WORK, ENERGY AND POWER P.1

Transcription

1 WORK, ENERGY AND OWER.1 HKCEE AER I Figure 6 shows an experimental setup, which is used to find the friction between a block and a table. A weight is connected to the block through a frictionless pulley with a light inextensible string. The masses of the weight and the block are. kg and 1 kg respectively. The weight and the block are initially at rest. pulley block table weight h Q Figure 6 The weight is released at and falls with uniform acceleration. The time taken for the weight to fall a certain distance h (from to Q) is measured. When h =.7 m, the time taken is.95 s. Neglect air resistance. (a) Determine the acceleration of the weight. ( marks) (b) Find the speed of the weight at Q. ( marks) (c) By the law of conservation of energy, or otherwise, find the friction acting on the block. 9 A fire breaks out in a building. A 6 kg man in the building falls vertically from rest from a height of 15 m. He is rescued by a cushion of thickness.5 m (see Figure ). Neglect the size of the man. Figure building 15 m rescue cushion.5 m ground (a) Find the kinetic energy of the man just before reaching the cushion. ( marks) (b) The man is stopped by the cushion when he is.5 m above the ground. Find the average resistive force acting on the man by the cushion. ( marks) *(c) In a thicker cushion is used and the man is again stopped when he is.5 m above the ground, explain why the thick cushion is better for rescuing the man. (4 marks) 8 1 Figure 1 shows an athlete lifting a barbell of mass 115 kg by a vertical distance of 1.8 m from the ground. 1.8 m barbell Figure 1 ground 1

2 WORK, ENERGY AND OWER. (a) Find the potential energy gained by the barbell after it is lifted up. (1 mark) (b) The mass of the athlete is 7 kg. Find the normal reaction acting by the ground on the athlete when she has lifted the barbell and stands still. ( marks) (c) After finishing the lifting, the athlete releases the barbell. It falls from rest to the ground freely. Find the time required for the barbell to reach the ground. ( marks) 8 An electric toy boat (see Figure ) of mass 1. kg is moving horizontally in still water with a constant velocity of 1.5 m s -1. The water resistance on the boat is.45 N. propeller Figure (a) (i) Find the magnitude of the propelling force acting on the boat. (1 mark) (ii) Find the power developed by this force. ( marks) (b) (i) Find the kinetic energy of the boat. (1 mark) (ii) Using the result in (b)(i), find the distance traveled by the boat before it comes to rest after the propeller is turned off. Assume the water resistance on the boar remains constant throughout the motion. ( marks) 6 A student releases a book of mass.154 kg from rest under a motion sensor as shown in Figure 5. The velocity-time graph is recorded in Figure 6. Velocity / m s -1.5 computer and data-logger motion sensor book table ground Time /s Figure 5 Figure 6 (a) From the graph in Figure 6, estimate the distance traveled by the book. ( marks) (b) Find the loss in potential energy of the book during the journey in (a) (1 mark) (c) From the graph in Figure 6, find the maximum kinetic energy of the book. ( marks) (d) Account for the difference in the values obtained in (b) and (c). (1 mark)

3 WORK, ENERGY AND OWER. 6-9 Read the following descriptions about a `crash cushion system and answer the questions that follow. Figure 16 and Figure 17 show a crash cushion system installed at some junctions on highways. The system consists of a number of identical cushion boxes, containing sand or water, lined up and fixed on the road surface. During a crash, the boxes will burst one after another when the car runs through them. The boxes will act as series of cushions and offer protection to the passengers. In a pilot test on the cushion boxes, a car of mass 16 kg traveling at a speed of 7 m s -1 runs through the boxes on a road (see Figure 18). The speed v of the car after running through all the boxes is recorded. The test is repeated by varying the number of boxes N installed in the system. Table 4 shows the results obtained. N 1 4 v / m s Table 4 (a) Assume that the deceleration of the car remains unchanged in the test. (i) Using the data in Table 4, plot a graph of v against N in Figure 19, with v ranging from to 1 m s - and N from to 1. Hence or otherwise, estimate (1) the average resistive force exerted by the cushion boxes on the car during the collision (given that the thickness of each cushion box is 1 m), () the minimum number of cushion boxes required in order to stop the car in the test. (8 marks) (ii) If the test is repeated with a heavier car traveling at an initial speed lower than 7 m s -1, sketch a graph of v against N in Figure 19 that you would expect to obtain. Use a dotted line to sketch the graph. Assume that the average resistive force acting on the car remains unchanged throughout all the tests. ( marks)

