PC1431 Term Test 2012

PC1431 Physics IE 2012 – 2013 Semester I TERM TEST 5th October Time Allowed: ONE hour THIRTY minutes INSTRUCTIONS 1. 2. 3. 4.

5. 6. 7. 8.

This is a closed book test. This paper contains 20 multiple choice questions. Answer all questions. Marks will NOT be deducted for wrong answers. Each of the questions or incomplete statements is followed by the suggested answers or completions. Select the one that is best in each case and then shade the corresponding bubble on the answer sheet. Only the answer sheet will be collected at the end of the test. Use 2B pencil only. Using any other type of pencil or pen may result in answers unrecognizable by the machine. Take the acceleration due to gravity, g  9.80 m s 2 . You may find the following mathematical formulae useful:

ax 2  bx  c  0 x

 b  b 2  4ac 2a

sin 2  2 sin  cos  d n x  nx n1 dx

1. The cheetah can run as fast as 100 km/h, the sailfish can swim as fast as 120 km/h, and the falcon can fly as fast as 250 km/h. The three of them take part in a relay with each covering a distance L at maximum speed. The average speed of this triathlon team a) cannot be determined since L has not been specified. b) is 120 km/h. c) is approximately 157 km/h. d) is approximately 134 km/h. e) is approximately 78 km/h. 2. Two blocks with masses M 1 and M 2 , such that M 1  M 2 , are placed in contact with each other on a frictionless, level surface. We can apply a constant horizontal force F either from the left or from the right, as shown in Figure 1.

F

M1

M2

M1

M2

F

Figure 1 The contact forces between the blocks are a) zero. b) the same in either case. c) larger when F is applied from the left. d) larger when F is applied from the right. e) impossible to determine based on this data. 3. An elevator supported by a single cable descends a shaft at a constant speed. The only forces acting on the elevator are the tension in the cable and the gravitational force. Which one of the following statements is true? a) The work done by the tension force is zero. b) The net work done by the two forces is zero. c) The work done by the gravitational force is zero. d) The magnitude of the work done by the gravitational force is larger than that done by the tension force. e) The magnitude of the work done by the tension force is larger than that done by the gravitational force. 4. A roadway for motor racing is designed for race cars moving at a speed of 40 m/s. A curved section of the roadway is a circular arc of radius 230 m. This section is banked so that a race car can go around the curve without friction. At what angle is it banked? a) 29 b) 31 c) 33 d) 35 e) 37

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5. A block is dropped from a high tower and is falling freely under the influence of gravity. Neglect air resistance. Which one of the following statements is true concerning this situation? a) The kinetic energy increases by equal amounts over equal distances. b) The kinetic energy of the block increases by equal amounts in equal times. c) The potential energy of the block decreases by equal amounts in equal times. d) The total energy of the block increases by equal amounts over equal distances. e) As the block falls, the net work done by all of the forces acting on the block is zero. 6. Two children, A and B, are playing on two trampolines as shown in Figure 2.

Figure 2 Child A can bounce up to one-and-a-half times higher than child B. The initial speed up of child B is 5.00 m/s. How long was child A in the air? a) 1.53 s b) 1.25 s c) 1.02 s d) 0.625 s e) 0.510 s 7. Two boxes are connected to each other as shown in Figure 3.

Figure 3 The system is released from rest and the 1.00-kg box falls through a distance of 1.00 m. The surface of the table is frictionless. What is the kinetic energy of box B just before it reaches the floor? a) 2.45 J b) 4.90 J c) 9.80 J d) 29.4 J e) 39.2 J Department of Physics, National University of Singapore

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8. Neglect air resistance. If the bullet leaves a gun at a speed of 145 m/s, at what angle should the gun be aimed so a target (on the same level) 65.0 m away will be hit? a) 45.0 b) 26.6 c) 24.1 d) 1.74 e) 0.868 9. A cart is being pushed down an incline with a force F, as shown in Figure 4.

Figure 4 The coefficient of kinetic friction between the cart and the incline is  k . If the cart accelerates down the incline with acceleration a  g , the force F is given by a) Mg . b) (1   k cos   sin ) Mg . c) (1   k cos   sin ) Mg . d) (1   k sin   cos ) Mg . e) (1   k sin   cos ) Mg .

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10. The speed of a car moving along a level circular track of radius 50 m is increased uniformly in time. When the car is East of the centre, its total acceleration is 10 m s 2 at 37  West of North, as shown in Figure 5.

10 m s 2 37 

North

West

East

South Figure 5 How long does it take to return to the same point? a) 7.0 s b) 9.0 s c) 11 s d) 14 s e) 18 s 11. Consider two blocks, of masses m1  7 kg and m2  5 kg , hung by a massless string from a frictionless pulley as shown in Figure 6.

