Physics Lens

Simulation of a Bouncing Ball

While I have shared a simulation of a bouncing ball made using Glowscript before, I felt that one made using GeoGebra is necessary for a more comprehensive library.

It took a while due to the need to adjust the equations used based on the position of the graphs, but here it is:

The kinematics of a bouncing ball can be explained by considering the dynamics and forces involved in its motion. In this simulation, air resistance is assumed negligible. When a ball is dropped from a certain height and bounces off the ground, several key principles of physics come into play. Let’s break down the process step by step:

Free Fall: When the ball is released, it enters a state of free fall. During free fall, the only force acting on the ball is gravity. This force is directed downward and can be described by W = mg

W is the gravitational force.
m is the mass of the ball.
g is the acceleration due to gravity (approximately 9.81 m/s² near the surface of the Earth).

Impact with the Ground and Bounce: When the ball reaches the ground, it experiences a force due to the collision with the surface. This force is an example of a contact force and much larger than the gravitational force. This force depends on the elasticity of the ball and the surface it bounces off.

During the collision with the ground, the ball’s momentum changes rapidly. If the ball and the ground are both ideal elastic materials, the ball will bounce back with the same speed it had just before impact. In reality, some energy is lost during the collision, causing the bounce to be less than perfectly elastic. This simulation assumes elastic collisions.

Post-Bounce Motion: After the bounce, the ball starts moving upward. Gravity acts on it as it ascends, decelerating its motion until it reaches its peak height.

Second Descent: The ball then starts descending again, experiencing the force of gravity pulling it back down towards the ground.

This process continues with each bounce. In practice, with each bounce, some energy is lost due to the non-ideal nature of the collision and other dissipative forces like air resistance. As a result, each bounce is typically lower than the previous one until the ball eventually comes to rest. However, for simplicity, the simulation assumes no energy is lost during the collision and to dissipative forces.

An animated gif file is included here for use in powerpoint slides:

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