4 WORK, ENERGY AND OWER.4 (b) Explain why it is undesirable to replace the cushion boxes with concrete blocks. ( marks) 5 Kenneth, of mass 6 kg, falls vertically from rest from a 1 m platform into a swimming pool (see Figure ). In the following calculations, you may neglect the size of Kenneth. (a) Find the potential energy of Kenneth when he stands on the platform, taking potential energy at the water surface as zero. (1 mark) (b) Find the speed of Kenneth at the instant he reaches the water surface. ( marks) (c) If Kenneth reaches a maximum depth of m in the water, estimate the average resistive force exerted by the water on Kenneth. ( marks) Kenneth 1 m 4 7 Figure 9 In a road test, John drives his car along a straight horizontal road (see Figure 9). The car takes 9. s to accelerate from rest to 1 km h -1. The total mass of John and his car is 14 kg. (a) Show that a speed of 1 km h -1 is approximately equal to 7.8 m s -1. (1 mark) (b) Find the total kinetic energy of John and his car when traveling at 1 km h -1. Hence estimate the average output power of the car when it is accelerating to 1 km h -1. ( marks) (c) Figure 1 A similar road test is conducted on an inclined road. The car now takes 16. s to accelerate from rest to 1 km h -1 along the road (see Figure 1). Assume the output power of the car remains unchanged. (i) Explain why it takes a longer time for the car to accelerate up an incline road than along a horizontal road. ( marks) (ii) Find the increase in height of the car after accelerating for 16. s along the inclined road. ( marks) 4

5 WORK, ENERGY AND OWER.5 (d) On a certain day, the car was involved in a traffic accident. John braked hard to stop and skid marks were left on a horizontal road. (see Figure 11). Investigation by the police revealed the following information: length of the skid marks =.5 m average frictional force between the tyres of the car and the road surface = 11 N Figure 11 (i) Describe the energy change involved when the car was braking. ( marks) (ii) John claimed that he was driving at a speed below 7 km h -1 before the accident. Explain whether John was telling the truth or not. (4 marks) A Figure 1 m B Figure shows a water chute in a swimming pool. A boy of mass 5 kg slides down from rest at point A and reaches point B with a speed 1 m s -1, where A is 1 m above B. (a) Find (i) the potential energy of the boy at A (taking the potential energy at B as zero), (ii) the kinetic energy of the boy at B. ( marks) (b) the kinetic change as the boy slides from A to B. ( marks) HKCEE AER II 11 direction of motion T Q S A ball moves along a smooth curved rail and passed at a certain speed as shown in the figure above. Neglecting air resistance and friction, which of the following statements about the motion of the ball are correct? (1) The ball has maximum kinetic energy at R. () The speed of the ball at S is the same as that at Q. () The ball can never reach T. A. (1) and () only B. (1) and () only C. () and () only / J D. (1), () and () R 11 7 A car of mass 15 kg is accelerating from rest along a straight road. The figure below shows the variation of its kinetic energy () with the square of time t. What is the acceleration of the car? A..89 m s B m s C.. m s D. 4. m s t / s 5

6 WORK, ENERGY AND OWER In the figure below, a mass is released from rest at from a high platform into a swimming pool. After a while, the mass reaches the water surface at Q and enters the water. Finally, it reaches a maximum depth at R. Which of the following descriptions about the motion of the mass is/are correct? (1) From to Q, the acceleration of the mass is platform increasing. () From Q to R, the net force acting on the mass is pointing upward. () From to R, the gravitational potential energy loss of the mass equals to its kinetic energy gain. Q B. () only water surface C. (1) and () only R D. () and () only 9 6 F A constant force F is applied to an object which is initially at rest on horizontal smooth surface. Which of the graphs below best represents the variation of the power developed by the force with time t? A. B. C. D. t t t t 9 8 A diver jumps up vertically in the air from a high platform and falls into water. The v-t graph below shows the variation of the velocity of the diver against time from the point he jumps. () until he is at lowest point (Q) in the water. platform v / m s t / s Q 1 Which of the following is correct? not to scale Total distance travelled from to Q (m) Height of the platform above water surface (m) A B C D

