Why does a bouncing ball not bounce perpetually but instead lose height with each bounce?

Answer 1

The Theoretical: As strange and "counter-intuitive" as it seems, if a ball has perfect elasticity and falls on a surface that absorbs absolutely no energy, and if there is absolutely no atmosphere to interfere with the ball's movement, and if there are no other possible ways for any of the materials involved to absorb or give up energy in any form (including heat and sound), the ball would bounce without losing height in subsequent bounces for eternity. As you will see, the question is about the conservation of energy, and not about Newton's third law. The Practical: There are no such conditions as described above. The ball loses energy at many stages, and as a result, it eventually stops. In other words, don't put much effort into using this concept to build the long-sought-after Perpetual Motion Machine. Although all the energy is accounted for, some is irretrievable to the system and no longer useful for propelling the ball. As a result, the ball cannot reach its original height, which means it has less potential energy than it had before its initial drop. The difference between the original height and the height attained by any subsequent bounces represents the net loss of energy to entropy at that point. The energy in the system continues to dissipate until the ball lacks the energy to bounce and comes to rest on the surface. No laws are violated, but a little energy (the energy given by the experimenter to the ball originally) is lost forever. When a ball is dropped from a height, the primary force acting on it is Earth's gravity, and right before it is dropped, the ball possesses gravitational potential energy. (The gravitational potential energy is the arithmetic product of the ball's mass, the constant of acceleration due to gravity, and the ball's height: Ep = mgh.) When the ball falls freely, its potential energy is converted to kinetic energy (Ek = [1/2]mv2). When the ball hits the surface, its kinetic energy applies a "force of impact" on the surface, and the surface reacts with a nearly equal force of impact against the ball. Additionally, the surface and other materials involved will absorb some energy, leaving a little less energy to act upon the ball. The amount of energy absorbed by the surface depends on its nature and condition. It could be anything: loam, granite, a wooden table, ice, plastic. If the ball is a Bowling ball, it might end there, with no rebound, possibly a shattered bowling ball and damage to the surface. In that case, all of the ball's kinetic energy not absorbed by the atmosphere would work to deform or crack the surface and shatter the ball. All the energy would be accounted for. But if the ball is elastic, then the side impacting the surface is compressed and deformed. If the ball is hollow, then the ball and the air inside are compressed, creating increased pressure inside the ball. The reaction to this pressure and compression is for the ball and air inside it to expand. The expansion applies force against the surface, which reacts by pushing back against the ball with force. But how much force? It cannot be the same amount of force, because energy has been lost. The surface has absorbed energy and heats up. The air has absorbed heat and sound energy. The material of the ball, which isn't close to being perfectly elastic, has absorbed energy that cannot be converted back to kinetic energy, and the air inside the ball heats up and adds heat to the material of the ball. The ball bounces and is now going up. If the ball retained all of the lost energy described above, it would rise to its starting point, but it cannot. Once again, air friction acts on the ball, the air and ball warm up, which adds to entropy and the loss of useful energy, so the ball lacks the kinetic energy required to reach its original height. That should seem no stranger than the idea (considered preposterous by Newton's contemporaries) that an object in motion tends to remain in motion -- for eternity. You could imagine such a "bouncing ball" system in your mind, and you can see that it represents a "thought experiment" in the conservation of energy. Since potential energy is directly related to the original height of the ball, if no energy is lost during the drop and rebound, then the ball must attain the original height on the rebound.

Answer 2

We all know that there is no such thing as perpetual energy unfortunately. The scientific reason is that when a ball is traveling upward, it has kinetic energy. When the ball reaches it's maximum height, its energy is instantly transfered to potential energy. But no all of it gets transfered. When the ball falls again, this process is repeated. When energy is not fully transfered back to kinetic energy, the ball does not have enough energy to bounce up to the original height.