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The Impulse-Momentum Theorem

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We're going to be looking at some applications of the impulse-change in momentum relationship. Now according to that relationship, the impulse is equal to the change in momentum. As a good example, suppose I drop this brick on the table. The collision of the brick went under a change in momentum, that's its final momentum minus its initial. The final momentum is what it has now at its stop, which is zero. The initial momentum is what it had at the instant that it hit the table, and that depends on how far I dropped it from. Now if I were to drop the brick on this cushion, its change in momentum would be the same as for the table because the brick comes to a stop; that's its final momentum, which is zero, and its initial momentum is what it had at the instant it hit, and if I dropped it from the same height, that's the same as it was directly on the table. What is different in these two cases is the amount of time that the collision lasts. In the case of the cushion you can see the cushion depresses, the cushion compressed, and it takes more time than if I dropped it directly on the table. So you can see what the purpose of a cushion is. The cushioning effect that you get is basically its increasing the time that the collision lasts. When you walk across a carpeted floor you have the same sort of situation. For each step on the floor you feel less force that if you were to walk across a concrete floor for example, because the duration of each collision is less. Another example of that is when you jump from a height, when you hit the ground, you always bend your knees. That's essential if you want to protect to protect your bones, because by bending your knees, it makes a collision last a lot longer and as a result of that, the force of the impact is less. If you didn't bend your knees, you'd do serious damage to your bones and your joints.

Now, we can apply the impulse momentum relationship to another situation where in fact, we want to make the force as large as possible. When you pound a nail, you want greater force, not less force. When I drop the hammer on the head of the nail, the hammer undergoes a certain change in momentum while it's colliding, From whatever it had at the instant it hit, to zero when it comes to a stop, so again the equation is fixed, so if I pound with the piece of wood on the table, my collision is going to last a lot shorter time that if I pound with my block of wood on the cushion. Obviously, you'd never try doing something like that. That makes the collision last too long, so the force is going to be correspondingly small. You always have a hard surface underneath it, that makes the collision last for a shorter period of time.

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