| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2024 |
| Session | January |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Collision followed by wall impact |
| Difficulty | Standard +0.8 This M2 mechanics question requires multiple applications of conservation of momentum and restitution equations across two collision events, with careful consideration of direction reversals and inequality conditions for the second collision. While the individual principles are standard M2 content, the multi-stage reasoning (finding range of e, then energy loss, then conditions on f for second collision) and the need to track directions carefully elevates this above routine exercises. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10b Vectors in 3D: i,j,k notation1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication3.02d Constant acceleration: SUVAT formulae3.02e Two-dimensional constant acceleration: with vectors3.02g Two-dimensional variable acceleration3.02h Motion under gravity: vector form3.02i Projectile motion: constant acceleration model |
\begin{enumerate}
\item Particle $P$ has mass $m$ and particle $Q$ has mass $5 m$.
\end{enumerate}
The particles are moving in the same direction along the same straight line on a smooth horizontal surface.
Particle $P$ collides directly with particle $Q$.\\
Immediately before the collision, the speed of $P$ is $6 u$ and the speed of $Q$ is $u$.\\
Immediately after the collision, the speed of $P$ is $x$ and the speed of $Q$ is $y$.\\
The direction of motion of $P$ is reversed as a result of the collision.\\
The coefficient of restitution between $P$ and $Q$ is $e$.\\
(a) Find the complete range of possible values of $e$.
Given that $e = \frac { 3 } { 5 }$\\
(b) find the total kinetic energy lost in the collision between $P$ and $Q$.
After the collision, $Q$ hits a smooth fixed vertical wall that is perpendicular to the direction of motion of $Q$.
Particle $Q$ rebounds.\\
The coefficient of restitution between $Q$ and the wall is $f$.\\
Given that there is a second collision between $P$ and $Q$,\\
(c) find the complete range of possible values of $f$.
\hfill \mbox{\textit{Edexcel M2 2024 Q7 [14]}}