| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2023 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Collision with unchanged direction |
| Difficulty | Standard +0.3 This is a standard M2 momentum-collision question requiring conservation of momentum and Newton's experimental law. Part (a) is a straightforward 'show that' using momentum conservation, part (b) applies impulse-momentum theorem directly, and part (c) combines the restitution equation with given constraints. All techniques are routine for M2 with no novel insight required, making it slightly easier than average. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03k Newton's experimental law: direct impact |
\begin{enumerate}
\item Particle $P$ has mass $3 m$ and particle $Q$ has mass $k m$. The particles are moving towards each other on the same straight line on a smooth horizontal surface.\\
The particles collide directly.\\
Immediately before the collision, the speed of $P$ is $2 u$ and the speed of $Q$ is $3 u$. Immediately after the collision, the speed of $P$ is $u$ and the speed of $Q$ is $v$.
\end{enumerate}
The direction of motion of $P$ is unchanged by the collision.\\
(a) Show that $v = \frac { ( 3 - 3 k ) } { k } u$\\
(b) Find, in terms of $m$ and $u$, the magnitude of the impulse received by $Q$ in the collision.
The coefficient of restitution between $P$ and $Q$ is $e$.\\
Given that $v \neq u$\\
(c) find the range of possible values of $k$.
\hfill \mbox{\textit{Edexcel M2 2023 Q7 [10]}}