9 - Linear Momentum and Collisions

9 Linear Momentum - Chapter 9 Linear Momentum and Collisions CHAPTE R OUTLI N E 9.1 Linear Momentum and Its Conservation 9.2 Impulse and Momentum

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251 251 Linear Momentum and Collisions ± A moving bowling ball carries momentum, the topic of this chapter. In the collision between the ball and the pins, momentum is transferred to the pins. (Mark Cooper/Corbis Stock Market) Chapter 9 CHAPTER OUTLINE 9.1 Linear Momentum and Its Conservation 9.2 Impulse and Momentum 9.3 Collisions in One Dimension 9.4 Two-Dimensional Collisions 9.5 The Center of Mass 9.6 Motion of a System of Particles 9.7 Rocket Propulsion

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C onsider what happens when a bowling ball strikes a pin, as in the opening photo- graph. The pin is given a large velocity as a result of the collision; consequently, it ﬂies away and hits other pins or is projected toward the backstop. Because the average force exerted on the pin during the collision is large (resulting in a large acceleration), the pin achieves the large velocity very rapidly and experiences the force for a very short time interval. According to Newton’s third law, the pin exerts a reaction force on the ball that is equal in magnitude and opposite in direction to the force exerted by the ball on the pin. This reaction force causes the ball to accelerate, but because the ball is so much more massive than the pin, the ball’s acceleration is much less than the pin’s acceleration. Although F and a are large for the pin, they vary in time—a complicated situation! One of the main objectives of this chapter is to enable you to understand and analyze such events in a simple way. First, we introduce the concept of momentum , which is use- ful for describing objects in motion. Imagine that you have intercepted a football and see two players from the opposing team approaching you as you run with the ball. One of the players is the 180-lb quarterback who threw the ball; the other is a 300-lb line- man. Both of the players are running toward you at 5 m/s. However, because the two players have different masses, intuitively you know that you would rather collide with the quarterback than with the lineman. The momentum of an object is related to both its mass and its velocity. The concept of momentum leads us to a second conservation law, that of conservation of momentum. This law is especially useful for treating prob- lems that involve collisions between objects and for analyzing rocket propulsion. In this chapter we also introduce the concept of the center of mass of a system of particles. We ﬁnd that the motion of a system of particles can be described by the motion of one representative particle located at the center of mass. 9.1 Linear Momentum and Its Conservation In the preceding two chapters we studied situations that are complex to analyze with Newton’s laws. We were able to solve problems involving these situations by apply- ing a conservation principle—conservation of energy. Consider another situation—a 60-kg archer stands on frictionless ice and ﬁres a 0.50-kg arrow horizontally at 50 m/s.
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This note was uploaded on 02/24/2011 for the course PHYS 102 taught by Professor Wang during the Spring '11 term at Nanjing University.

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9 Linear Momentum - Chapter 9 Linear Momentum and Collisions CHAPTE R OUTLI N E 9.1 Linear Momentum and Its Conservation 9.2 Impulse and Momentum

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