PC1431 Term Test 2013

PC1431 Physics IE 2013 – 2014 Semester I TERM TEST 4th 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 d n x  nx n1 dx 1 n 1 n  x dx  n  1 x (n  1)

x

 b  b 2  4ac 2a

1

 x dx  ln x

1. Two balls are thrown from the top of a building.

Figure 1 Ball 1 is thrown very forcefully straight down, and Ball 2 is thrown with the same speed, but upward at an angle  with respect to the horizontal. After the balls are released, what can you say about their accelerations? Ignore air resistance. a) Both balls have the same acceleration at all times. b) Both Ball 1 and 2 have accelerations in both the horizontal and vertical directions. c) The acceleration of Ball 1 becomes larger and larger as it falls, because the ball is going faster and faster. d) Ball 2 has an acceleration in both the horizontal and vertical directions, but Ball 1 has an acceleration only in the vertical direction. e) The acceleration of Ball 2 decreases as it rises, becomes zero at the top of the trajectory, and then increases as the ball begins to fall toward the ground. 2. Which of the following free-body diagrams represents a car going downhill without acceleration?

a)

b)

c)

d)

e)

3. A car of mass 1250 kg is moving at a speed of 105 km/h. The total work that must be done to completely stop the car a) cannot be determined since we do not know the net force acting on and the path of the car. b) is approximately 0.532 MJ. c) is approximately 6.89 MJ. d) is approximately  6.89 MJ. e) is approximately  0.532 MJ.

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4. A 1.5-kg mass has an acceleration of (4.0i – 3.0j) m/s2. Only two forces act on the mass. If one of the forces is (2.0i – 1.4j) N, what is the magnitude of the other force? a) 2.4 N b) 4.1 N c) 5.1 N d) 6.1 N e) 7.1 N 5. A particle with total mechanical energy E moves in one dimension in a region where the potential energy is U(x). The acceleration of the particle is zero where a) U ( x)  0 . b) U ( x)  E . c) U ( x)  E . d) dU ( x) dx  0 . e) d 2U ( x) dx 2  0 . 6. Figure 2 shows three points 1, 2, 3 along the trajectory of a projectile.

Figure 2 The speeds at the points 1, 2, 3 are v1 , v2 , v3 respectively. Assume there is no air resistance. Rank the speeds from largest to smallest. a) v3  v2  v1 b) v1  v2  v3 c) v2  v3  v1 d) v2  v1  v3 e) v1  v3  v2 7. A 3.00-kg model rocket is launched vertically upward with sufficient initial speed to reach a maximum height of 100 m even though air resistance contributes  800 J of work on the rocket. If there were no air resistance, the rocket would have gone to a maximum height of approximately a) 72.8 m b) 100 m c) 127 m d) 154 m e) 182 m

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8. A swimmer heading directly across a river 200 m wide reaches the opposite bank in 6 min 40 s. She is swept downstream 480 m. How fast can she swim in still water? a) 0.50 m/s b) 0.80 m/s c) 1.2 m/s d) 1.4 m/s e) 1.8 m/s 9. Kim Seng, who likes physics experiments, hangs his watch on a thin piece of string while the plane he is in, takes off from Changi Airport. He notices that the string makes an angle of 25 with respect to the vertical while the plane accelerates for takeoff, which takes about 18 seconds. The take-off speed of the plane is approximately a) 270 km/h. b) 300 km/h. c) 350 km/h. d) 580 km/h. e) 640 km/h. 10. A marble dropped from a bridge strikes the water in 5.00 s. Ignoring air resistance, if the marble is dropped from rest, the speed v with which it strikes the water and the height h of the bridge are given by a) v  20.0 m s , h  49.0 m . b) v  24.5 m s , h  123 m . c) v  123 m s , h  123 m . d) v  49.0 m s , h  123 m . e) v  49.0 m s , h  245 m . 11. A horizontal ideal spring with force constant 17.49 N/m is compressed 23.31 cm from its equilibrium position. An object with mass 170.0 g is placed against the end of the spring.

