2.25 m. (a) Using Newton s laws of motion, explain why the student can gain an initial speed to leave the ground vertically.

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1 NAME : F.5 ( ) MARS: /70 FORM FIVE PHYSICS TEST on MECHANICS Time Allowe: 70 minutes This test consists of two sections: Section A (structure type questions, 50 marks); Section B (multiple choice, 20 marks) Answer ALL questions on the question paper. Section A (50 marks) 1. Figure 1 shows a stuent trying to jump up to a maximum height. Staning on the groun with her arms fully stretche upwars, she coul have her hans move vertically up from 2.25 m to 3 m above the groun. Figure 1 3 m 2.25 m (a) Using Newton s laws of motion, explain why the stuent can gain an initial spee to leave the groun vertically. (4 marks) By exerting a force on the groun, the groun exerts the same but opposite force on the stuent which is upwar. by Newton s 3r law. With such force larger than her weight, there is a net upwar force acting on her. (b) The stuent woul accelerate up accoring to Newton s 2n law. Estimate the initial spee of the stuent at the instant she leaves the groun. Assume that air resistance is negligible. 0 2 u 2 = 2( 9.81)(3 2.25) u = 3.84 m s -1 (b) Describe how an experiment can be conucte in the school laboratory to investigate the relation between acceleration of a boy an its mass. State clearly all the necessary measurements an the expecte result of the experiment. (7 marks) Set up friction-compensate plane by tilting the plank such that a trolley can runs own with uniform spee. Then measure the acceleration of the trolley by motion sensor (or ticker-tape r) when a force is applie own slope by a string whose extension is kept constant throughout. Repeat the experiment by aing loas on the trolley an recors the mass by balance in each case. plot a graph of acceleration against 1/m, where m is the mass of the loae trolley. a straight line passing through origin is expecte. showing that a is inversely proportional to m. 1

2 2. A uniform gangplank PQ of a ferry smoothly hinge at en P initially rests horizontally on the pier as shown in the figure. The gangplank has weight 500 N an length 2 m. It is raise by a man on the ferry using a light rope passing a smooth fixe light pulley an connecting to R on the gangplank as shown. R is 1.5 m from en P. P 50 o R Q ferry 1.5 m sea pier (a) With a suitable force applie, the gangplank can be hel horizontal without touching the pier. In such situation, fin (3 marks) (i) (ii) the moment prouce by the tension of the rope about P an hence (500)(1) = 500 Nm the value of the force applie. Fsin50 o (1.5) = 500 F = 435 N (b) If gangplank is then raise steaily, the subsequent force require woul change. State the change an briefly account for such change. Smaller Because moment ue to weight is reuce an angle mae by rope with plank is larger. 3. A trolley initially travels at a spee of 60 m s 1 along a straight horizontal railway. Due to mechanical failure, the trolley ecelerates at 2 m s -2 for 5 s before a plasticine is suenly roppe onto it as shown in Figure 3, an it takes 0.4 s for the plasticine to travel at the same spee with the trolley after impact. 60 m s 1 Figure 3 (a) (i) Fin the spee of the trolley just before the plasticine is roppe onto the trolley. v = 60 (2)(5) = 50 m s -1 (ii) Sketch on the graph below the variation of the spee of trolley within this 5 s. (1 mark) spee / m s / s

3 (b) Given the mass of the trolley an plasticine are 0.1 kg an 0.05 kg respectively. (i) Fin the final common spee of the trolley an the plasticine. (0.1)(50) = (0.15)v v = 33.3 m s -1 (ii) Just before impact with the trolley, the plasticine is travelling own at a spee of 2 m s -1. Fin the magnitue of the average vertical force acte on the plasticine by the trolley uring the 0.4 s. F (0.05)(9.81) = (0.05)(0 + 2)/0.4 F = N 4. (a) Figure 4(a) shows a cushione running shoe. It has a layer of air or liqui near the base of the shoe. Apply Physics principle to explain the major benefit of the cushion layer. (3 marks) When the runner runs, his feet hit the groun an the cushion helps to length the of impact Impulse = Ft, for the same impulse This leas to a smaller impact force. Figure 4(a) (b) Figure 4(b) shows the velocity- graph of a runner in a 100 m race, from the when the start signal soune. velocity / ms 1 (i) State his reaction. (1 mark) 0.5 s (ii) The runner fell own accientally an stoppe the race, ha he finish the race when he fell? Support your answer with calculations. The area uner graph = istance he run = (3+8)(17.5/2) = m The istance is smaller than 100 m, thus he hasn t finishe the race /s Figure 4(a) (iii) The runner has a mass of 50 kg, calculate the net force he require at t = 1s. What can he obtain such force? (3 marks) The acceleration is = 17.5/1 = 17.5 ms -2 Thus, the net force = 50 (17.5) = 875 N The runner shoul push his leg backwar on the groun an by action an reaction, the groun will push him with the require force (iv) The answer in (iii) is smaller than the actual force require ue to the presence of air resistance. Discuss the variation of the actual force in the first 2 s. Since air resistance increases with velocity As the runner runs faster, the force acting on him nees to increase 3

