ........................................................................................................................... ........................................................................................................................... (3) (Total 8 marks) 23. (a) Optical interference effects can be observed by the superposition of light waves from coherent sources. Explain the meanings of the words in italics. superposition .............................................................................................................. .................................................................................................................................... coherent ..................................................................................................................... .................................................................................................................................... (2) (b) A laser, emitting light, is used to illuminate two parallel slits, giving coherent sources. (i) Interference takes place where light beams from the two slits overlap. With the aid of a diagram, explain how this overlap is produced. .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... (ii) State and explain what two changes you would expect in the fringe system if each of the slits were made narrower, but their separation were kept the same. change 1 ........................................................................................................... .......................................................................................................................... .......................................................................................................................... change 2 ........................................................................................................... .......................................................................................................................... .......................................................................................................................... (4) (Total 6 marks) 24. (a) State what is meant by coherent sources of light. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (b) screen slit monochromatic source slits S1 S S2 Figure 1 Young’s fringes are produced on the screen from the monochromatic source by the arrangement shown in Figure 1. You may be awarded marks for the quality of written communication in your answers. (i) Explain why slit S should be narrow. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) Why do slits S1 and S2 act as coherent sources? ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (4) (c) The pattern on the screen may be represented as a graph of intensity against position on the screen. The central fringe is shown on the graph in Figure 2. Complete this graph to represent the rest of the pattern by drawing on Figure 2. intensity position on the screen centre of pattern Figure 2 (2) (Total 8 marks) 25. Explain the differences between an undamped progressive transverse wave and a stationary transverse wave, in terms of (i) amplitude, (ii) phase and (iii) energy transfer. (i) amplitude progressive wave ........................................................................................................ ..................................................................................................................................... stationary wave ........................................................................................................... ..................................................................................................................................... (ii) phase progressive wave ........................................................................................................ ..................................................................................................................................... stationary wave ........................................................................................................... ..................................................................................................................................... (iii) energy transfer progressive wave ........................................................................................................ ..................................................................................................................................... stationary wave ........................................................................................................... ..................................................................................................................................... (Total 5 marks) 26. screen narrow slit laser Figure 1 Red light from a laser is passed through a single narrow slit, as shown in Figure 1. A pattern of bright and dark regions can be observed on the screen which is placed several metres beyond the slit. (a) The pattern on the screen may be represented as a graph of intensity against distance along the screen. The graph has been started in outline in Figure 2. The central bright region is already shown. Complete this graph to represent the rest of the pattern by drawing on Figure 2. intensity distance along screen centre of pattern Figure 2 (4) (b) State the effect on the pattern if each of the following changes is made separately. (i) The width of the narrow slit is reduced. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) With the original slit width, the intense red source is replaced with an intense source of green light. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (Total 7 marks) 27. The diagram below shows a section of a diffraction grating. Monochromatic light of wavelength is incident normally on its surface. Light waves diffracted through angle form the second order image after passing through a converging lens (not shown). A, B and C are adjacent slits on the grating. d d C B E D A (a) (i) State the phase difference between the waves at A and D. ........................................................................................................................... (ii) State the path length between C and E in terms of . ........................................................................................................................... (iii) Use your results to show that, for the second order image, 2 = d sin , where d is the distance between adjacent slits. