engr 243 test 1 solutions PDF

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CIVE 206 DYNAMICS

TEST 1:

Student Name:_____________

February 15, 2013, 8:30 – 10:00 am

/60

Answer all questions. Questions 1 and 2 are quick questions. For questions 3, 4, and 5 write out full solutions with clearly labeled diagrams.

1.

( 3 marks) A 50 kg person stands on a 25 kg platform. He pulls on the rope that is attached to the platform via the frictionless pulley system shown here. If he pulls the platform up at a steady rate, with how much force is he pulling on the rope? Ignore friction and assume g = 10 m/s2.

2.

(5 marks) A golf ball is fired at a bowling ball initially at rest and bounces back elastically. Compare and explain the relative magnitudes of the momentum and kinetic energy of the golf ball and the bowling ball after the collision.

3. (18 marks) The two blocks shown are originally at rest. The coefficients of friction between block A and the incline are μs = 0.25 and μk = 0.20. Neglect the masses of the pulleys and the effect of friction in the pulleys. Determine a) The acceleration of each block. b) The tension in the cable.

100 kg

175 kg

4. (18 marks) A 200 g ball A and a 400 g ball B are mounted on a horizontal rod which rotates freely about a vertical shaft. The balls are held in the positions shown by pins. The pin holding B is suddenly removed and the ball moves to position C as the rod rotates. Neglect friction and the mass of the rod. The initial speed of A is vA = 2.4 m/s. Determine, a) the radial and transverse component of the acceleration of ball B immediately after the pin is removed, b) the acceleration of ball B relative to the rod at that instant, c) the total kinetic energy of the two balls when they are held in place by the pins and after B has moved to position C.

5. (16 marks) A 20 g bullet fired into a 4 kg wooden block suspended from cords AC and BD penetrates the block at point E, halfway between C and D, without hitting cord BD. Determine a) the maximum height h to which the block and the embedded bullet will swing after the impact b) the total impulse exerted on the block by the two cords during the impact.

Solution 1.

The tension in the cable is constant. Due to the pulley configuration there are 3 cables pulling upwards against the weight of the platform and the person. The total mass of the platform and the person is 25 kg + 50 kg = 75 kg 2 The total weight of the platform and person is 75 kg x 10 m/s = 750 N Therefore the tension in the cable is 750 N divided by 3 = 250 N.

2. The golf ball bounces back at nearly its incident speed, whereas the bowling ball hardly budges. Thus the change in momentum of the golf ball is nearly – 2mv, and the bowling ball must gain momentum at + 2 mv = MV to conserve momentum. Therefore the golf ball with momentum of – mv has less momentum than the bowling ball at MV=+2mv. Since the mass of the bowling ball is much larger than that of the golf ball, M>>m, the bowling ball`s velocity, V 2V Hence KE golf ball ½ m v2 >> ½ (2mv)V , KE bowling ball Therefore the golf ball has less momentum and more kinetic energy than the bowling ball....