Figure 3 The spring is released, and the object slides on a rough horizontal surface a distance of 12.13 m after it leaves the spring. What is the coefficient of kinetic friction between the object and the surface? (Take acceleration due to gravity to be 9.80 m/s2.) a) 2.28  102 b) 2.31  102 c) 2.35  102 d) 2.40  102 e) 2.46 102

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12. A car of mass m accelerates from rest at time t  0 along a level straight track, not at a constant acceleration but with constant engine power P. Assume that air resistance is negligible. The car’s acceleration as a function of time t  0 is given by P a) 2mt b)

2P mt

c)

P mt

d)

2 Pt m

e)

2 2 Pt 3 m 3

13. A train slows down uniformly as it rounds a horizontal turn, from 90.0 km/h to 50.0 km/h in 15.0 s. The radius of the curve is 150 m. What is the magnitude of the acceleration at the moment the train speed reaches 50.0 km/h? a) 1.22 m s 2 b) 1.48 m s 2 c) 2.78 m s 2 d) 5.25 m s 2 e) 7.79 m s 2 14. Two packages start sliding down the 20 ramp as shown in Figure 4.

Figure 4 Package A has a mass of 5.0 kg and the coefficient of kinetic friction between package A and the ramp is 0.20. Package B has a mass of 10 kg and a coefficient of kinetic friction of 0.15. How long does it take for package A to reach the bottom? a) 0.66 s b) 1.1 s c) 1.5 s d) 2.0 s e) 2.5 s

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15. A ball is fired at an angle of 45°, the angle that yields the maximum range in the absence of air resistance. What is the ratio of the ball's maximum height to its range? a) 1.0 b) 0.75 c) 0.67 d) 0.50 e) 0.25 16. A 0.100-kg ball is projected vertically upward with a speed of 1.00 m/s from a height of 1.00 m and landed on a light cup mounted on top of a vertical ideal spring initially at its equilibrium position.

1.00 m/s

1.00 m

Figure 5 The maximum compression of the spring is to be 10.0 cm. What is the required force constant of the spring? Ignore air resistance. a) 166 N/m b) 186 N/m c) 206 N/m d) 226 N/m e) 246 N/m

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17. A ball on the end of a string is whirled around in a horizontal circle of radius 0.300 m. The plane of the circle is 1.20 m above the ground. The string breaks and the ball lands 2.00m (horizontally) away from the point on the ground directly beneath the ball’s location when the string breaks. What is the radial acceleration of the ball during its circular motion? a) 8.15 m s 2 b) 11.8 m s 2 c) 16.3 m s 2 d) 35.8 m s 2 e) 54.4 m s 2 18. Consider an object of mass m resting on a frictionless horizontal surface at the origin O.

f (x)

O Figure 6 A variable force

f ( x)  4 x 3 acts on the object from time t  0 . If the velocity of the object at a later time t  0 is v, what is the position x of the object? a) 24vt m v b) 24 c)

m1 2 t 14

m d)   2

v

14

m e)   8

v

19. An object with a mass of m  8.0 103 kg falls from rest through a fluid. The resistive force due to the fluid is F  kv , where k  2.0  102 kg s 1 . What is its speed after 0.4 s? a) 1.5 m/s b) 2.5 m/s c) 3.9 m/s d) 9.8 m/s e) 39 m/s

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20. A race car travelling at 100 m/s enters a turn of radius 400 m. The turn is banked at 10. The coefficient of static friction between the tyres and the track is 1.1. The track has an inner and outer wall. Which statement is correct? a) The race car will crash into the outer wall. b) The race car will crash into the inner wall. c) The race car will stay at the centre of the track. d) The race car will stay at the centre of the track only if it speeds up. e) What would happen depends on the mass of the race car and driver. – End of Paper –

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