Chapter 7 Momentum and Impulse

1. Chapter 7Momentum and Impulse

2. Collisions • What happens when there is a rapid change of motion, such as a collision? Can we apply Newton’s Law?

3. What happens when a ball bounces? • Does the velocity change? • Is there an acceleration? • Is there a force? If so, what is the direction of the force? • Forces in collision may be difficult to analyze: • Strong forces acting for a very short time that may change rapidly during the collision. • Newton’s second law

4. Momentum and Impulse • Impulse: the (average) force acting on an object multiplied by the time interval over which the force acts (Unit: Ns) • Momentum: the mass of the object times its velocity (Unit: kg.m/s). • Change in momentum: • (Units of Ns and Kg.m/s are actually equivalent)

5. Impulse-Momentum Principle

6. Momentum A bowling ball and a tennis ball may have the same momentum.

7. Application of Impulse and Momentum Principle • Example: (Box 7.1) • A golf club exerts an average force of 500N on a • 0.1 kg golf ball, but the club is in contact with the • ball for only a hundredth of a second. • What is the magnitude of the impulse delivered by the club? • What is the change in velocity of the golf ball?

8. Impulse-Momentum Principle Example (E8) A ball traveling with an initial momentum of 2.5 kg.m/s bounces off a wall and comes back in the opposite direction with a momentum of -2.5 kg.m/s. a) What is the change in momentum of the ball? b) What impulse would be required to produce this change?

9. More Examples Q9. What is the advantage of an air bag in reducing injuries during collision? Explain. Q11. If you catch a baseball or softball with your bare hand, will the force exerted on your hand by the ball e reduced if you pull your arm back during the catch? Explain. E2. An average force of 300N acts for a time interval of 0.04 s on a golf ball. What is the magnitude of the impulse acting on the golf ball? What is the change of the golf ball’s momentum?

10. Conservation of Momentum In collision, does Newton’s third law hold? • For every action, there is an equal but opposite reaction. • The impulse acting on two objects are equal in magnitude but opposite in sign. If the net external force acting on a system of objects is zero, the total momentum of the system is conserved.

11. Conservation of Momentum Two useful simple cases: • Two object stick together after collision. • The initial velocity is zero for both objects before collision (recoil).

12. Example (Box 7.2) A 100-kg fullback moving straight downfield collides with a 75-kg defensive back. The defensive back hangs on to the fullback, and the two players move together after the collision. What is the initial momentum of each player? What is the total momentum of the system?

13. What is the velocity of the two players immediately after the collision?

14. Recoil • A brief force between two objects causes the objects to move in opposite directions. • Momentum Conservation Principle applies to the system. • The systemincludes both objects involved in the collision.

15. Two skaters of different masses prepare to push off against one another. Which one will gain the larger velocity? Why? Example: E11. An ice skater with a mass of 80 kg pushes off against a second skater with a mass of 32 kg. Both skaters are initially at rest. a) What is the total momentum of the system after they push off? b) If the larger skater moves off with a speed of 3 m/s, what is the corresponding speed of the smaller skater?

16. Is momentum conserved when shooting a shotgun? • The explosion of the powder causes the shot to move very rapidly forward. • If the gun is free to move, it will recoil backward with a momentum equal in magnitude to the momentum of the shot. • If the shotgun is held firmly against your shoulder, it doesn’t hurt as much. Why?

17. Example: E 12A rifle with a mass of 1.2 kg fires a bullet with a mass of 6.g (0.006kg). The bullet moves with a muzzle velocity of 600 m/s after the rifle is fired.a) What is the momentum of the bullet after the rifle is fired?B) If the external force against the rifle is ignored, what is the recoil velocity of the rifle?

18. How does a rocket accelerate in empty space when there is nothing to push against? • The exhaust gases rushing out of the tail of the rocket have both mass and velocity and, therefore, momentum. • The momentum gained by the rocket in the forward direction is equal (in magnitude) to the momentum of the exhaust gases in the opposite direction. • The rocket and the exhaust gases push against each other (Newton’s third law applies).

19. Elastic and Inelastic Collisions • Different kinds of collisions: • objects stick together after collision. • objects bounce apart after collision. • What is the difference between these types of collisions? • Is energy conserved as well as momentum?

