Jeremy performs an experiment in which he drops a rubber ball to bounce

Question

on a stone floor and record the height the ball reaches after the bounce.
However, his partner, Maria, states out front that no matter what height he
drops the rubber ball from, it will never bounce higher than the original
height he drops it at. Using what you know about the Law of Conservation
of Energy, explain why Maria was able to come to that conclusion

Answer 1

Maria's conclusion that the rubber ball will never bounce higher than the height from which it is dropped can be understood through the principles of the Law of Conservation of Energy. This law states that energy cannot be created or destroyed, only transformed from one form to another.

When Jeremy drops the rubber ball, it initially possesses potential energy due to its height (gravitational potential energy), which is given by the equation:

\[ PE = mgh \]

where \( PE \) is the potential energy, \( m \) is the mass of the ball, \( g \) is the acceleration due to gravity, and \( h \) is the height from which it is dropped.

As the ball falls, this potential energy is converted into kinetic energy (the energy of motion) just before it impacts the floor. Upon hitting the floor, some of the kinetic energy is transformed into elastic potential energy stored in the ball as it deforms, and then back into kinetic energy as it bounces.

However, during this process, several factors prevent the ball from bouncing back to its original height:

1. Energy Losses: In real-world scenarios, not all energy is perfectly conserved. Some of the energy is lost to non-conservative forces such as air resistance and internal friction within the material of the ball. This energy loss manifests as sound energy (the sound of the ball hitting the ground) and thermal energy (the heat generated during deformation).

2. Elasticity Limits: The rubber ball does not perfectly conserve all its kinetic energy when it deforms upon impact. This means that only a portion of the energy is converted back into potential energy as it rebounds, which limits the height it can reach.

3. Maximum Energy Transfer: The maximum height the ball can bounce back to is equal to the height it was dropped from, minus any energy losses. Thus, it will always bounce lower than the height from which it was originally dropped because energy has been lost during the bounce.

In summary, Maria's conclusion is supported by the Law of Conservation of Energy, which dictates that while energy can change forms, the total mechanical energy in the process will always be less than the initial potential energy due to energy losses. Consequently, the ball will never bounce higher than the height from which it was dropped.