Why does the ball's speed parallel to the wall not change during the collision?

In this idealized model, we assume a frictionless surface. The only force during the collision acts perpendicular (normal) to the wall, as the wall cannot pull or push along its surface. Since force is the rate of change of momentum, a zero force in the tangential direction means the tangential component of momentum, and thus velocity, is conserved.

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

A value of e=0.5 indicates a partially inelastic collision. It means the relative speed of separation after the collision is half the relative speed of approach along the normal direction. Energy is lost to sound, heat, or deformation. For e=1 (perfectly elastic), kinetic energy is conserved; for e=0, the objects stick together (perfectly inelastic) along the normal direction.

How is the 'angle of reflection' related to the 'angle of incidence'?

For a perfectly elastic collision (e=1) with a frictionless wall, the angle of reflection equals the angle of incidence, both measured from the normal. This mirrors the law of reflection in optics. However, if e < 1, the normal component of velocity is reduced, causing the reflection angle to be larger than the incidence angle. Friction would further complicate this relationship.

Does this simulator model real-world ball bounces accurately?

It captures the essential first-order physics but makes significant simplifications. Real bounces involve friction (changing the tangential speed), ball rotation (spin), and deformation, which are not included here. This model is an excellent tool for understanding the core principles of momentum exchange before adding complexity.

Oblique Wall Impact

Q: Does this simulator model real-world ball bounces accurately?

It captures the essential first-order physics but makes significant simplifications. Real bounces involve friction (changing the tangential speed), ball rotation (spin), and deformation, which are not included here. This model is an excellent tool for understanding the core principles of momentum exchange before adding complexity.

Oblique Wall Impact visualizes the two-dimensional collision of a point mass with a rigid, tilted wall. The core physics principle is the conservation of momentum, applied separately to components parallel and perpendicular to the wall's surface. For a perfectly elastic collision, the component of velocity parallel to the wall (tangential component, v_t) remains unchanged due to the absence of friction. The component perpendicular to the wall (normal component, v_n) reverses direction, with its magnitude scaled by the coefficient of restitution (e). This is described by the equations: v_n' = -e * v_n and v_t' = v_t, where primes denote post-collision velocities. The simulator allows users to manipulate the wall's tilt angle, the ball's initial velocity vector, and the elasticity parameter. By observing the resulting trajectory changes, students learn to decompose vectors into normal and tangential components relative to an arbitrary surface, a fundamental skill in mechanics. The model simplifies reality by treating the ball as a point mass, ignoring rotational effects, air resistance, and any deformation of the wall or ball. It also contrasts open boundaries, where the ball continues unimpeded, with a closed 'wall bounce' environment to study repeated collisions. This interactive exploration reinforces Newton's laws of motion, the vector nature of velocity, and the idealized rules of elastic and inelastic collisions.

Who it's for: High school and introductory undergraduate physics students learning about momentum conservation, vector components, and the kinematics of collisions.

Key terms

Coefficient of Restitution
Elastic Collision
Normal Component
Tangential Component
Momentum Conservation
Oblique Impact
Vector Decomposition
Angle of Incidence

Live graphs

How it works

Unlike the closed box in Wall Bounce, this lab shows a single flat segment with adjustable tilt. A puck approaches from the left; the wall normal n is drawn at the center. Impulses are normal-only: the tangential component of velocity is unchanged, while the normal component is reversed and scaled by the coefficient of restitution e. With e = 1 kinetic energy is conserved and the acute angle to n matches before and after; with e < 1 the outgoing speed along n is smaller and total K drops.

Key equations

v′ = v − (1+e)(v·n)n · v·n < 0 (approaching)

v′_n = −e v_n · v′_t = v_t (smooth wall)

Frequently asked questions

Why does the ball's speed parallel to the wall not change during the collision?: In this idealized model, we assume a frictionless surface. The only force during the collision acts perpendicular (normal) to the wall, as the wall cannot pull or push along its surface. Since force is the rate of change of momentum, a zero force in the tangential direction means the tangential component of momentum, and thus velocity, is conserved.
What does a coefficient of restitution (e) of 0.5 mean physically?: A value of e=0.5 indicates a partially inelastic collision. It means the relative speed of separation after the collision is half the relative speed of approach along the normal direction. Energy is lost to sound, heat, or deformation. For e=1 (perfectly elastic), kinetic energy is conserved; for e=0, the objects stick together (perfectly inelastic) along the normal direction.
How is the 'angle of reflection' related to the 'angle of incidence'?: For a perfectly elastic collision (e=1) with a frictionless wall, the angle of reflection equals the angle of incidence, both measured from the normal. This mirrors the law of reflection in optics. However, if e < 1, the normal component of velocity is reduced, causing the reflection angle to be larger than the incidence angle. Friction would further complicate this relationship.
Does this simulator model real-world ball bounces accurately?: It captures the essential first-order physics but makes significant simplifications. Real bounces involve friction (changing the tangential speed), ball rotation (spin), and deformation, which are not included here. This model is an excellent tool for understanding the core principles of momentum exchange before adding complexity.