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (b) A diffraction grating has 4.5 × 105 lines m–1. It is being used to investigate the line spectrum of hydrogen, which contains a visible blue-green line of wavelength 486 nm. Determine the highest order diffracted image that could be produced for this spectral line by this grating. ................................................................................................................................… ................................................................................................................................… ................................................................................................................................… ................................................................................................................................… ................................................................................................................................… ................................................................................................................................… (2) (Total 5 marks) 28. (a) A helium-neon laser produces monochromatic light of wavelength 632.8 nm which falls normally on a diffraction grating. A first order maximum is produced at an angle of 18.5° measured from the normal to the grating. Calculate (i) the number of lines per metre on the grating, .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... (ii) the highest order which is observable. .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... (6) (b) When the grating is used with a different monochromatic source, the first order maximum is observed at an angle of 17.2° Calculate the wavelength of this second source. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (Total 8 marks) 29. Two prisms made from different glass are placed in perfect contact to form a rectangular block surrounded by air as shown. Medium 1 has a smaller refractive index than medium 2. medium 2 air ry nda bou medium 1 incident ray air 70º (a) A ray of light in air is incident normally on medium 1 as shown. At the boundary between medium 1 and medium 2 some light is transmitted and the remainder reflected. (i) Sketch, without calculation, the path followed by the refracted ray as it enters medium 2 and then emerges into the air. (ii) Sketch, without calculation, the path followed by the reflected ray showing it emerging from medium 1 into the air. (4) (b) The refractive index of medium 1 is 1.40 and that of medium 2 is 1.60. (i) Give the angle of incidence at the boundary between medium 1 and medium 2. ........................................................................................................................... (ii) Calculate the angle of refraction at this boundary. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (4) (c) Calculate the critical angle for a ray passing from medium 2 into the air. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (Total 10 marks) 30. (a) A double slit interference experiment is set up in a laboratory using a source of yellow monochromatic light of wavelength 5.86 × 10–7 m. The separation of the two vertical parallel slits is 0.36 mm and the distance from the slits to the plane where the fringes are observed is 1.80 m. (i) Describe the appearance of the fringes. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (ii) Calculate the fringe separation, and also the angle between the middle of the central fringe and the middle of the second bright fringe. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (iii) Explain why more fringes will be seen if each of the slits is made narrower, assuming that no other changes are made. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (b) (8) Light of wavelength 5.86 × 10–7 Tim falls at right angles on a diffraction grating which has 400 lines per mm. (i) Calculate the angle between the straight through image and the first order image. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (ii) Determine the highest order image which can be seen with this arrangement. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (5) (c) Give two reasons why the diffraction grating arrangement is more suitable for the accurate measurement of the wavelength of light than the two-slit interference arrangement. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. (2) (Total 15 marks) 31. The graph shows the variation of displacement of the particles with distance along a stationary transverse wave at time t = 0 when the displacement of the particles is greatest. The period of the vibrations causing the wave is 0.040 s. displacement /mm 20 Z W 0 20 60 40 20 (a) (b) 100 80 120 distance/mm V Using the same axes, (i) draw the appearance of the wave at t = 0.010 s, labelling this graph B, (ii) draw the appearance of the wave at t = 0.020 s, labelling this graph C, (iii) show an antinode labelled A and a node labelled N. (i) Describe the motion of the particle at V, giving its frequency and amplitude. (3) ......................................................................................................................... ......................................................................................................................... (ii) State the amplitude of the particle at W and its phase relations with the particle at V and the particle at Z. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (6) (Total 9 marks) 32. metal plate detector movement microwave transmitter A microwave transmitter directs waves towards a metal plate. When a microwave detector is moved along a line normal to the transmitter and the plate, it passes through a sequence of equally spaced maxima and minima of intensity. (a) Explain how these maxima and minima are formed. You may be awarded marks for the quality of written communication in your answer. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (b) The detector is placed at a position where the intensity is a minimum. When it is moved a distance of 144 mm it passes through nine maxima and reaches the ninth minimum from the starting point. Calculate (i) the wavelength of the microwaves, ........................................................................................................................... ........................................................................................................................... (4) (ii) the frequency of the microwave transmitter. ........................................................................................................................... ........................................................................................................................... (3) (Total 7 marks) 33. The diagram shows a cross-section of one wall and part of the base of an empty fish tank, viewed from the side. It is made from glass of refractive index 1.5. A ray of light travelling in air is incident on the base at an angle of 35 as shown. wall inside the tank glass tank base 35° (a) Calculate the angle . ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (b) (i) Calculate the critical angle for the glass-air interface. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) Hence, draw on the diagram the continuation of the path of the ray through the glass wall and out into the air. Mark in the values of all angles of incidence, refraction and reflection. (6) (Total 8 marks) 34. Red light of wavelength 7.00 × 10–7 m, incident normally on a diffraction grating, gave a first order maximum at an angle of 75°. (a) Calculate the spacing of the diffraction grating. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... (1) (b) Calculate the angle at which the first order maximum for violet light of wavelength 4.50 × 10–7 m would be observed. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... (1) (c) At what angle or angles would a detector receive radiation which is of wavelength 7.50 × 10–7 m transmitted by the grating? Explain your answer. .................................................................................................................................... .................................................................................................................................... .................................................................................................................................... (2) (Total 4 marks) 35. (a) State Snell’s law of refraction of light and explain the conditions under which the law applies. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (b) The diagram shows a glass pentaprism as used in the viewfinder of some cameras. Light enters face AB and leaves face BC. The faces AE, ED and DC are silvered and the refractive index of the glass is 1.52. E D A 112.5° 112.5° B C (i) On the diagram draw the path of the incident ray from face AB to CD. (ii) State why you have drawn the ray in this direction. ........................................................................................................................... ........................................................................................................................... (2) (c) Explain, with the aid of a calculation, why the face CD needs to be silvered if the ray shown is not to be refracted at face CD. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (3) (d) On the diagram, continue the ray until it leaves the prism. (1) (Total 9 marks) 36. (a) white screen not to scale grating n=5 0.860 m n=4 0.687 m n=3 0.499 m n=2 0.316 m n=1 0.173 m central maximum laser 2.0 m figure 1 In a laboratory experiment, monochromatic light of wavelength 633 nm from a laser is incident normal to a diffraction grating. The diffracted waves are received on a white screen which is parallel to the plane of the grating and 2.0 m from it. Figure 1 shows the positions of the diffraction maxima with distances measured from the central maximum. By means of a graphical method, use all these measurements to determine a mean value for the number of rulings per unit length of the grating. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (Allow one sheet of graph paper) (6) (b) Describe and explain the effect, if any, on the appearance of the diffraction pattern of (i) using a grating which has more rulings per unit length, ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) using a laser source which has a shorter wavelength, ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (iii) increasing the distance between the grating and the screen. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (6) (c) Figure 2, below, shows the diffracted waves from four narrow slits of a diffraction grating similar to the one described in part (a). The slit separation AB = BC = CD = DE = d Q A and EQ is a line drawn at a tangent to several wavefronts and which makes an angle with the grating. figure 2 (i) Explain why the waves advancing perpendicular to EQ will reinforce if superposed. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) Show that this will happen when sin = . d ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (Total 15 marks) 37. The diagram for this question is drawn to scale and 1 mm on the diagram represents an actual distance of 5 mm. Y R S1 Q P S2 Y' S1 and S2 are identical coherent transmitters emitting, in phase, microwaves with a wavelength of 25 mm. They are positioned 250mm apart on a horizontal surface and a detector can be placed anywhere along the line YY which is in the same plane as the transmitters and parallel to the line containing S1 and S2. (a) Explain what is meant by coherent. ..................................................................................................................................... ..................................................................................................................................... (2) (b) By making measurements on the diagram and using the scale, determine the number of wavelengths in the path (i) S1R, ........................................................................................................................... ........................................................................................................................... (ii) S2R. ........................................................................................................................... ........................................................................................................................... (iii) Use your answers to (i) and (ii) to determine whether or not you expect the signal received by a detector placed at R to be a maximum. Explain your answer. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (5) (c) Describe how you would expect the signal strength to vary as the detector is moved from R to P via Q. