Elastic Collision of Two Spheres

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

A moving sphere collides elastically with a sphere at rest. You can change the masses of the spheres and the impact parameter to study their influence on the paths of the spheres after the collision. A motion view and a trace view are provided.

Contributed by: Hans-Joachim Domke (March 2011)
Open content licensed under CC BY-NC-SA



The elastic collision in two dimensions is derived mathematically by splitting the momentum of the first (moving) body in a radial component in the direction of theline between the two centers at the moment of impact and a second component that is perpendicular to the first, hence tangential to the surfaces of the two bodies in contact. The first component provokes a central collision of the two bodies and results in and , while the second remains unaltered if there is no friction between the two surfaces. After the collision, =+ and =.

The motion view shows the movement of the bodies as in a real experiment. With "show traces" you get a view similar to seeing the movement as a static image taken in stroboscopic light. You can extract the velocities of the two bodies and the scattering angle and calculate the mass ratio as an exercise. Because all changes of the parameters are shown instantly in this view, you can investigate, for example, the dependence of the scattering angle on the impact parameter.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.