2070HW_Momentum_Soln

2070HW_Momentum_Soln - Physics 2070 Homework 5 1 A bowling...

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Physics 2070 Homework 5 1. A bowling ball rolls into a stationary bowling pin, which is much lighter than the ball. a. During the collision, is the force exerted by the ball on the pin greater than, less than, or equal to the force exerted by the pin on the ball? Explain. According to Newton’s 3 rd law, the forces are equal. b. During the collision, is the bowling ball’s change in speed greater than, less than, or equal to the pin’s change in speed? Explain. The pin’s change in speed is greater. Since the forces are equal and the pin has a smaller mass, it must have a larger acceleration. By definition, then, it has a larger change in speed. c. During the collision, is the bowling ball’s change in momentum greater than, less than, or equal to the pin’s change in momentum? Explain. The ball’s change in momentum is equal to the pin’s change in momentum. According to conservation of momentum, the total momentum of the system does not change during the collision. So the momentum of the pin must change by an equal and oppositely directed amount as the momentum of the ball. d. A student makes the following argument about part (C): In the collision, the pin’s momentum changes more than the ball’s momentum, because the ball’s motion hardly changes, while the pin’s motion changes a lot; it bounces off the ball really fast. How could you help this student reconcile his intuitive ideas about the “changes in motion” with the fact that the ball’s momentum and the pin’s momentum change by the same amount? In terms of the Impulse-Momentum theorem and conservation of momentum, which is an alternate statement of Newton’s 3 rd law, we know that the force on the bowling ball is equal and opposite to the force on the pin during the interaction, but because the pin has a much smaller mass, it will feel a larger effect of that force (acceleration) than the ball. Because the time of the collision is the same for both the ball and the pin, the pin’s larger acceleration ( Δ v/ Δ t) means it will undergo a larger change in velocity during that time than the ball.
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2. The diagram shows two pucks at rest on a nearly frictionless (horizontal) table.
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