#### Created By

This web page was created by Brad Smith, Bryan Shoffner, Adam Norris, and Daniel Blackwell. Also, the page was designed in response to a homework assignment in a physics class at the University of North Carolina at Chapel Hill. We hope you enjoy the page and if you have any questions feel free to contact either of us at brads@email.unc.edu, bshoffne@email.unc.edu, alnorris@email.unc.edu, and dhbunc12@email.unc.edu.

# Bouncing Balls

A bouncing ball is an everyday occurrence that usually goes overlooked. However, this common phenomenon is caused by several different natural forces: gravity, mass, and velocity. Also there are three types of energy, gravitational potential energy, potential energy, and kinetic energy, which play major roles in the ball's ability to bounce. Each of these forces and types of energy has a different effect which allow for a ball to speed towards a surface and bounce back away from the surface.

# Types of Energy in a Bouncing Ball

Before a ball is dropped, it contains gravitational potential energy. This is the energy that coincides with the force gravity. Therefore before the ball is dropped the gravitational potential energy is equal to the force of gravity exerted on the ball by the Earth. After the ball is dropped and as it falls, the ball uses kinetic energy, or the energy of motion. Once the ball hits the ground, or its surface of contact, the ball naturally wants to contintue falling but is stopped by the surface. This explains why a ball appears as though it is being squished into the surface. The ball is stopped by the surface and the energy is then potential energy. Potential energy is a stored form of energy which can easily produce motion, or kinetic energy. Since the ball has acquired potential energy upon contact this energy must somehow be released. A very small amount of the energy is released as thermal energy, which for this phenomenon can be ignored, while a large amount of energy is released in the form of kinetic energy as the ball proceeds in motion back up. The ball has bounced.

# The Effects of Gravity

Gravity is a natural force that is created by Earth's rotation. The rotation causes an inward pull directed towards Earth's center. This explains why balls naturally fall towards the ground when dropped. Assuming that everyone reading this will only be concerned with bouncing balls on Earth, this is the only instance that will be considered. Also for the simplicity of the explanation it will be assumed that the ball has no initial velocity in any direction: it will be free falling. Gravity, on Earth, is a constant and is approximately 9.8 m/s2. In other words, the inward pull towards Earth's center, or gravity, causes a ball to accelerate at 9.8 m/s2 in a direction pointing towards the earth. A balls gravitational potential energy is equal in magnitude to the force of gravity. Since gravity is a constant balls of different masses will fall at the same rate: 9.8 m/s2. The ball's kinetic energy can also be represented by the force of gravity.

# The Effects of Mass

A ball's mass affects the way it bounces in such a way that as the mass of a ball increases, it will take it less time to stop bouncing if zero net force is applied to the ball as it bounces.

# The Effects of Velocity

The velocity of the ball is the speed in which the ball is traveling and is measured in meters per second. If the ball is dropped, or free falling, the initial velocity is zero meaning that the ball is traveling at a rate of 0 m/s. If this is the case, then the ball's velocity will be the same as its acceleration due to gravity: 9.8 m/s2. In another instance, the ball may have an intial velocity meaning that at the moment is dropped the ball's velocity is not 0 m/s. In this case, the ball's velocity will still follow its acceleration due to gravity, but will just start at a faster rate. Refer to table below for further explanation. Since velocity is the speed at which the ball is traveling, this rate will also control the amount of kinetic and potential energy which the ball has. A higher velocity will result in a higher kinetic energy as well as potential energy, thus causing a higher bounce. A smaller velocity will display a smaller amount of kinetic as well as potential energy and will cause the ball to have a lower bounce.

Here is a video of a bouncing ping pong ball, watch it and try to identify the physics concepts which have been explained above!