Why does the ball sometimes seem to speed up after bouncing when gravity is on?

This is due to the conversion of gravitational potential energy into kinetic energy. If the ball bounces and then falls downward under gravity, it gains speed just like any falling object. The kinetic energy graph will show an increase during these falls, even if some energy was lost in the bounce itself.

What does a coefficient of restitution (e) of 0.5 actually mean?

An e of 0.5 means the ball rebounds from the wall with half the speed (in the direction perpendicular to the wall) that it had just before impact. It also indicates that only 25% (since kinetic energy is proportional to v²) of the relevant kinetic energy is retained in that direction after the collision, with the rest dissipated as heat, sound, or deformation.

Is momentum conserved in these wall collisions?

Yes, but you must consider the entire system. The particle's momentum is not conserved alone because the wall exerts an external force on it during the collision. However, the total momentum of the particle *and the wall (plus the Earth, if attached)* is conserved. In the direction parallel to the wall, the particle's momentum is conserved because there is no force in that direction in this frictionless model.

How is this model different from a real ball bouncing?

Real bounces involve factors like air resistance, friction that can change spin and parallel velocity, deformation of the ball and wall during contact, and sound energy loss. This simulator strips away these complexities to focus on the idealized core concepts of impulse, restitution, and energy conversion.

Wall Bounce

A point particle moves within a two-dimensional rectangular box. The core physics involves analyzing its motion and collisions with the perfectly rigid, frictionless walls. When the particle strikes a wall, its velocity component perpendicular to that wall is reversed and scaled by the coefficient of restitution, 'e'. This is governed by the relation v_perpendicular_after = -e * v_perpendicular_before, where e ranges from 0 (perfectly inelastic) to 1 (perfectly elastic). The parallel velocity component remains unchanged. This models a simplified, momentum-based collision. Users can optionally introduce a uniform gravitational field, which applies a constant downward acceleration, g, transforming the trajectory into a projectile motion between bounces. The simulator visually tracks the particle's path with trails and plots its kinetic energy over time. From this, one can explore core principles: conservation of momentum perpendicular to a wall during a collision, the loss of mechanical energy when e < 1, the independence of perpendicular motion components, and how gravity introduces an exchange between kinetic and potential energy. The model simplifies reality by ignoring air resistance, treating the particle as a point mass, and assuming instantaneous collisions with perfectly smooth walls.

Who it's for: High school and introductory college physics students studying kinematics, conservation laws, and the principles of collisions and projectile motion.

Key terms

Coefficient of Restitution
Elastic Collision
Inelastic Collision
Conservation of Momentum
Kinetic Energy
Projectile Motion
Newton's Laws of Motion
Trajectory

Live graphs

How it works

A puck slides inside a rectangular enclosure with smooth walls. Each impact reverses the normal component of velocity scaled by the coefficient of restitution e while leaving the tangential component unchanged. With e = 1 kinetic energy is conserved at every bounce; with e < 1 each collision dissipates energy until the puck nearly stops (especially with gravity, when it settles on the floor).

Key equations

v′ = v − (1+e)(v·n)n · n into interior, v·n < 0

e = 1: elastic · e = 0: no bounce along n

Frequently asked questions

Why does the ball sometimes seem to speed up after bouncing when gravity is on?: This is due to the conversion of gravitational potential energy into kinetic energy. If the ball bounces and then falls downward under gravity, it gains speed just like any falling object. The kinetic energy graph will show an increase during these falls, even if some energy was lost in the bounce itself.
What does a coefficient of restitution (e) of 0.5 actually mean?: An e of 0.5 means the ball rebounds from the wall with half the speed (in the direction perpendicular to the wall) that it had just before impact. It also indicates that only 25% (since kinetic energy is proportional to v²) of the relevant kinetic energy is retained in that direction after the collision, with the rest dissipated as heat, sound, or deformation.
Is momentum conserved in these wall collisions?: Yes, but you must consider the entire system. The particle's momentum is not conserved alone because the wall exerts an external force on it during the collision. However, the total momentum of the particle *and the wall (plus the Earth, if attached)* is conserved. In the direction parallel to the wall, the particle's momentum is conserved because there is no force in that direction in this frictionless model.
How is this model different from a real ball bouncing?: Real bounces involve factors like air resistance, friction that can change spin and parallel velocity, deformation of the ball and wall during contact, and sound energy loss. This simulator strips away these complexities to focus on the idealized core concepts of impulse, restitution, and energy conversion.

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Key equations

Frequently asked questions