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (d) Calculate the frequency of the microwaves. ..................................................................................................................................... ..................................................................................................................................... (1) (Total 10 marks) 38. A small intense light source is 1.5 m below the surface of the water in a large swimming pool, as shown in the diagram. X Y 30° Z 60° light source (i) Complete the paths of rays from the light source which strike the water surface at X, Y and Z. (ii) Calculate the diameter of the disc through which light emerges from the surface of the water. speed of light in water = 2.25 × 108 m s–1 speed of light in air = 3.00 × 108 m s–1 ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (Total 7 marks) Materials 39. (a) The Young modulus is defined as the ratio of tensile stress to tensile strain. Explain what is meant by each of the terms in italics. tensile stress ............................................................................................................... ..................................................................................................................................... ..................................................................................................................................... tensile strain ............................................................................................................... ..................................................................................................................................... (3) (b) A long wire is suspended vertically and a load of 10 N is attached to its lower end. The extension of the wire is measured accurately. In order to obtain a value for the Young modulus of the material of the wire, two more quantities must be measured. State what these are and in each case indicate how an accurate measurement might be made. quantity 1 .................................................................................................................... method of measurement ............................................................................................. ..................................................................................................................................... quantity 2 .................................................................................................................... method of measurement ............................................................................................. ..................................................................................................................................... (c) (4) Sketch below a graph showing how stress and strain are related for a ductile substance and label important features. stress strain (2) (Total 9 marks) 40. The diagram below shows a liquid droplet placed on a cube of glass. A ray of light from air, incident normally on to the droplet, continues in a straight line and is refracted at the liquid to glass boundary as shown. refractive index of the glass = 1.45 air 29.2° liquid glass 26.6° (a) Calculate the speed of light (i) in the glass, ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) in the liquid droplet. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3) (b) Calculate the refractive index of the liquid. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (2) (c) On the diagram above, complete the path of the ray showing it emerge from the glass cube into the air. No further calculations are required. (2) (Total 7 marks) 41. The diagram shows tensile stress-strain curves for three different materials X, Y and Z. stress X Y Z strain For each material named below, state which curve is typical of the material, giving the reasoning behind your choice. (a) copper .................................. reasoning .................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (b) glass .................................... reasoning .................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (c) hard steel .............................. reasoning .................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (Total 6 marks) 42. (a) Describe an experiment to determine the Young modulus for a material in the form of a wire. Draw a labelled diagram and explain how you would make the necessary measurements. Show how you would use your measurements to calculate the result. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (8) (b) rigid support F aluminium copper A copper wire and an aluminium wire, each of diameter 0.72 mm, are joined end to end as shown in the diagram with the aluminium wire fixed at right angles to a rigid support. A steadily increasing force, F, is applied. Use data from the Data Sheet to (i) explain which wire will yield, ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) determine the value of F at which yield should occur. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (4) (Total 12 marks) 43. As part of a quality check, a manufacturer of fishing line subjects a sample to a tensile test. The sample of line is 2.0 m long and is of constant circular cross-section of diameter 0.50mm. Hooke’s law is obeyed up to the point when the line has been extended by 52mm at a tensile stress of 1.8 × 108 Pa. The maximum load the line can support before breaking is 45 N at an extension of 88 mm. (a) Calculate (i) the value of the Young modulus, ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) the breaking stress (assuming the cross-sectional area remains constant), ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (iii) the breaking strain. ........................................................................................................................... (5) (b) Sketch a graph on the axes below to show how you expect the tensile stress to vary with strain. Mark the value of stress and corresponding strain at (i) the limit of Hooke’s law, (ii) the breaking point. stress strain (4) (Total 9 marks) 44. (a) (i) Describe the behaviour of a wire that obeys Hooke’s law. ........................................................................................................................... ........................................................................................................................... (ii) Explain