Asked by T
Suppose that you wanted to close a door by throwing a ball at the door. One ball will bounce back and another is made of clay and will stick to the door. Each ball has the same mass and hits the door with same velocity. Which method will close the door quicker? Explain
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The bouncing ball will close the door quicker.
Reason: the door responds to impulse (change in momentum). For a clay ball that sticks, the ball's momentum goes from m v to 0, so the impulse delivered to the door is m v. For a ball that bounces back elastically (velocity reverses to −v), the ball's momentum change is m(−v) − m v = −2 m v, so the door receives an impulse of 2 m v. That larger impulse (and hence larger angular impulse about the hinge) gives the door more angular momentum and closes it faster. (If the bounce is not perfectly elastic the impulse is less than 2 m v but is still larger than m v so long as the ball actually rebounds.)
Reason: the door responds to impulse (change in momentum). For a clay ball that sticks, the ball's momentum goes from m v to 0, so the impulse delivered to the door is m v. For a ball that bounces back elastically (velocity reverses to −v), the ball's momentum change is m(−v) − m v = −2 m v, so the door receives an impulse of 2 m v. That larger impulse (and hence larger angular impulse about the hinge) gives the door more angular momentum and closes it faster. (If the bounce is not perfectly elastic the impulse is less than 2 m v but is still larger than m v so long as the ball actually rebounds.)
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