I recently conducted an experiment, where I dropped tennis balls from various heights and recorded their rebound heights. The higher the drop, the higher the rebound height, obviously. However, the higher the drop, the smaller the bounce efficiency also became. For example, a drop from 50cm had a 38 cm rebound whereas a drop from 200cm had a 102cm rebound. That is, the ratio becomes smaller with higher drops.
Why is this so?
Is it something to do with air resistance? Theoretically, shouldn't the ball have the same bounce efficiency no matter the height?
Best Answer
When a ball bounces, it is deformed at the contact point to become a compressed spring, having almost all of the kinetic energy converted to spring compression, as the velocity downward goes to zero. It then is forced upward by the springiness of the material of the ball.
The efficiency of the bounce depends on how greatly the ball is deformed; a thick rubber ball may lose more energy to internal heating if it is deformed to a near-hemisphere, though be very lively when a low-velocity impact makes a small dent.
Also, some ball structures may include viscous or viscoelastic materials (which have different mechanical constants at different strain rates). A fast impact would imply a high strain rate, but the rebound may be slow by comparison. Such materials don't make good toys, but are excellent for sound-deadening.
One way of determining the hardness of steel is to bounce a hardened ball against a sample: the hardest steel does the least energy-absorbing deformation, so returns the ball higher than softer metal.
In the case of a tennis ball, remember that a long drop creates more airspeed-related losses than a short one; there's more than rebound energy efficiency involved in that experimental setup.