what is meant by the elastic limit of the wire. ........................................................................................................................... ........................................................................................................................... (iii) Define the Young modulus of a material and state the unit in which it is measured. ........................................................................................................................... ........................................................................................................................... (b) A student is required to carry out an experiment and draw a suitable graph in order to obtain a value for the Young modulus of a material in the form of a wire. A long, uniform wire is suspended vertically and a weight, sufficient to make the wire taut, is fixed to the free end. The student increases the load gradually by adding known weights. As each weight is added, the extension of the wire is measured accurately. (i) What other quantities must be measured before the value of the Young modulus can be obtained? (5) ........................................................................................................................... ........................................................................................................................... (ii) Explain how the student may obtain a value of the Young modulus. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (iii) How would a value for the elastic energy stored in the wire be found from the results? ........................................................................................................................... ........................................................................................................................... (6) (Total 11 marks) 45. A student carries out an experiment to investigate how the extension of a steel wire varies with an increasing tensile force. The results of the experiment are shown plotted on the graph. The initial length of the wire is 0.50m and its diameter is 0.80 mm. The wire breaks at an extension of 1.46 mm. force/N 110 100 90 80 70 60 50 40 30 20 10 0 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 extension/mm Use information from the graph to determine the Young modulus for the material, ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... an estimate of the yield stress for the material. ............................................................................................................................................... ............................................................................................................................................... ............................................................................................................................................... (Total 6 marks) 46. An aerial system consists of a horizontal copper wire of length 38 m supported between two masts, as shown in the figure below. The wire transmits electromagnetic waves when an alternating potential is applied to it at one end. 38 m of copper wire 14.0 m 12.0 P mast (a) Q mast The wavelength of the radiation transmitted from the wire is twice the length of the copper wire. Calculate the frequency of the transmitted radiation. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (1) (b) The ends of the copper wire are fixed to masts of height 12.0 m. The masts are held in a vertical position by cables, labelled P and Q, as shown in the figure above. (i) P has a length of 14.0 m and the tension in it is 110 N. Calculate the tension in the copper wire. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (ii) The copper wire has a diameter of 4.0 mm. Calculate the stress in the copper wire. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (iii) Discuss whether the wire is in danger of breaking if it is stretched further due to movement of the top of the masts in strong winds. breaking stress of copper = 3.0 × 108 Pa ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (7) (Total 8 marks) Unit 2 Mechanics, Materials and Waves Answers 1. (a) (b) scalars have magnitude (or size) (1) vectors have magnitude and direction (1) (i) s = t (1) s = 100 × (ii) 2 3 =5 km (1) 60 1.59 (1) km (or other correct unit) (1) 4 [6] FB (1) 2. (a) 2 FA (1) (b) (i) taking moments (about A) (1) (400 × 4.0) + (300 × 2) = FB × 1.6 (1) 2200 = FB so FB = 1375(N) (1) 1.6 (ii) FA = 1375 – 700 = 675 (1) N (1) allow e.c.f. from FB (no marks if weight of board not used) max 4 [6] 3. accept mirror image for (a) and (b) (a) (b) velocity 1 acceleration time straight line sloping up (1) sudden change to negative velocity (1) time constant value shown (1) smaller negative velocity (1) same gradient as positive line (1) (c) (i) vertically down at P (1) (ii) vertically down at Q (1) (iii) along tangent at P (1) (iv) along tangent at Q (1) 4 4 [9] 4. (a) (b) 2 .1 = 3.0 ms–2 (1) 0 .7 (i) gradient = (ii) distance is area under graph (to t = 0.1 s) 1 or × 0.7 × 2.1 2.1 2.5 0.3 (1) = 1.4(2) m (1) 2 2 (i) 3 T – mg = ma [or T = 1500(9.8+3.0)] (1) = 1.9 × 104 N (1) T = mg = l.5 × 104 N (1) (ii) (c) EF (1) 4 power = F or l.5 × 104 × 2.5 (1) = 3.7[3.8] × 104 W (1) 2 [9] 5. (a) (i) region A: uniform acceleration (or (free-fall) acceleration = g( = 9.8(i) m s–2)) force acting on parachutist is entirely his weight (or other forces are very small) (1) (ii) region B: speed is still increasing acceleration is decreasing (2) (any two) because frictional (drag) forces become significant (at higher speeds) (iii) region C: uniform speed (50 m s–1) because resultant force on parachutist is zero (2) (any two) weight balanced exactly by resistive force upwards 6 QWC (b) (c) (d) deceleration is gradient of the graph (at t = 13s) (1) (e.g. 20/1 or 40/2) = 20 m s–2 (1) 2 distance = area under graph (1) suitable method used to determine area (e.g. counting squares) (1) with a suitable scaling factor (e.g. area of each square = 5 m2) (1) distance=335m (±15m) (1) 4 (i) speed = (5.02 + 3.02) = 5.8 m s–1 (1) (ii) tan = 3 5 gives = 31°(1) 2 [14] 6. (a) (i) and (ii) energy A (1) B same height as A and above C C(1) Q distance along slope (iii) A + B = constant (1) loss in potential energy = gain in kinetic energy for A and B [or potential energy at P = kinetic energy at Q for A and B] (1) reason for C