7 WORK, ENERGY AND OWER pulling force tram o A tram of mass 15 kg is being pulled by a steel cable. It goes up a o slope with uniform speed. The average resistive force acting on the tram is N. What is the energy required for the tram to move 1 m up along the slope? A. kj B. 75 kj C. 77 kj D. 15 kj 9 h t = t = t 1 h t = t An object is released from rest at the top of a building of height h. At time t 1, the object is at the half of the height of the building as shown in the figure. At time t, the object just reaches the ground. Which of the following is/are correct? (Neglect air resistance.) (1) velocity of the object at t = velocity of the object at t 1 () t = t 1 () of the object at t = of the object at t 1 A. () only B. () only C. (1) and () only D. (1) and () only 8 A car is traveling at a constant speed of 15 m s -1 along a horizontal straight road. The total resisting force acting on the car is 5 N. Which of the following statements are correct? (1) The car travels a distance 1 m in 8 s. () The work done by the car in overcoming the resisting force in 8 s is 6 kj. () The output power of the car is 7.5 kw. A. (1) and () only B. (1) and () only C. () and () only D. (1), () and () 8 4 The figure above shows the velocity-time graph of a car traveling on a horizontal straight road. Which of the following statements is/are correct? (1) Area under the graph is equal to the total displacement of the car. v / m s -1 () The acceleration of the car is maximum at time t 1. () The kinetic energy of the car remains unchanged throughout the whole journey. B. () only C. (1) and () only t 1 t / s D. () and () only 7

8 WORK, ENERGY AND OWER An object is released from rest. Which of the following graphs best describes the variation of the kinetic energy of the object with time during falling? (Neglect air resistance.) A. B. C. D. Time Time Time 8 8 When a skydiver falls steadily in air under no net force, which of the following descriptions about his gravitational potential energy, kinetic energy and power in overcoming air resistance is correct? Time Gravitational potential energy Kinetic energy ower in overcoming air resistance A. decreases increases increases B. decreases increases remains unchanged C. decreases remains unchanged remains unchanged D. remains unchanged increases increases 8 John performs a bungee jump from a bridge above a river. He (assume to be a particle) is tied to the bridge at A with an elastic cord. He falls from rest at A. When he reaches B, the elastic cord starts to stretch. John is momentarily at rest at C and then bounces up. Which of the following descriptions about the motion of John is/are correct? (Neglect the air resistance.) (1) From A to B, John is under free falling. () From B to C, the gravitational potential energy of John increases. () At C, there is no net force acting on John. B. () only C. (1) and () only D. () and () only 7 4 A skier slides down a slope as shown in the diagram below. Assume constant friction along the slope, which of the following graphs best describes the change of energy of the skier with distance down the slope? A B C bridge river A. B. Energy Energy.E..E. Distance C. D. Distance Energy.E. Energy.E. Distance Distance 8

9 WORK, ENERGY AND OWER An electrical toy car of mass m goes up an inclined plane of inclination o with constant speed v. The friction acting on the car is half of the weight of the car. What is the average power of car? 1 A. mgv B. mgv C. mgv D. mgv 7 A block of mass 1 kg is sliding down with constant speed along an inclined plane of inclination o to the horizontal. What are the gain in kinetic energy and the work done against friction by the block after traveling a distance of m along the plane? Gain in kinetic energy / J Work done against friction / J A. 1 B. 1 1 C. D. 1 6 table marble o rail A rail B ground John releases a marble from the top of a smooth rail A placed at the edge of a table as shown above. He repeats the same process by using another smooth rail B. Which of the following statements about the marble is/are correct? (1) The marble has the same velocity when it reaches the ends of both rails. () The marble has the same kinetic energy when it reaches the ends of both rails. () It takes the same time for the marble to travel through both rails. B. () only C. () only D. (1), () and () 6 4 A car stopped after emergency braking. The skid mark left by the car was. m long. Assume that the friction between the road and tyres was.65 time that of the weight of the car. Estimate the speed of the car when it began to skid. A. 5.8 m s -1 B. 1. m s -1 C. 16. m s -1 D. 17. m s A high-diver jumps into the air from a spring board and then falls into a swimming pool. Which of the following graphs best shows the variation of her kinetic energy K with time t from the time she just leaves the board up to the moment just before she enters the water? (Neglect air resistance.) A. K B. K C. K D. K t t t t 9

