Bounce Lab: Exploring the Dynamics of Ball Rebound |…

What is Restitution?

Restitution refers to the coefficient of restitution (COR) which quantifies the ratio of the relative velocity after impact to that before impact. It essentially measures how much energy is conserved during a collision, with values ranging from 0 for perfectly inelastic collisions where objects stick together, to 1 for perfectly elastic collisions where no kinetic energy is lost.

In Bounce Lab, you can observe and measure this COR by comparing the heights of successive bounces. This allows you to understand how different factors like friction and spin influence the ball's behavior.

Factors Affecting Bounce

Several physical factors come into play during a bounce, including Coulomb friction which resists motion between surfaces in contact, and air drag that opposes the motion of the ball through the atmosphere. These forces can significantly reduce the height of each successive bounce.

Additionally, spin on the ball at impact introduces Magnus lift, causing the ball to curve as it bounces, a phenomenon crucial for sports like tennis or soccer.

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Energy Conservation and Loss

The principle of energy conservation dictates that in an ideal scenario without any dissipative forces (like friction), the total mechanical energy before and after impact should remain constant. However, real-world interactions involve energy loss due to these forces, manifesting as heat or deformation.

In Bounce Lab, you can simulate this by observing how much height is lost with each bounce compared to the initial drop height.

Stopping Time and Geometric Series

The stopping time of a bouncing ball can be analyzed using the concept of geometric series. Each successive bounce represents a fraction of the previous one, forming a geometric progression that theoretically never reaches zero but approaches it asymptotically.

This simulation allows you to check your understanding by comparing the simulated stopping times with theoretical predictions based on the sum of an infinite geometric series.

Frequently asked questions

How does spin affect the bounce?

Spin introduces Magnus lift, which causes the ball to curve as it bounces. This effect can be observed in sports like tennis or soccer where spin influences the trajectory and behavior of the ball.

What is Coulomb friction and how does it impact the bounce?

Coulomb friction is a force that resists motion between surfaces in contact. In Bounce Lab, it reduces the height of each successive bounce by dissipating energy as heat or deformation.

Why do bounces eventually stop?

Bounces eventually stop due to continuous energy loss from various forces like friction and air drag. Each impact transfers a small amount of energy, leading to a decrease in the height of each bounce until it becomes negligible.

How does the geometric series formula apply to bouncing balls?

The stopping time of a bouncing ball can be modeled using a geometric series where each term represents the height of successive bounces. The sum of this infinite series gives an estimate of the total time before the ball comes to rest.

Try it live

Everything above runs in your browser — open Bounce Lab: Restitution from Bounce Heights, Energy Loss & Spin and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.

▶ Open Bounce Lab: Restitution from Bounce Heights, Energy Loss & Spin simulation