Figure 6 The bottoms of the blocks are 20 meters above the top of a horizontal table. When they are released from rest, how many seconds will it take for one of the blocks to hit the table? a) 6 b) 5 c) 4 d) 3 e) 2

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12. A dart is loaded into a spring-loaded toy dart gun by pushing the spring in by a distance d. For the next loading, the spring is compressed by a distance 2d. How much faster does the second dart leave the gun compared to the first? a) Half as fast. b) Four times as fast. c) The same. d) One-fourth as fast. e) Two times as fast. 13. Block A, of mass 5.0 kg, and block X are attached to a rope that passes over a light and frictionless pulley, as shown in Figure 7.

Figure 7 An 80-N force P is applied horizontally to block A, keeping it in contact with a rough vertical wall. The coefficients of static and kinetic friction between the wall and block A are  s  0.40 and  k  0.30 respectively. The mass of block X is adjusted until block A moves upward with an acceleration of 1.6 m/s 2 . What is the mass of block X? a) 9.9 kg b) 9.3 kg c) 8.7 kg d) 8.1 kg e) 7.5 kg

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14. A ball is fixed to the end of a string, which is attached to the ceiling at point P. As shown in Figure 8, the ball is projected downward at A with the launch speed v0 . Travelling on a circular path, the ball comes to a halt at point B.

Figure 8 Ignore air resistance and friction. What enables the ball to reach point B, which is above point A? a) The ball's initial gravitational potential energy. b) The work done by the tension in the string. c) The work done by the gravitational force. d) The ball's initial kinetic energy. e) None of the above. 15. The position x (in m) of a race car on a straight track at time t (in s) is given as x(t )  at 3  bt 2  ct  d , where a, b, c, and d are some constants. What is the average acceleration (in m s 2 ) between time t1  4.0 s and t2  9.0 s ? a) 133a + 13b + 1.0c b) 54a + 2.0b c) 39a + 2.0b d) 24a + 2.0b e) 15a 16. A book of mass m is projected with a speed v across a horizontal surface. The book slides until it stops due to the friction between the book and the surface. The surface is now tilted at an angle  (0     90  ) with respect to the horizontal, and the book is projected up the surface with the same initial speed v. When the book has come to rest, how does the decrease in mechanical energy of the book - Earth system compare with that when the book slid over the horizontal surface? a) It’s the same. b) It’s larger on the tilted surface. c) It’s smaller on the tilted surface. d) It can be larger or smaller, depending on the value of  . e) It can be larger or smaller, depending on the coefficient of kinetic friction between the book and the surface.

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17. A flying saucer is moving with constant acceleration. At an earlier time t1 , it was observed   to have position vector r1  0 and velocity vector v1  (200ˆj) m s . At a later time t2 , it   has position vector r  (2000ˆi  1000ˆj) m and velocity vector v  (200ˆi  100ˆj) m s . 2

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The saucer’s acceleration  a) is given by a  (20ˆi  30ˆj) m s 2 .  b) is given by a  (20ˆi  30ˆj) m s 2 .  c) is given by a  (10ˆi  15ˆj) m s 2 .  d) is given by a  (10ˆi  15ˆj) m s 2 . e) cannot be determined since t1 and t2 have not been specified. 18. A block with mass m is being pushed by a constant force F that makes an angle of  with the horizontal, as shown in Figure 9.

Figure 9 The coefficient of kinetic friction between the block and the surface is k . If the block moves with constant velocity on a level surface, which one of the following equations gives the correct magnitude of F?  mg a) F  k sin   k mg b) F  tan  c) F   k mg cos   k mg d) F  cos    k sin   k mg e) F  cos    k sin 

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19. Two wooden blocks, A and B, each of mass 0.30 kg are connected by a string that passes over a light, frictionless pulley. Block A slides on a horizontal table, while block B hangs suspended by the string, as shown in Figure 10.

Figure 10 At time t  0 , block B is 0.80 m over the floor, and two blocks are released from rest. After 2.5 s, block B reaches the floor. What is the coefficient of kinetic friction between the table and block A? a) 0.35 b) 0.52 c) 0.65 d) 0.84 e) 0.95

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20. A child slides without friction from a height h along a curved water slide as shown in Figure 11.

Figure 11 She is launched from a height h 5 into the pool. Determine her maximum airborne height y in terms of h and  . a) (1  4 cos 2 )h 5 b) (1  4 sin 2 )h 5 c) (1  2 cos 2 )h 5 d) (1  2 sin 2 )h 5 e) (1  4 tan 2 )h 5 – End of Paper –

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