Can you explain why if you drop 3 balls they bounce back at different heights?

Question

The balls are a tennis ball, a golf ball, and a rubber bouncy ball.
Based on the concept of elastic potential energy

Answer 1

The more rigidly elastic an object the more energy will be conserved when it bounces.

Essentially when a ball bounces it is being deformed by the impact with the ground. If the ball is very elastic, it will return to it's original shape will nearly the same force as the deformation, causing it to bounce. A tennis ball is not terribly elastic, really it's just air pressure, so it doesn't bounce as well. Also, the felt covering absorbe some of this energy. A golf ball and hard rubber ball are quite elastic and will rebound with much greater energy.

Answer 2

Think of each ball being like a spring. The force on a spring is proportional to how much compression is put on it. In math talk, this is F = k dx; where k is a constant and dx is the amount of compression.

Each ball has a k value of sorts, based on a number of characteristics, including elasticity, internal pressure, and things like that. These determining factors come up with a different value for the k of each ball. Thus, when dropped from the same height, for example, the force created when each one hits the ground is different. F = K dx for one ball and f = k dx for another.

As luck would have it, force exerted over some distance is work energy. And that energy is stored up as potential energy as each ball compresses on impact. It is then released as kinetic energy when the ball decompresses (bounces back).

Because the k's are different, the amount of potential energy and, therefore, kinetic energy produced on decompressing and rebounding is different. And that means the height on rebound will be different because KE = 1/2 mv^2 = mgH = PE; where H = KE/mg is the height of rebound for a given kinetic energy KE. In other words h = ke/mg and H = KE/mg where KE > ke kinetic energies and H > h rebound heights even if the masses of the two balls are the same.

Answer 3

Perfect elastic collisions are useful idealizations, but they don't translate well into actual objects very well.

Basically, the objects that retain energy less efficiently will bounce back lower. Energy can be lost to air resistance, of course (which will vary largely between different objects), but the main source of energy loss will be inelasticity in the collision (that is, a conversion of some of the energy to heat upon bouncing on the ground). Some objects retain this energy better than others.

Answer 4

Due to how much mass they contain and how they are shaped will make them bounce up at different heights. Hope this helps:P