10 WORK, ENERGY AND OWER The diagram shows a weight-lifter lifting a weight of mass 8 kg from the floor to a height of m. Find the work done by the weight-lifter. A. 16 J B. 8 J C. 16 J D. J 5 6 The diagram shows Edmund riding the `Ferris Wheel in an amusement park. If wheel is rotating at a uniform speed, which of the following physical quantities of Edmund would remain unchanged? A. velocity B. kinetic energy C. potential energy D. total mechanical energy Edmund 4 1 Consider a baby sitting on a push-chair and her mother Amy is pushing the push-chair with a uniform velocity v along the horizontal ground. Let F = horizontal force exerted by Amy on the push-chair, and m = total mass of the baby and the push-chair. Which of the following expressions denotes the average output power of Amy in pushing the pushchair? A. Fv B. Mgv C. (F mg)v D. (F + mg)v 8 A block is projected up a smooth inclined plane. Which of the following graph shows the variation of the kinetic energy () of the block with its potential energy (.E.) during the upward motion? A. B. C. D..E..E..E..E. 1 The figure above shows a flying wheel in an amusement park. The wheel is of diameter 18 m and carries eight cages. There is only one passenger of mass 6 kg inside one of the cages. The wheel rotates with uniform speed and it takes 8 s for the passenger to travel from the bottom to the top of the wheel. Find the average useful power output of the motor of the wheel. A. ( ) W B ( ) W 8 C ( ) W 8 D. ( ) W 1

11 WORK, ENERGY AND OWER.11 1 A stone is thrown vertically upwards. Assuming air resistance is negligible which of the following statements is/are correct? (1) The acceleration of the stone decreases throughout the upward motion. () The net force acting on the stone becomes zero when the stone reaches the highest point. (4) The total energy of the stone remains unchanged throughout the motion. B. () only C. (1) and () only D. () and ( )only E. (1), () and () 1 1 A man is pulling a suitcase along the horizontal ground as shown below. It the rope is inclined at an angle to the horizontal and the tension in the rope is 1 N, find the work done by the man in pulling the suitcase for a distance of 5 m along the ground. A. 5 J B. 5 sin J C. 5 cos J 5 D. J sin E. 5 J cos 11 A kg block is initially at rest on the ground. A machine is used to pull up the block as shown above. It the tension in the string is kept at 4 N and the block reaches a height of 4 m in s, which of the following statements is/are correct? (1) The potential energy of the block is increasing when the block is rising. () The kinetic energy of the block is increasing when the block is rising. () The average power developed by the machine during the two seconds is 4 W. B. () only C. (1) and () only D. () and () only string Machine 4 N Block HKAL AER II 11 A uniform rectangular block QRS, 5 cm 1 cm and of mass 1 kg, rests on the ground as shown. A force is applied to rotate the block about an axis normal to the paper through so that it then takes an upright position Q R S. Find the maximum change in gravitational potential energy of the block in the process. Q R A. 5 J B. 4 J R 1 cm S C. 7 J 5 cm D. 8 J Q S 6 Two objects A and B of masses m and m respectively are initially at rest on a smooth horizontal surface. If each of them is acted upon by the same force for the same period of time, the ratio of the gain in kinetic energy of A to that of B is A. : 1 B. 1 : C. 1 : 1 D. 1 : 4 E. 4 : 1 ground 11

12 WORK, ENERGY AND OWER A ball of mass m is projected vertically downward with speed v from a certain height and rebounds from the ground back to the same height. Which of the following statements is/are correct? (Neglect air resistance) (1) The collision between the ball and the ground is not perfectly elastic. () The loss in energy of the ball in the collision is mv /. () In the ball is projected vertically upwards form the same height with the same speed, it would rebound to a greater height. B. () only C. (1) and () only D. () and () only E. (1), () and () 1995 Two small spheres A and B of masses 1 kg and kg respectively are released form rest at heights 4h and h above the ground as shown. Which of the following statements is/are correct? (Assume air resistance is negligible) (1) The acceleration of sphere A doubles that of sphere B. () The time taken for sphere A to reach the ground is double that of sphere B. () The kinetic energy of sphere A when reaching the ground is double that of sphere B. B. () only C. (1) and () only D. () and () only E. (1), () and () A 4 h B h 1987 A parachutist of mass m falls in air under the influence of gravity. The air resistance is equal to bv, where v is his speed and b is a constant. After falling a height s from rest, he reaches a terminal speed u. His kinetic energy at that instant is A. mgs. B. mga bus. C. mgs ( m g ) /(b ). D. mgs ( m g ) /(b ). E. m g /(b ) Which of the following physical quantities is a vector? (1) Velocity () Displacement () ower A. (1), () and () B. (1) and () only C. () and () only D. (1) only E. () only 1