4 5. A ping-pong ball is hit an it follows a trajectory as shown in figure 5. The ball flies off with an angle 40 0 with the horizontal m Figure 5 1 m 0.6 m 76 cm (a) Calculate the spee at which the ball flies off? (3 marks) Vertical motion: -(1-0.76) = v sin40 0 t 1/2 (9.81)t 2 Horizontal motion: v cos 40 0 t = ( ) Therefore = (38.3/v 2 ) v = 4.34 ms -1 (b) Calculate the vertical velocity of the ball when it hits the table. (3 marks) Initial vertical velocity = 4.34 sin 40 0 = 2.79 ms -1 v 2 - (2.79) 2 = 2 (-9.81)(-0.24) v = 3.53 ms -1 (c) If the table is smooth, sketch the subsequent path of the ball after hitting the table on figure 5. Explain your answers briefly. Soun an heat energy loss cannot be ignore. (3 marks) If the table is smooth, the ball will leave with the same horizontal spee However, the vertical velocity is smaller ue to the impact an energy loss to soun an heat Therefore, it flies with a smaller velocity (smaller range) an a smaller angle with horizontal. 6. A boy of mass 30 kg is staning on a balance, place in a lift which is moving upwar slower an slower. The balance reaing keeps at a value of 285 N while the lift comes to a stop after moving a istance of 20 m. (a) Calculate the acceleration of the lift. State the irection clearly. (3 marks) 30 (9.81) 285 = 30 a a = 0.31 ms -2 ownwar (b) Calculate the change in velocity of the boy in travelling the state 20 m. ecrease in ke. = gain in pe - workone against the lift force (accept other approaches) 1/2 (30)v 2 = (30)(9.81)(20) - 285(20) v = 3.52 ms -1 En of Section A 4

5 Section B (20 marks) Write your answers on the spaces provie below. D A B B B C 7. B 8. D 9. C 10. D 1. A ball is falling from rest uner gravity at a height H an bouncing back from the groun two s. Assume that the collision with the groun is perfectly elastic an neglect air resistance. (Downwar measurement is taken to be positive.) (1) (2) 0 0 (3) (4) 0 0 Which of the above graphs correctly represents the motion graph of the ball? Displacement- graph Velocity- graph Acceleration- graph A. (1) (2) (3) B. (2) (4) (1) C. (4) (1) (3) D. (4) (2) (3) 2. The string of a bow is rawn taut with a force of F an an arrow is hel stationary as shown. Each string makes an angle of with the horizontal. As the value of changes from 90 o to 10 o C, the value of F shoul A. increase throughout. B. ecrease throughout. C. increase an then ecrease. D. ecrease an then increase. F string string bow arrow 3. A hunter stans at about 60 m away from a tree an he uses the bow to release the arrow in orer to shoot a coconut hel by a monkey (not shown in the figure) in the tree. The coconut is at a height of 25 m from the groun. The hunter aims irectly at the coconut an the arrow leaves the bow at a spee u making an angle of 20º to the horizontal. At the moment the hunter releases the arrow, the monkey rops the coconut such that it falls vertically from rest. coconut hunter s position u m 60 m 5

6 4. The arrow hits the coconut at a height of 12 m. Neglect air resistance an the arrow s size an take g = 9.81 m s 2, fin the value of u. A m s -1 B m s -1 C m s -1 D m s -1 m F a A block of mass m initially resting on a horizontal surface is pulle along the surface by a horizontal force F increasing from zero. The graph (soli line) shows the relation between the acceleration of the block a an force F, which of the following statements is/are correct? (1) There is friction between the surface an the block. (2) The otte line shows the expecte graph if a heavier block is use. (3) If the surface is tilte at a suitable angle, the block coul slie own with uniform spee. A. (1) an (2) only B. (1) an (3) only C. (2) an (3) only D. (1), (2) an (3) 0 F 5. On a smooth horizontal surface, a circular isk P moving at velocity u along the x irection collies obliquely with an ientical isk Q initially at rest as shown below. The mass of each isk is m. Which statements about the collision must be correct? (1) Momentum of the system in the x irection is not conserve. P u Q P Q y x (2) The total kinetic energy of P an Q after collision is (3) Spee of Q after collision is less than u. A. (1) only B. (3) only C. (1) an (2) only D. (2) an (3) only 1 mu Two forces F 1 an F 2 are acting on a particle an if a thir leftwar force now acts on the particle, it will then experience no net force, which of the following iagrams best shows the situation? A. B. C. D. 6

7 7. A 100 N block is suspene by two threas as shown. Threa S 1 makes an angle with the horizontal an its tension 150 N, calculate the tension in S 2. A. 83 N B. 112 N C. 125 N D. It cannot be foun because of insufficient ata. S N S 2 8. A horizontal force of 15 N pushes blocks A an B of mass 1 kg an 4 kg respectively on a horizontal smooth surface as shown. The force acting on block A by block B is A. 3 N to the right B. 3 N to the left C. 12 N to the right D. 12 N to the left 15 N 1 kg 4 kg 9. A block rests on a rough incline as shown. Which of the following graphs correctly shows all force acting on it? A. B. C. D. 10. An object is projecte upwar. Which of the following graphs best shows the variation of its kinetic energy with the istance that it moves up? A. B. C. D. En of Test 7