being below B e.g. transfer to heat [or work done against friction] (1) (b) (i) clear reference to energy c(= 2 gh ) = –1 = 31(.3)m s (1) (ii) (iii) 2 80 (31.3) 2 F m c = (1) 20 r = 3.9(2) × 103 N towards centre of circle (1) gain in gravitational potential energy 2 9.8 50 (1) 6 ( = mgh sin ) = 620 × 9.8 × 60 × sin 20° (1) = 1.25 × 105 J (iv) 620 × 9.8 × 50 = (F × 60) (1) +1.25 ×105 (1) F = 3000N (1) alternative (iv) calculation of acceleration = (–)8.0 m s–2 (1) use of F + mg sin = ma (1) F = 3000N (1) max 9 [15] 7. (a) (b) (i) T = 2.0 × 9.8 = 19.6N (1) (ii) moments about B 19.6cos30° × 1.6 (1) = mg × 0.8 (1) 33.9 mass = (1) (= 3.46 kg) 9.8 maximum support when wire vertical (1) moments about B 2.0 × 9.8 × 1.6 = (M × 9.8 × 1 .2) (1) + 33.9 × 0.8 (1) M = 0.36 kg (1) [n.b. 0.33 kg if 3.5 used] 4 4 [8] 8. (a) N (1) F (1) T (1) lines of action of the three forces pass through single point (1) max 3 (b) (i) F = 350N (1) (ii) N = 550N (1) if “sine” used in (i) and “cos” in (ii) allow one mark allow calculation from drawing scale diagram if (i) and (ii) not awarded marks, then award one mark for correct vector diagram 2 [5] 9. (a) T = mg = 890 × 10 = 8900 (1) N (1) (accept alternative correct value using g = 9.81 N kg–1) 30° 2 T (b) F mg resolve vertically T cos 30° =mg (1) mg T= = 10280(1.03 × 104 )N (1) cos 30 (c) (i) (ii) (iii) 2 vertical height fallen = l(1 – cos ) = 15(1 – 0.866) = 2.0(1) m (1) (allow e.c.f if h calculated wrongly) 1 m2 = mgh or reference energy (1) = 2 (max 1/3 if equations of motion used) 2 10 2.01 = 6.34 m s–1 (1) 890 6.34 F (m ) = = 2.8 × 104 N (1) 0 . 2 t (allow e.c.f of and m as before) 5 [9] 10. (a) F T W 2 components at right angles (1) vertical component in line with the weight (1) vertical components to start from the ) (b) (c) (i) (horizontal component) = 25 sin = 12 (or 13) N (12.5) (1) ( 0.5N if scale drawing) (ii) (vertical component) = 25 cos = 22 N (21.7) (1) (± 0.5 N if scale drawing) (i) vertical component of F = 21.7 + 2.5 = 24 N (24.2) 2 [or 25 (24.5)] (1) (allow C.E. from (b)) (ii) horizontal component of F.= 12 (or 13) N (1) (12.5) (allow C.E. from (b)) (iii) F = (12.52 + 24.22) (1) (allow C.E. from parts (i) and (ii)) = 27 N (27.2) [or 28 (28.2) ] (1) (26 N to 29 N if scale drawing) [if measured on diagram and F cos used, (1) (1) (same tolerance)] 4 [8] 11. (a) (b) (i) (use of v2 = u2 + 2as gives) 0 = 252 - 2 × 9.81 × s (1) 19.6 s = 625 and s = 32 m (1) (ii) t= (iii) (use of v2 = u2 + 2as gives) v2 = 252 – 2 × 9.81 × 16 (1) (allow C.E. from (a)(i)) and v = 18 m s–1 (1) max 4 25 = 2.5 s (1) 9.81 time to stop the ball is greater (1) rate of change of momentum is less (1) [or work done on ball is the same but greater distance (1) less force (1) ] 2 [6] 12. (a) F cos 20 = 300 gives F = 319 N(1) (b) (i) work done = force × distance moved in direction of force (1) F is not in the direction of motion (1) (ii) work done = force × distance = 300 × 8000 = 2.4 × 106 J (iii) power = (c) work done (1) time taken 2.4 = 10 6 (1) (allow e.c.f. for work done in (ii)) 5.0 (60 60) = 133 W (1) (allow e.c.f. for incorrect time conversion) 1 6 on the level, work is done only against friction (1) uphill, more work must be done to increase in potential energy (1) sensible conclusion drawn (e.g. increased work at constant power requires longer time) (1) 3 [10] 13. (a) (i) F s two forces opposing (1) forces parallel (1) s correct (1) F (b) (c) (ii) N m (1) 4 (i) anticlockwise moments = clockwise moments (1) (ii) weight of beam acts at centre (1) this is through the pivot (1) 3 (equating moments gives) 400 × 1.0 = 200 × 0.50 + 250 × d (1) 400 – 100 = 250 × d and d = 1.2 m (1) 2 [9] 14. (a) (i) F1 weight / mg (1) F2 reaction or normal contact force (1) F3 driving force (1) F4 friction or air resistance (1) (ii) zero acceleration (1) zero resultant force (1) max 5 QWC (b) (P = Fv gives) 18 × 103 = F × 10 (1) (and F = 1.8 × 103 N) (c) (i) 1800 – 250 = 1.6 × 103 N (1) (ii) force = 4 × 1.55 × 103 = 6.2 × 103 N (1) (allow e.c.f. from(i)) (iii) total force = 6200 + 250(N) (1) (1.55 × 103 N) (= 6.45 × 103(N)) 1 (P = Fv gives) P = 6.45 × 103 × 20 = 1.3 × 105 W (1) (allow e.c.f. for value of total force) (1.29 × 105 W) 4 [10] 15. (a) (i) C (1) B (1) A (1) n.b. B must make an appreciable angle with wall and bar (ii) A B C weight of sign and bar (accept gravity) (1) reaction of wall (1) tension in wire (1) max 5 40° (b) 0.375m 118N use of mg (1) clockwise moments 118 × 0.375 (1) = anticlockwise moments (Tcos40° (1)) × 0.750 (1) T = 77 N (1) max 4 [9] 16. (a) (i) initial acceleration/increase of speed (1) reaches a constant speed/velocity (1) acceleration decreases to become zero (at this speed) (1) (ii) drag/frictional forces increases with speed (1) drag equal to weight (– upthrust) (1) no resultant force at terminal speed [or balanced forces or forces cancel] (1) max 5 (b) (c) column C 26.6 39.7 49.4 75.2 118 173.5 (i) (ii) (d) (i) (ii) column E 1.42 1.60 1.69 1.88 2.07 2.24 four values correct (1) all values correct and to 3 or 4 s.f. (1) 2 all values correct and to 3 or 4 s.f. (1) axes labelled and suitable scales chosen (1) at least 5 points plotted correctly (1) acceptable line (1) 4 gradient = (e.g) 2.40 – 1.00 = 2.0 (1) 0.7 = n gradient (= 2) (1) intercept on y-axis = log k (1) intercept = 1.0 (1) k (= 101.0) = 10 (1) units of k: for n = 2, mm–1 s–1 (1) max 5 [16] 17. (a) component (parallel to ramp) = 7.2 × 103 × sin 30 (1) (= 3.6 × 103 N) (b) mass = (c) (d) 7.2 10 3 = 734 (kg) (1) 9.81 3600 a= = 4.9(1) m s–2 (1) 734 (use of v2 = u2 + 2as gives) 0 = 182 – (2 × 4.9 × s) (1) s = 33(.1) m (1) (allow C.E. for value of a from (b)) frictional forces are acting (1) increasing resultant force [or opposing motion] (1) hence higher deceleration [or car stops quicker] (1) energy is lost as thermal energy/heat (1) 1 2 2 Max 2 [7] 18. (a) (b) product of the force and the perpendicular distance (1) reference to a point/pivot (1) (i) since W is at a greater distance from A (1) then W must be less than P if moments are to be equal (1) (ii) P must increase (1) since moment of girl’s weight increases as she moves from A to B (1) correct statement about how P changes (e.g. P minimum at A, maximum at B, or P increases in a linear fashion) (1) 2 max 4 [6] 19. (a) (b) (c) (d) suitable calculation using a pair of values of x and corresponding t to give an average of 2.2 m s–1 ( 0.05 m s–1) (1) valid reason given (1) (e.g. larger values are more reliable/accurate or use of