________________________ Name PH101-001 Exam 2a-key March 12, 2008
1. A soldier wants to knock down a door by firing a round of bullets from a machine gun into the door. He can use either lead bullets which become embedded in the door or rubber bullets that bounce off the door. Assume that the masses of the lead and rubber bullets are the same and they hit the door with the same speed. Which should he use? (a) rubber bullets (b) lead bullets (c) doesn't matter p (door ) = - p (bullet ) = mvi - mv f If elastic collision (rubber ), then v f = -vi and p (door ) = 2mvi If lead , then v f = 0 and p(door ) = mvi 2. How much work is required to push a 50-kg block up 2 m up a frictionless 30o incline at a constant speed? (a) 100 J (b) 245 J (c) 490 J (d) 50 J (e) 625 J W = mgh = (50)(9.8)(2) sin(30 o ) = 490 N
3. A pulley in the shape of a uniform disk is pivoted about a fixed axis. A rope wrapped around the pulley is pulled with a force of 5 N. What is the angular speed of the pulley after 8 sec, assuming it starts from rest? (a) 1.5 rad/s (b) 10 rad/s (c) 2.5 rad/s (d) 0.75 rad/s (e) 5 rad/s I= 1 1 MR 2 = (40)(0.2) 2 = 0.8 kg m 2 2 2
m = 40 kg R = 0.2 m
= FR / I = (5)(0.2) /(0.8) = 1.25 rad / s 2 = 0 + t = (1.25)(8) = 10 rad / s
4. A 5-kg block is pulled along a level surface by a rope that makes an angle of 30o above the surface. The force exerted by the rope is 40 N, and a frictional force of 10 N acts on the block. If the block starts from rest, what is its kinetic energy after it has moved 8 m? (a) 197 J (b) 246 J (c) 100 J (d) 45 J (c) 349 J
W = KE = ( F cos - f k )x = (40 cos(30 0 ) - 10)(8) = (24.6)(8) = 197 J
5. A 3-kg shell initially at rest explodes into 1-kg and 2-kg fragments. The speed of the 1-kg fragment is 100 m/s. How much kinetic energy is released in the explosion? (a) 1000 J (b) 2500 J (c) 4000 J (d) 7500 J (e) 3750 J v 2 = m1v1 / m2 = (1)(100) /( 2) = 50 m / s KE = 1 m1v12 + 1 m2 v 2 2 = 1 (1)(100) 2 + 1 (2)(50) 2 = 5000 + 2500 = 7500 J 2 2 2 2
6. A man weighs 200 lb on the surface of earth. What would he weigh on top of a tower of height equal to the radius of earth? (a) 50 lb (b) 100 lb (c) 150 lb (d) 200 lb (e) he would be weightless
W = GMm /(2 R E ) 2 = 1 GMm / R E 2 = 1 (200 lb) = 50 lb
4 4
7. What would the 200-lb man weigh at the bottom of a mine shaft of depth equal to the radius of earth? (a) 100 lb (b) 200 lb (c) 400 lb (d) 800 lb (e) he would be weightless W = GMmR / R E 3 = (GMm(0.5R E ) / R E 3 = (0.5)(200 lb) = 100 lb
8. A 0.2-kg cart, initially at rest, is subjected to a force which varies with time as shown below.
F (N) 40 20 0 0 0.02 0.04 0.06 0.08
t (sec)
What is the speed of the cart at 0.08 sec? (a) 1.6 m/s (b) 4 m/s (c) 12 m/s (d) 2.4 m/s (e) 6 m/s
Impulse = area = 1 (0.04)(40) = 0.8 N s = p = mv f - mvi
2
v f = Impulse / m = (0.8) /(0.2) = 4 m / s
9. A 120-kg lineman going east at 2 m/s tackles an 80-kg running back going west 4 at m/s. The lineman holds onto the running back and they move together after the tackle. What is their speed immediately after the collision? (a) 0.4 m/s (b) 1.6 m/s (c) 2.5 m/s (c) 3 m/s (d) 0 m/s
(ml + mr )v f = ml vl + mr v r vf = ml vl + mr v r (120)(2) + (80)(-4) 240 - 320 = = = -0.4 m / s ml + mr 200 200
10. Find the tension in the rope tied to the left end of the beam. The beam has a mass of 50 kg and a length of 4 m. The right end is attached to a wall and a 100-kg mass hangs 2 m from the left end of the beam.
30o
(a) 980 N (b) 250 N (c) 1715 N (d) 4000 N (e) 1960 N
Choose pivot at wall - = 0 = -T sin(30 o )(4m) + (100kg )(9.8m / s 2 )(3m) + (50kg )(9.8m / s 2 )(2m) - 2T + 2940 + 980 = 0 T = 1960 N
11. A 200-kg satellite is in a circular orbit 5x106 m above the surface of earth. What is its speed? (a) 1200 m/s (b) 3250 m/s (c) 5920 m/s (d) 4930 m/s (e) 8190 m/s
F = mv 2 / r = GMm / r 2 v= GM = r (6.67e - 11)(5.98e24) = 5920 m / s (6.38e6 + 5e6)
(escape speed = v / 2 = 4186 m / s )
12. What is the acceleration of the satellite? (a) 1.5 m/s2 (b) 3.1 m/s2 (c) 4.5 m/s (d) 9.8 m/s (e) zero a = v 2 / r = (5920) 2 /(11.38e6) = 3.08 m / s 2
13. A block is released from rest at the position shown on a frictionless track. Which position best represents how far the block will move to the right on the track?
B
E D C A
(a) A (b) B (c) C (d) D (e) E Conservation of energy - E f = Ei mgh f = mghi , h f = hi position E
14. A wheel rotating at 30 rev/min slows to 20 rev/min in a time of 12 sec. How many revolutions does the wheel make during this 12 sec time? (a) 2.5 rev (b) 5 rev (c) 10 rev (d) 15 rev (e) 22.5 rev
= avg t = (25 rev / min)(0.2 min) = 5 rev
15. A child stands on the edge of a rotating platform and walks t...