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Using the principle of the conservation of energy, the COR can be used to relate the bounce-back height to the original height of a ball dropped from rest. In fact, this ratio is equal to the square of the COR. Mathematically, if a ball is dropped from a height h(0), and bounces back to a height h(1), then:
As the object hits the ground, it is compressed (like a spring) such that the energy of the ball is transferred into the compression of the material. Some of this energy is converted to heat, and lost. The remainder is available to launch the object back up into space after the bounce. The fact that the ball bounces back to less than its original height indicates that the maximum value of COR is 1, and values progressively less than this indicate that less and less of the original energy is available after the bounce...
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