20. Perfect Inelastic Collisions • A collision in which the objects stick together after collision is called a perfectly inelastic collision. • The objects do not bounce at all. • If we know the total momentum before the collision, we can calculate the final momentum and velocity of the now-joined objects. • For example: • The football players who stay together after colliding. • Coupling railroad cars.

21. Four railroad cars, all with the same mass of 20,000 kg, sit on a track. A fifth car of identical mass approaches them with a velocity of 15 m/s. This car collides and couples with the other four cars. a) What is the initial momentum of the system? b) What is the velocity of the five coupled cars after the collision? c) Is the kinetic energy after the railroad cars collide equal to the original kinetic energy of the cars ?

22. Elastic and Inelastic Collisions • Energy is not conserved in a perfectly inelastic collision. • If the objects bounce apart instead of sticking together, the collision is either elastic or partially inelastic. • An elastic collisionis one in which no energy is lost. • A partially inelastic collisionis one in which some energy is lost, but the objects do not stick together. • The greatest portion of energy is lost in the perfectly inelastic collision, when the objects stick.

23. A ball bouncing off a floor or wall with no decrease in the magnitude of its velocity is an elastic collision. • The kinetic energy does not decrease. • No energy has been lost. • A ball sticking to the wall is a perfectly inelastic collision. • The velocity of the ball after the collision is zero. • Its kinetic energy is then zero. • All of the kinetic energy has been lost. • Most collisions involve some energy loss, even if the objects do not stick, because the collisions are not perfectly elastic. • Heat is generated, the objects may be deformed, and sound waves are created. • These would be partially inelastic collisions.

24. What happens when billiard balls bounce? Simplest case: a head-on collision between the white cue ball and the eleven ball initially at rest. • If spin is not a factor, the cue ball stops and the eleven ball moves forward with a velocity equal to the initial velocity of the cue ball. • The eleven ball’s final momentum is equal to the cue ball’s initial momentum (Momentum is conserved). • The eleven ball also has a final kinetic energy equal to the cue ball’s initial kinetic energy (Energy is conserved). • For equal masses, the only way for momentum and energy to both be conserved is for the cue ball to stop and the eleven ball to move forward with all the velocity.

25. What happens to the swing-ball toy? • The swinging-ball toy has a row of steel balls hanging by threads from a frame. • If one ball is pulled back and released, the collision with the other balls results in a single ball from the other end flying off with the same velocity as the first ball just before the collision. • Both momentum and kinetic energy are conserved. • If two balls on one side are pulled back and released, two balls fly off from the opposite side. • Why doesn’t one ball fly off with twice the velocity?

26. Collisions at an Angle • Two football players traveling at right angles to one another collide and stick together. • What will be their direction of motion after the collision?

27. Collisions at an Angle • The total momentum of the two football players prior to the collision is the vector sum of their individual momentums. The key is that momentum is a vector quantity

28. Two lumps of clay of equal mass are traveling at right angles with equal speeds as shown, when they collide and stick together. Is it possible that their final velocity vector is in the direction shown?

29. Two cars of equal mass Collide at right angles to one another in an intersection. Their direction of motion after the collision is as shown. Which car had the greater velocity before the collision?

30. On a perfectly still day, a sailboat enthusiast brings a battery-operated fan to provide an air current for his sail. A) What are the directions of the change in momentum of the air at the fan and at the sail? B) What are the directions of the forces acting on the fan and on the sail due to these changes in momentum? C) Would the sailor be better off with the sail furled (down) or unfurled (up)?

31. 1. Suppose you are out on a frozen lake, where there is no friction. Which of the following would start you moving towards the shore?a) Shouting at someone on the shore.b) Removing a shoe and throwing it towards the shore.c) Removing a shoe and throwing it away from the shore.d) None of these would work. Conceptual Question

32. Conceptual Question Suppose two boys are trapped on the ice atop a frozen pond, and that the ice is completely frictionless. The boys are initially at rest, but they do have a baseball. They begin to play catch with the ball. Which of these is true?a) This will not help the boys get to shore.b) They will get to shore more quickly if they hold hands.c) If the first boy to catch the ball doesn’t throw it back, both will reach shore more quickly.d) Each boy will speed up as he throws the ball, and slow down as he catches it.e) If at least one catch is made, both should make it to shore.