Queensland Physics

CHAPTER 9 BATS, BALLS AND BOOTS — COLLISIONS IN SPORT

QUESTIONS

9.2 Momentum and impulse 1. A 70 kg basketball player lands on the ground after a jump at a speed of 10 m s–1 and is brought to a stop by the ground in 0.35 s. What is the average force exerted on her by the ground?

2. A sprinter with a mass of 60 kg leaves the blocks at the start of a race by pushing off with a force of 700 N exerted over a 0.4 s interval of time. At what speed does the sprinter leave the blocks?

3. A 60 kg trampolinist jumps straight up in the air by exerting an average force of 1060 N on the trampoline bed for a time of 0.5 s. (a) What is the impulse of the trampolinist on the trampoline?

(b) At what speed does he leave the trampoline?

(c) What will be the maximum height that he reaches?

4. In a billiards game, the white ball is travelling at a speed of 3 m s–1 when it strikes the yellow ball, which is initially at rest. If the white ball is slowed to a speed of 0.5 m s–1 after the collision, what will be the speed of the yellow ball? (Assume that the two balls have the same mass.)

5. While Bev is playing bowls, she hits the stationary jack (which has a mass of 285 g) with her 1.6 kg bowl. After they have collided, the jack is travelling at 3 m s–1 and the bowl at 0.5 m s–1. If the bowl and the jack are travelling in the same direction after collision, what was the speed of the bowl before it hit the jack?

6. A 7.2 kg bowling ball strikes a pin at the end of the bowling alley with a speed of 10 m s–1. If the pin has a mass of 1.6 kg and leaves the collision with a speed of 10 m s–1, with what speed will the bowling ball leave the collision?

9.3 Explosive motion and momentum 7. A .22 rifle that has a mass of 4.6 kg recoils backwards at a speed of 0.6 m s–1 when it fires a 3.6 g bullet. At what speed did the bullet leave the barrel (ignoring the frictional effects of the barrel)?

8. A 1.2 t cannon fires a 5 kg cannonball when lit. If the cannonball is given a muzzle speed of 120 m s–1, what will be the recoil speed of the cannon?

9.4 Conservation of momentum in two dimensions

9. A 5 kg ball moving due east at 4.0 m s–1 collides with a 4.0 kg ball moving due west at 3.0 m s–1. Just after the collision, the 5.0 kg ball has a velocity of 1.2 m s–1 due south. (a) What is the magnitude of the 4.0 kg ball’s velocity just after the collision?

(b) In what direction does it move?

9.5 Kinetic energy

10. Calculate the kinetic energy of a 160 g cricket ball that is moving at 15 m s–1.

11. At what speed is a 420 g soccer ball travelling if it has a kinetic energy of 22 J?

12. Which has the greater kinetic energy: a 6 kg bowling ball travelling at 5 m s–1 or a 160 g cricket ball travelling at 15 m s–1?

Review questions

Understanding

13. Joggers are advised to run on a soft surface such as grass rather than on hard surfaces like bitumen or concrete to reduce knee injury. Why is this so?

14. What is the difference between an energy transfer and an energy transformation?

15. Why is a heavy bowling ball able to knock over more pins on average than a lighter ball?

16. Why does the use of boxing gloves make modern boxing safer than bare-knuckle fighting?

17. Most dance halls have what are referred to as sprung wooden floors, which are very bouncy. Why would such floors be needed in a dance hall?

Application

18. Calculate the momentum of each of the following. (a) A 50 kg runner moving at 5 m s–1

(b) A 4 g bullet travelling at 320 m s–1

(c) A 420 g soccer ball kicked at 20 m s–1

19. A 160 g cricket ball is accelerated from rest by a force of 18 N acting on it for 0.15 s. Calculate: (a) the change in momentum experienced by the ball

(b) the acceleration experienced by the ball.

20. A 75 kg basketball player lands vertically on the court with a speed of 3.4 m s–1. (a) What total impulse is applied to the basketballer’s feet by the court’s surface?

(b) If his speed changed from 3.4 m s–1 to zero in 0.10 s, what total force does the surface apply to his feet?

(c) (a) What will be the impulse that causes a 90 kg football player running at 7 m s–1 to stop when he collides with a goal post?

(b) What force does the goalpost exert on the player if he is brought to rest in a 0.08 s time interval?

21. Andrew and Sefa are keen rollerbladers. Andrew approaches his stationary brother at a speed of 2 m s–1 and bumps into him. As a result of the collision, Andrew, who has a mass of 60 kg, stops moving, and Sefa, who has a mass of 70 kg, moves away in a straight line. The surface on which they are blading is smooth enough to ignore friction. (a) With what speed does Sefa move away?

(b) What is the magnitude of the impulse on Andrew as a result of the bump?

(c) What is the magnitude of Andrew’s change in momentum?

(d) What is the magnitude of Sefa’s change in momentum?

(e) If Andrew held onto Sefa so that they moved off together, what would be their final velocity?

22. A 3.0 kg target is balanced on a post at the end of an archery range. Michelle fires a 45 g arrow at it that is travelling at 20 m s–1 as it enters the target. If the arrow moves through the target and emerges on the other side with a speed of 12 m s–1, what will be the speed of the target as it is knocked from the post?

23. A 60 g tennis ball is travelling at 18 m s–1 when it strikes a player’s racquet on the full. If the ball rebounds backwards from the racquet with a speed of 12 m s–1, calculate: (a) the ball’s change in momentum

(b) the force exerted on the ball by the racquet if they are in contact for 0.008 s.

24. A bullet of mass 30 g is fired at a speed of 450 m s–1 from a rifle that has a mass of 3.5 kg. What is the recoil speed of the rifle? 25. (a) Two billiard balls of equal mass, one coloured red and one coloured blue, collide head on. Before the collision, the red ball was moving at 2 m s–1 and the blue was moving at 1 m s–1. If the red ball moves off at an angle of 20° to its original direction at a speed of 1.5 m s–1, what is the speed and direction of motion of the blue ball after collision?

(b) Is this an elastic collision? If not, calculate the percentage of kinetic energy that is lost in the collision.

26. A 58 g tennis ball initially travelling at 30 m s–1 is struck by a 360 g racquet travelling at 50 m s–1. After hitting the ball, the racquet has a speed of 40 m s–1. (a) What is the change in momentum of the tennis racquet?

(b) What is the change in momentum of the tennis ball?

(c) If the ball is in contact with the strings of the racquet for 0.3 s, what is the average force acting on the ball?

(d) What will be the ball’s speed when it leaves the racquet?

27. Calculate the kinetic energy of the following. (a) A 4 g bullet travelling at 430 m s–1

(b) A 7.25 kg bowling ball moving at 10 m s–1

(c) A 1.3 t truck moving at 80 km h–1

Challenges

28. A 1.20 kg sports pistol discharges while lying on a highly polished tabletop, firing a 3 g bullet at 420 m s–1 in one direction while it recoils in the opposite direction. How far along the tabletop will the gun move before coming back to rest if the coefficient of friction between the gun and the tabletop is 0.12?

29. Two identical hockey pucks slide along the ice towards each other. At the moment that they collide elastically, one has a speed of 10 m s–1 and the other has a speed of 5 m s–1. If they bounce off each other, what will be their speeds after collision?

30. The figure below shows a billiards shot that causes a red ball to be sunk in the corner pocket. If the white ball and the red ball have the same mass and the red ball was initially stationary, what speed did the red ball have after collision? (Note: in reality, the white ball is slightly smaller than the other balls on the table.)

Notes: