MOMENTUM - problems / questions (honors)

1. A fullback of mass 100. kg traveling at +10.0 m/s collides with another player and comes to rest in 0.750 s. Calculate the force exerted on the fullback.

2. A golf ball of mass 0.050 kg acquires a speed of 80.0 m/s when hit with a force of 3.00 x 103 N. How long was the club in contact with the ball?

3. What force, acting for 1.35 milliseconds, will change the velocity of a 95.0-gram baseball from 50.0 m/s east to 45.0 m/s west?

4. A 65.0-kg ice skater traveling at +6.0 m/s runs head-on into an 85.0-kg ice skater traveling at 4.50 m/s. At what velocity do the ice skaters travel if they move together after the collision?

5. A 4.00-kg object traveling west at 25.0 m/s hits a 15.0-kg object at rest. The 4.00-kg object bounces east at 8.00 m/s. What is the velocity of the 15.0-kg object?

6. A bullet of mass 0.650 kg is fired from a 4.00-kg gun with a speed of 500. m/s. What is the recoil speed of the gun?

7. A 62.0-kg child is sitting on a wagon full of bricks that has a mass of 150. kg. In order to move the wagon without touching the ground the child throws two bricks, each of mass 4.00 kg, in the direction opposite to the direction the wagon is to go. How fast will the wagon move if the bricks are thrown at 2.00 m/s?

8. A pool ball of mass 0.500 kg rolling at 10.0 m/s east catches up to and collides with another pool ball of equal mass rolling in the same direction at 2.00 m/s. After the collision, the first pool ball continues rolling east at 5.00 m/s. What is the velocity of the second ball?

9. Two children are standing on a 150.-kg wagon which is at rest. The children jump off the wagon in opposite directions. The 40.0-kg boy jumps off at +4.00 m/s and the 50.0-kg girl jumps off at -2.00 m/s. What is the velocity of the wagon?

10. An archer shoots a 0.100-kg arrow with a velocity of +60.0 m/s at a 0.400-kg apple resting on a level table. If the arrow sticks in the apple while traveling horizontally and the entire thing slides to a stop in 1.75 s, how much frictional force acted on it while it slid?

11. An object originally at rest explodes; as a result a 2.00-kg piece moves north at 4.00 m/s and a 4.00-kg piece moves east at 1.50 m/s. What is the momentum of the third piece? What is the mass of the third piece if it moves at a speed of 4.00 m/s?

12. A ball traveling north collides with another ball of the same mass that is at rest. The first ball moves away at an angle of 60° (from its original direction) with a speed of 2.00 m/s while the second ball moves off perpendicularly to the first. What was the velocity of the first ball before the collision?

13. A car of mass 1210 kg traveling south at 30.0 m/s hits a stationary car of equal mass. The resulting collision is off-center, causing the first car to move off east of south and the second car to move off perpendicularly to it at a speed of 11.0 m/s. In what direction does the second car move?

14. Three subatomic particles are traveling toward one another: a 1.00 x 10-30-kg particle moving south at

12000. m/s, a 3.00 x 10-30-kg particle at 8000. m/s east, and a third particle moving at 30000. m/s. When they collide they all stop. Determine the mass and direction of motion of the third particle.

15. A space vehicle (mass = 100. kg) is moving 25.0 m/s upward from the surface of Mars at an angle of 50° to the horizontal. A small rocket is fired and ejects gas horizontally at a speed of 125 m/s after which the vehicle is moving vertically. What is the mass of the gas ejected? What is the vehicle's new mass and speed?

16. Two bicyclists approach an intersection, one from the west and the other from the north. The cyclist from the west has a mass of 110. kg, and the one from the north has a mass of 140. kg and is traveling at 10.0 m/s. They collide and the bicycles become locked together. The two move together at a direction of 50° S of E. What was the speed of the 110.-kg cyclist?

17. During a game of billiards, the cue ball is propelled eastward by the cue stick. It collides with the stationary 8-ball (same mass), after which the cue ball moves 65° N of E at a speed of 0.20 m/s while the 8-ball moves off perpendicularly it. Find the velocity of the 8-ball after the collision.

18. A radioactive nucleus, initially at rest, decays by emitting an electron and a neutrino at right angles to one another. The momentum of the electron is 1.2 x 10-22 kg×m/s north and that of the neutrino is

6.4 x 10-23 kg×m/s west. Calculate the resulting momentum of the recoiling nucleus.

19. A vessel explodes, breaking into three pieces. Two pieces, having equal mass, fly off perpendicular to one another (one to the east, the other to the south) with the same speed of 30. m/s. The third piece is three times the mass of each other piece. What is the direction and magnitude of its velocity immediately after the explosion?

20. A bocce ball moving west at a speed of 2.2 m/s strikes an identical stationary ball a glancing blow. After the collision one ball is found to be moving in a direction 60° N of W. Calculate the speed of the other ball, knowing that it moves off at 30˚ S of W.

21. A hockey puck sliding to the east across a frozen pond strikes a stationary puck of equal mass. After the collision the once-stationary puck moves off south of east at 2.0 m/s while the first puck moves at a new speed of 4.0 m/s (final motions at 90˚ to each other). Calculate the first puck’s new direction of motion.

22. A hockey puck of mass 0.165 kg, sliding across the ice, collides with a stationary hockey puck (same mass). The first puck moves off at 35.0 m/s to the left of its original motion line and the second puck moves off at 20.0 m/s to the right of the original line (final motions are perpendicular to each other). What was the magnitude of the original momentum of the first puck?

23. The Galileo space probe (m = 2450 kg) `is traveling through empty space at a speed of 950. mi/hr when it experiences a fatal malfunction of its electrical system which causes it to explode into two pieces. A 1950 kg piece flies off at a speed of 1325 mi/hr, perpendicularly to the left of the probe's original line of motion. What is the velocity of the second piece?

24. A 1000.-kg car traveling west collides with a 1200.-kg car that was initially at rest. After the collision, the lighter car moves at 20.0 km/hr 30° S of W. The heavier car moves at 12 km/hr 44° N of W. What was the original speed of the lighter car?

25. A 7.00-kg bowling ball with an initial velocity of 10.0 m/s south strikes a 5.00-kg bowling ball that is at rest. The collision is off-center, causing the larger bowling ball to move in a direction 10° E of S at a speed of

3.00 m/s. Find the (a) momentum and (b) speed of the lighter ball after the collision.

26. Four horses (all of equal mass) are standing around a feeding trough when a nearby gun shot spooks them and they take off running. The first horse runs at 15.0 m/s east, the second at 20.0 m/s north, and the third at 10.0 m/s, 15° E of S. If the center-of-mass of the 4-horse system stays at rest throughout the stampede, find the velocity of the fourth horse.

27. Two 2.00-kg masses collide. Before the collision object A was traveling 33.5 km/hr 63° N of E while object B was traveling 11.2 km/hr 27° N of W. After the collision object A is traveling 20.6 km/hr 76° N of W. What is the new velocity of object B?

28. A car of mass 1000. kg traveling south at 30. m/s reaches an intersection and collides with a pickup truck of mass 2500. kg traveling west at 20. m/s. After the collision the truck travels at 15 m/s 40° S of W. Calculate the new velocity of the car.

29. A 20.0-kg body is moving at a velocity 200. m/s 45° N of W when, due to an internal explosion it breaks into three parts. One part, who’s mass is 10.0 kg, moves away from the explosion point at a velocity of 250. m/s north while a second fragment of mass 4.00 kg moves west with a speed of 500. m/s. Calculate the velocity of the third fragment.

30. A baseball (m = 145 g) rolling east along the floor at 2.50 m/s collides with a softball (m = 185 g) that is at rest. After the collision, the softball moves off 25° S of E at a speed of 2.00 m/s. Find the final momentum of the baseball.

31. A 10.0-kg dog running at +4.00 m/s slams head-on into a 5.00-kg cat moving at 1.20 m/s. At what velocity do they travel if they move together after the collision? What type of collision is this?

32. A 0.200-kg billiard ball moving at +3.00 m/s collides with a second 0.200-kg ball that is at rest. If the first billiard ball stops, what is the velocity of the second ball? What type of collision is this?

33. A car with a mass of 1850 kg moving east at 20.0 m/s collides with a truck (mass of 2510 kg) traveling north at 35.0 m/s. If they move together after the collision, what is their resulting velocity? What type of collision is this?

34. A 4.00-kg ball moving at +20.00 m/s collides with a stationary 11.0-kg ball. If after the collision the 4.00-kg ball moves backward at 9.333 m/s, what will the resulting velocity of the 11.0-kg ball be? What type of collision is this?

35. What type of collision was that described in #27?

36. During a 1-dimensional collision – staged by two physics students so enraptured with the current subject matter that they had to try this stuff on their own time (you know how that is) – a stone of mass 185 grams moving north at 35.0 m/s along a frictionless lake collides with a second stone of mass 370.0 grams sitting motionless. If the collision is elastic, find the velocity of each stone after the collision.

37. Is there an advantage to following through when hitting a baseball or softball and thereby maintaining a longer time of contact between the bat and the ball? Explain.

38. Two ice skaters, initially at rest, push against one another. What is the total momentum of the system after the push-off? Explain.

39. A compact car and a tractor trailer have a head-on collision. During the collision, which vehicle experiences the larger change in momentum? Explain.

40. Is it possible for a rocket to work in empty space, where there is nothing to push against? Explain.

41. If momentum is conserved in a collision, does this indicate that the collision is elastic? Explain.

42. One object strikes a second object of equal mass, initially at rest. The first object stops, and the second object moves forward with a velocity equal to the initial velocity of the first object. Is the collision elastic? Explain.

ANSWERS:

1. -1330 N 2. 0.00133 s 3. 6690 N, west 4. +0.050 m/s 5. 8.80 m/s W 6. 81.3 m/s

7. 0.0784 m/s 8. 7.00 m/s, E 9. -0.400 m/s 10. 3.43 N 11. 10.0 kgm/s, 53° S of W , 2.50 kg

12. 4.00 m/s, north 13. 68° E of S 14. 8.94 x 10-31 kg , 27° N of W 15. 12.9 kg , 87.1 kg , 22.0 m/s

16. 10.7 m/s 17. 0.43 m/s, 25° S of E 18. 1.4 X 10-22 kg×m/s, 28° E of S 19. 14 m/s, 45° N of W

20. 1.9 m/s 21. 27° N of E 22. 6.65 kg·m/s 23. 6960 mi/hr, 48° right of original line 24. 27.7 km/hr

25. a. 49.5 kgm/s, 86° S of W b. 9.89 m/s 26. 20.4 m/s, 30° S of W 27. 18.1 km/hr, 56° N of E 28. 22 m/s, 15° S of W

29. 149 m/s, 22° N of W 30. 159 g·m/s, 80° N of E 31. +2.27 m/s , completely inelastic 32. +3.00 m/s , elastic

33. 21.9 m/s, 67° N of E , completely inelastic 34. +10.7 m/s , elastic 35. inelastic (Ktotal (o) = 96.3 J , Ktotal (f) = 58.0 J)

36. v1 = 11.7 m/s, S v2 = 23/.3 m/s, N