Paper 3 Dynamics Drills

Q1 Collision and energy classification

A trolley A of mass $0.80\mathrm{kg}$ moving at $1.50\mathrm{m}{\mathrm{s}}^{-1}$ collides with trolley B of mass $1.20\mathrm{kg}$ moving at $0.30\mathrm{m}{\mathrm{s}}^{-1}$ in the same direction. After collision, A moves at $0.42\mathrm{m}{\mathrm{s}}^{-1}$ in the same direction.

1. State the condition under which momentum is conserved for the two-trolley system. [2]
2. Calculate the final velocity of trolley B. [4]
3. Determine whether kinetic energy is conserved. [4]
4. Classify the collision as elastic or inelastic. [1]
5. Explain why momentum can be conserved even when kinetic energy is not conserved. [2]

Q2 Variable force and impulse

A padded barrier stops a $65\mathrm{kg}$ runner from $5.0\mathrm{m}{\mathrm{s}}^{-1}$ to rest. The force-time graph during the collision is triangular, rising from zero to a maximum force $F_{\max }$ in $0.080\mathrm{s}$ and falling back to zero at $0.200\mathrm{s}$.

1. Calculate the impulse on the runner. [2]
2. Determine $F_{\max }$. [3]
3. Explain why increasing the stopping time reduces the maximum force for the same change in momentum. [3]
4. State the direction of the force exerted by the barrier on the runner. [1]
5. Explain how Newton’s third law applies during the collision. [2]