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Example: If you were to jump off of a building would you prefer to land on a large air mattress or a concrete slab? Why? (Assume you stop after impact) Concrete slab – a very large force is applied to change your momentum in a very short period of time. Air Mattress – A smaller force is applied over a much longer time. Both situations correspond to the same change in momentum (same change in velocity with a constant mass). This is the definition of the average force. It is typically more convenient to use the average force, especially when the contact time is very small.

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Example: A 10 g bullet is fired at a steel plate. The velocity of the bullet just before it strikes the plate is 200 m/s. The contact time for the bullet and the plate is 1 s. Assume all motion is along one dimension. a)If the bullet stops after contact, what is the average force applied to the bullet by the steel plate? b)If the bullet rebounds from the steel plate with a speed of 90 m/s what average force was applied to the bullet by the steel plate? c)How would these values change if the contact time was extended to 1 ms? a) b) c)

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Consider these situations: (i) a ball moving at speed v is brought to rest; (ii) the same ball is projected from rest so that it moves at speed v ; (iii) the same ball moving at speed v is brought to rest and then projected backward to its original speed. In which case(s) does the ball undergo the largest change in momentum? 1. (i) 2. (i) and (ii) 3. (i), (ii), and (iii) 4. (ii) 5. (ii) and (iii) 6. (iii)

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Consider two carts, of masses m and 2 m, at rest on an air track. If you push first one cart for 3 s and then the other for the same length of time, exerting equal force on each, the momentum of the light cart is 1. four times 2. twice 3. equal to 4. one-half 5. one-quarter the momentum of the heavy cart.

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Consider two carts, of masses m and 2 m, at rest on an air track. If you push first one cart for 3 s and then the other for the same length of time, exerting equal force on each, the kinetic energy of the light cart is 1. larger than 2. equal to 3. smaller than the kinetic energy of the heavy car. The smaller mass undergoes a larger acceleration and therefore has a larger final velocity.

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Suppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the time intervals to stop them compare? 1. It takes less time to stop the ping-pong ball. 2. Both take the same time. 3. It takes more time to stop the ping-pong ball.

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Suppose a ping-pong ball and a bowling ball are rolling toward you. Both have the same momentum, and you exert the same force to stop each. How do the distances needed to stop them compare? 1. It takes a shorter distance to stop the ping-pong ball. 2. Both take the same distance. 3. It takes a longer distance to stop the ping-pong ball.

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