differences eliminates zero errors) (i) column D (y/t (cm s–1) 186 210 233 259 284 307 2 all values correct to 3 s.f. (1) (ii) graph: chosen graph gives a straight line (e.g. y/t against t) (1) axes labelled correctly (1) suitable scale chosen (1) minimum of four points correctly plotted (1) best straight line (1) (iii) u (= y - intercept) = 162 cm s–1 ( 4 cm s–1) (1) gradient = 495 (cm s–2) ( 25 cm s–2) (1) k = gradient (= 495 cm s–2) (1) (i) u : initial vertical component of velocity (1) (ii) k : = ½ g (1) v2 = u2 + 2.22 (1) gives v = (1.622 + 2.22)1/2 = 2.7 m s–1 ( 0.1 m s –1) (1) 9 2 2 [15] 20. (a) (b) energy of closed system is constant (or energy is neither created or destroyed) (1) energy is only converted from one form to another (1) (i) 2 loss in p.e. = gain in k.e. + work done against resistance (1) work appears as heat (1) total energy constant (1) energy p.e. shapes (1) p.e. = k.e. + work, always (1) (ii) k.e. 0 (c) 5 work t time (i) use of power × time and mcT (1) correct substitution to find T (or to calculate t or to check both sides of equation using sensible T) e.g. 2300 × 94, 0.57 × 4200 × 90 ( 2.2 × 10 J) (1) assume no heat loss (1) justification of claim (figures alone are acceptable) (1) (ii) energy to boil away 1/2 pint = 0.5 × 0.570 × 2.3 × 106 ( = 6.55 × 105 J) (1) 6.55 10 5 time taken = =285 s (1) 2300 max 5 [12] 21. (a) (i) superposition (1) between waves in phase (1) gives constructive interference (1) (ii) at D or E waves out of phase (1) so destructive interference (1) max 4 (b) (i) = 330 = 0.165m (1) 2 10 3 separation between maxima = 0.165 5 = 1.10(m) (1) 0.75 D s (1) distance CE (= 1 2 × separation)= 0.55 m (1) 4 [8] 22. (a) (b) (i) 0.270 2 = 0.18m (1) 3 (ii) 340 f c = = 1.89 × 103 Hz (1) 0.18 transverse direction of vibration perpendicular to propagation [or can be polarised] (1) longitudinal direction of vibration parallel to propagation [or cannot be polarised] (1) longitudinal (1) (c) 2 3 (i) frequency same (1) (ii) ap aq (iii) phase difference = (1) 3 [8] 23. (a) superposition two or more vibrations(or waves) give a single vibration (or wave) (1) coherent same wavelength (or frequency) and constant phase relationship (1) 2 (b) (i) fringes in overlap diagram showing overlap (1) waves diffracted at slits, stated or shown (1) (ii) diffraction pattern wider (or more overlap or more diffraction) (1) more fringes (1) fringes less bright because less light through narrow slit (1) max 4 [6] 24. (a) (b) same wavelength or frequency (1) (same phase or) constant phase difference (1) (i) narrow slit gives wide diffraction (1) 2 (to ensure that) both S1 and S2 are illuminated (1) (ii) slit S acts as a point source (1) S1 and S2 are illuminated from same source giving monochromatic/same λ (1) paths to S1 and S2 are of constant length giving constant phase difference (1) [or SS1 = SS2 so waves are in phase] Max 4 QWC 1 (c) graph to show: maxima of similar intensity to central maximum (1) [or some decrease in intensity outwards from centre] all fringes same width as central fringe (1) 2 [8] 25. amplitude: each point along wave (1) has same amplitude for progressive wave but varies for stationary wave (1) phase: progressive wave, adjacent points vibrate with different phase (1) stationary wave, between nodes all particles vibrate in phase [or there are only two phases] (1) energy transfer: progressive wave, energy is transferred through space (1) stationary wave, energy is not transferred through space (1) max 5 [5] 26. (a) (b) graph to show: maxima of successively smaller intensity (1) subsidiary maxima/minima equally spaced (1) (at least two each side of central axis) width of subsidiary sections half width of central section (1) symmetrical pattern each side of central axis (1) (i) broader maxima or pattern (1) [or fringes wider apart] dimmer pattern (1) (ii) maxima are closer (1) [or narrower fringes] green and dark regions (1) max 3 27. (a) (i) 0, 2 or 4 [or 0, 360° or 720°] (1) 4 [7] (ii) 4 (1) (iii) sin = CE (1) AC [or sin = BD ] AB CE = 4 and AC = 2d (1) (hence result) [or BD = 2 and AB = d] max 3 (b) 28. (a) (limiting case is when = 90° or sin = 1) 2.22 10 6 (1) d sin (1) (= 4.6) n 486 10 9 highest order is 4th (1) (i) 2 [5] (since d sin = n) d sin l8.5° = 632.8 × 10–9 (1) d = 1.99 × 10–6 (1) number of lines per metre = (ii) 1 = 5.01 × 105 (1) d n = 1.99 × 10–6 sin 90° (1) n=– 1.99 = 3.1(5) (1) 0.6328 hence highest order is third (1) (b) new = 632.8 10 –9 sin 17.2 = 590nm(1) sin 18.5 or 1.994 10 6 –6 sin 17.2 (1) 2 [8] 29. (a) Ray diagram to show: (b) (i) refraction towards normal at boundary (1) emerging ray refracted away from normal (1) (ii) reflection at boundary with i r emerging ray refracted away from normal (1) (i) 20° (1) (ii) 1n2 = 4 n2 sin 1 (1) n1 sin 2 1.60 sin 20 (1) 1.40 sin 2 = 17 (.4)° (1) (c) (sin c = 1/n gives) 4 sin c = 1/1.60 (1) = c = 38.7° (1) 2 [10] 30. (a) (i) vertical or parallel (1) equally spaced (1) black and yellow [or dark and light] bands (1) (ii) (iii) D 5.86 10 –7 1.8 w (1) = s 0.36 10 –3 = 2.9 × 10–3 m (1) 2 2.9 10 –3 tan = (1) gives = 0.18° (1) 1.8 narrower slits give more diffraction (1) more overlap (so more fringes) (1) fringes same width (1) max 8 (b) (c) 1 (1) 400 10 3 1 × sin = 5.86 × 10–7 (1) 3 400 10 = 13.6° (1) (i) d= (ii) = 90° and correctly used (1) 1 n= = 4.3 4th order (1) 3 400 10 5.86 10 – 7 5 brighter images (1) large angles (1) sharper (or narrower) lines (1) max 2 [15] 31. (a) (b) (i) B line along distance axis (1) (ii) C negative sine wave starting at O (1) (iii) A, N (1) (i) s.h.m. [or particle stationary] (1) amplitude = 20 mm (1) 1 f= = 25 Hz or s–1 (1) T (ii) 10 mm (1) W,V phase difference [or antiphase or 180°] (1) W,Z in phase (1) 3 6 [9] 32. (a) interference or superposition (1) reflection from metal plate (1) two waves of the same frequency/wavelength (1) travelling in opposite directions (or forward/reflected waves) (1) maxima where waves are in phase or interfere constructively (1) minima where waves are out of phase/antiphase or interfere destructively (1) nodes and antinodes or stationary waves identified (1) max 4 QWC 2 (b) (i) (distance between minima = ) (1) 2 144 gives = 32.0 mm (1) 9 2 (ii) c = f and c = 3 × 108 (m s–1) (1) 8 f = 3 10 – 3 = 9.38 × 109 Hz (1) 32 10 (allow C.E. for value of from (i)) 3 [7] 33. (a) (b) sin 1 sin 35 o gives) 1.5 = (1) sin 2 sin = 22° (1) (22.48°) (1n2 = (i) (sinc = 1/n gives) sinc = c = 42° (1) (41.8°) (ii) 2 1 (1) 1.5 ray diagram to show: one total internal reflection (1) with one angle of reflection marked as 68° (1) correct refraction of ray on exit from top surface with 35° marked (1) angle of incidence of 22° marked at point of exit (1) 6 [8] 34. (a) –7 d = n = (1 7.00 10 ) = 7.2 × 10–7 m (accept 7.3) (1) sin 75 sin (b) = sin–1 (c) 4.5 10 –7 –7 1 7.2 10 = 39° (accept 38°) (1) 1 1 –7 = 7.5 10 > 1 (or sin > 1) (1) d 7.2 10 – 7 0° (or straight through position) because no first order line (1) 2 [4] 35. (a) for monochromatic light (1) travelling from one medium to another (1) sin (angle of incidence) = constant 3 sin (angle of refraction) E D A (b) (c) (d) B C (i) correct ray (1) (ii) no deviation because i = 0° [or because ray is normal to AB] (1) 2 1 c = 41° (1) i= 22.5° (1) 1.52 i < c , refracted angle = 35.6° so no total internal reflection [or rays would emerge] (1) 3 correct ray (1) 1 sinc = [9] 36. (a) 1 2 3 4 5 x/m 0.173 0.316 0.499 0.687 0.860 sin 0.086 0.156 0.242 0.325 0.395 If angles only calculated 1/2 at least 4 points plotted correctly (1) best straight line (1) gradient calculated from suitable triangle, 50% of each axis (1) correct value from readings (1) appropriate use of d sin = n (1) hence N (rulings per metre) = 1.25 × 105 m–1 (1.1 to 1.4 ok) (1) max 2/6 if no graph and more than one data set used correctly, 1/6 only one set if tan calc but plotted as sin, mark as scheme tan or distance plotted, 0/6 max 6 (b) (c) (i) maxima wider spaced [or pattern brighter] (1) sin or increases with N [or light more concentrated] (1) (ii) maxima spacing less (1) sin or decreases with [or statement] (1) (iii) maxima wider spaced [or pattern less bright] (1) same but larger D [or light more spread out] (1) (i) waves in phase from (1) any sensible ref to coherence (1) whole number of wavelengths path difference (1) (ii) use of geometry to show that sin = 6 (1) d max 3 [15] 37. (a) (b) constant phase relationship (1) (1) [or same frequency (wavelength) (1) and same phase difference (1)] 2 S1R = 15cm on diagram (1) =75cm 30 waves (1) S2R = 16cm on diagram (1) = 80cm 32 waves (1) 2 whole waves difference so in phase at R (1) maximum (1) max 5 (c) (d) (falls then rises to) maximum at Q (1) (then falls and rises to) maximum at P (1) c 3.0 10 8 f = = 1.2 × 1010 Hz (or 12 GHz) (1) –3 25 10 2 1 [10] 38. (i) (ii) ray straight through at X (1) ray refracted at >30° at Y (1) ray totally internally reflected at Z (1) sin water c water 2.25 10 8 = [or = ] sin air c air 3.00 10 8 at critical angle sinair = 1 (1) sinwater = 0.75, water = 48.6° (1) radius = 1.5tan48.6° (1) =1.7m, diameter = 3.4m (1) [Max 7] 39. (tensile) force (1) cross – sectional area extension tensile strain = (1) original length mention of tensile and original (1) 3 (a) tensilestress = (b) diameter of wire (1) in several places [or repeated] (1) using a micrometer (1) (original) length of wire (1) using a metre rule (or tape measure) (1) max 4 stress (1) (plastic region) (c) 2 (1)(linear region) strain [9] 40. (a) (i) (use of n = c1 gives) c2 8 cglass = × 3.00 10 1.45 = 2.07 × 108 m s–1 (1) (ii) use of sin 1 c1 (1) sin 2 c 2 8 cliquid = 2.07 10 sin 29.2 = 2.26 × 108 m s–1 (1) sin 26.6 (allow C.E. for values of cglass from (i)) (b) use of 1n2 = c1 n and 1n2 = 2 c2 n1 to give nliquid = 1.45 2.07 810 = 1.33 (1) 2.26 10 8 8 c1 3 10 8 1.33 or n1 c 2.26 10 liquid (allow C.E. for value of cliquid) 3 [or use 1n2 = (c) sin 1 n and 1n2 = 2 = to give correct answer] sin 2 n1 diagram to show : total internal reflection on the vertical surface (1) refraction at bottom surface with angle in air greater than that in the liquid (29.2°) (1) 2 2 [7] stress X Y 41. Z strain (a) Y (1) significant plastic deformation (or Young modulus less than X) (1) (b) Z (1) no plastic deformation (or smallest value of Young modulus) (1) (c) X (1) small amount of plastic deformation (or Young modulus greater than Y) (1) [6] 42. (a) diagram showing two supported wires and vernier [or long wire and appropriate scale] (1) one justification of design (1) measurements: identified length with ruler (1) diameter with micrometer (1) in several places [or in different directions] (1) add load [mass] and read vernier (1) repeat for range of loads (1) within limit of proportionality [allow elastic limit] (1) calculation of at least one value from readings (1) graph or calc and average (1) if apparatus unsuitable, mark to scheme to max 6/8 max 8 (b) aluminium yields, has smaller yield strength identified from data sheet (1) use of F(=sA) (1) = 50 × 106 × × (0.36 × 10–3)2 (1) = 20.3N (1) 4 [12] 43. (a) (i) strain = 0.026 (1) E = 6.92 × 109 Pa (1) (ii) A = 1.96 × 10–7 (m2) (1) stress = 230 × 108 Pa (1) (iii) stress/ 108 Pa breaking strain = 0.044 (1) (i) 2.5 5 (ii) 2.0 1.5 1.0 (b) 0.5 0 0 0.01 0.02 0.03 0.04 0.05 strain shape overall (1) (i) straight line (1) 0 to (0.026, 1.8) (1) (ii) curve (1) to (0.044, 2.3) (1) Max 4 [9] 44. (a) (b) (i) the extension produced (by a force) in a wire is directly proportional to the force applied (1) applies up to the limit of proportionality (1) (ii) elastic limit: (iii) the Young modulus: ratio of tensile stress to tensile strain (1) unit: Pa or Nm–2 (1) the maximum amount that a material can be stretched (by a force) and still return to its original length (when the force is removed) (1) [or correct use of permanent deformation] (i) length of wire (1) diameter (of wire) (1) (ii) graph of force vs extension (1) reference to gradient (1) 5 gradient = E A (1) l [or graph of stress vs strain, with both defined reference to gradient gradient = E] area under the line of F vs e (1) [or energy per unit volume = area under graph of stress vs strain] 6 [11] 45. uses slope of straight line region (1) slope = 1.54 × 105 (Nm–1) (1) l E = slope × (1) A A = 5.03 × 10–7 (m2) (1) E = 1.5 × 1011 Pa (1) Fy = 87 (N) (1) yield stress = 1.7 × 108 Pa (1) 46. (a) c 3.0 10 8 3.9(4) MHz (1) f 76 (b) [6] (=2 × 38) = 76(m) (i) 12 angle between cable and horizontal = sin –1 59 (1) 14 T= 110cos59° = 57N • (56.7N) (1) (allow C.E. for value of angle) (ii) cross-sectional area (= (2.0 × 10–3)2) =1.3 × 10–5(m2) (1) (1.26 × 10–5(m2)) 57 tension stress = (1) –5 area 1.3 10 = 4.4 × 106Pa (1) (4.38 × 106Pa) (use of 56.7 and 1.26 gives 4.5 × 106 Pa) (allow C.E. for values of T and area) (iii) breaking stress is 65 × stress copper is ductile copper wire could extend much more before breaking because of plastic deformation extension to breaking point unlikely 1 any three (1)(1)(1) 7 [8]
