Elastic collisions

Equipment

• Two virtual carts on a frictionless track
• Sliders for m₁, m₂, u₁, u₂ and restitution e
• Readouts for post-collision velocities and total momentum

Procedure

1. Set up the collision and measure velocities

   Set "Restitution e" to 1.00 (ideal elastic). Choose m₁ = 2 kg, m₂ = 3 kg, u₁ = 5 m/s, u₂ = −1 m/s, watch the collision and read v₁, v₂ in the "After collision" readout. Compute $P$ before/after and confirm momentum conservation.

2. Check kinetic-energy conservation

   With the same data, compute $K = \frac{1}{2}m_1u_1^2 + \frac{1}{2}m_2u_2^2$ before and after; for $e = 1$ the two values are equal. Change m₂ so v₂ shifts while $P$ stays conserved. Verify the formula $v_1 = \frac{m_1 - m_2}{m_1+m_2}u_1 + \frac{2m_2}{m_1+m_2}u_2$ for the $e = 1$ case.

3. Scan the restitution coefficient

   Lower e to 0.5 then 0 and repeat the collision. Check $e = (v_2 - v_1)/(u_1 - u_2)$ with the new readings: separation speed scales with e. At $e = 0$ the bodies stick (perfectly inelastic) — compare with the "Inelastic collision" lab. Conclude which e conserves K and which converts K into heat/deformation.

Simulation

Experiment history

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