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324 Chapter 8 | Linear Momentum and Collisions
can be immense if you land stiff-legged on a hard surface. Rolling on the ground after jumping from the table, or landing with a parachute, extends the time over which the force (on you from the ground) acts.
Making Connections: Illustrations of Force Exerted
Figure 8.3 This is a graph showing the force exerted by a fixed barrier on a block versus time.
A 1.2-kg block slides across a horizontal, frictionless surface with a constant speed of 3.0 m/s before striking a fixed barrier and coming to a stop. In Figure 8.3, the force exerted by the barrier is assumed to be a constant 15 N during the 0.24-s collision. The impulse can be calculated using the area under the curve.
(8.20) Note that the initial momentum of the block is:
(8.21)
We are assuming that the initial velocity is −3.0 m/s. We have established that the force exerted by the barrier is in the positive direction, so the initial velocity of the block must be in the negative direction. Since the final momentum of the block is zero, the impulse is equal to the change in momentum of the block.
Suppose that, instead of striking a fixed barrier, the block is instead stopped by a spring.Consider the force exerted by the spring over the time interval from the beginning of the collision until the block comes to rest.
Figure 8.4 This is a graph showing the force exerted by a spring on a block versus time.
In this case, the impulse can be calculated again using the area under the curve (the area of a triangle):
Again, this is equal to the difference between the initial and final momentum of the block, so the impulse is equal to the change in momentum.
(8.22)
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