Solving an Inelastic Collision With e=0.25
A worked example walks through a 1D collision between a 1.0 kg sphere moving at 4.0 m/s and a stationary 1.5 kg sphere, with coefficient of restitution 0.25. The animation pairs the moving spheres with side-by-side equations for momentum conservation and restitution, solving simultaneously for final velocities of 1.0 m/s and 2.0 m/s, then computes the kinetic energy lost (4.5 J). Useful for students learning to combine momentum and restitution equations in collision problems.
Narrated · 16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
Scene 3: Solved Example 1 - Inelastic Collision with $e=0.25$Visual Prompt: Step-by-step animated solution on a coordinate axis (Right = Positive): Initial State: Sphere A ($1.0\text{ kg}$) moves right at $+4.0\text{ m/s}$ towards stationary Sphere B ($1.5\text{ kg}$). Collision Animation: Spheres impact and separate at new speeds. Math Overlay:Conservation of Momentum: $1.0(4.0) + 1.5(0) = 1.0 v_A' + 1.5 v_B' \Rightarrow v_A' + 1.5 v_B' = 4.0$ Restitution Equation: $v_B' - v_A' = 0.25(4.0 - 0) = 1.0$ Solving: $v_A' = 1.0\text{ m/s}$, $v_B' = 2.0\text{ m/s}$. Kinetic Energy Loss: $E_{k,\text{initial}} = 8.0\text{ J}$, $E_{k,\text{final}} = 3.5\text{ J} \Rightarrow \Delta E_k = 4.5\text{ J}$. Text / Voiceover: "Using momentum conservation and $e=0.25$, Sphere A slows to $1.0\text{ m/s}$ and Sphere B launches at $2.0\text{ m/s}$, losing $4.5\text{ Joules}$ of kinetic energy to internal energy."
Make the next one in this series
- Show the same collision with e=1 to compare energy loss in a perfectly elastic case.
- Animate an example with e=0 to illustrate a perfectly inelastic collision where spheres stick together.
- Create a graph showing how kinetic energy loss varies continuously as e ranges from 0 to 1.
