| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Collision with unchanged direction |
| Difficulty | Standard +0.8 This M2 collision problem requires applying both conservation of momentum and the restitution equation, then manipulating algebraic expressions to find constants and deduce a range for e. It involves multiple steps with careful sign conventions and algebraic manipulation beyond routine textbook exercises, but uses standard mechanics techniques without requiring novel insight. |
| Spec | 6.03i Coefficient of restitution: e6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \([v - (-u/2)] / (-u - u) = -e\) \(\quad v + \frac{1}{2}u = 2ue\) \(\quad v = \frac{1}{2}u(4e - 1)\) | M1 A1 M1 A1 | |
| (b) If \(v > 0\) then \(4e - 1 > 0\), so \(\frac{1}{4} < e \leq 1\) | M1 A1 A1 | Total: 7 marks |
**(a)** $[v - (-u/2)] / (-u - u) = -e$ $\quad v + \frac{1}{2}u = 2ue$ $\quad v = \frac{1}{2}u(4e - 1)$ | M1 A1 M1 A1 |
**(b)** If $v > 0$ then $4e - 1 > 0$, so $\frac{1}{4} < e \leq 1$ | M1 A1 A1 | Total: 7 marks2. Two small smooth spheres $P$ and $Q$ are moving along a straight line in opposite directions, with equal speeds, and collide directly. Immediately after the impact, the direction of $P$ 's motion has been reversed and its speed has been halved. The coefficient of restitution between $P$ and $Q$ is $e$.
\begin{enumerate}[label=(\alph*)]
\item Express the speed of $Q$ after the impact in the form $a u ( b e + c )$, where $a , b$ and $c$ are constants to be found.
\item Deduce the range of values of $e$ for which the direction of motion of $Q$ remains unaltered.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 Q2 [7]}}