| Exam Board | Edexcel |
|---|---|
| Module | FM1 (Further Mechanics 1) |
| Year | 2022 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Direct collision with given impulse |
| Difficulty | Standard +0.3 This is a standard Further Mechanics collision problem requiring impulse-momentum relationships and conservation of momentum. While it involves algebraic manipulation and solving a quadratic, the techniques are routine for FM1 students with no novel insight required. The two-part structure and need to consider direction makes it slightly above average difficulty. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation6.03i Coefficient of restitution: e6.03k Newton's experimental law: direct impact |
\begin{enumerate}
\item A particle $A$ of mass $3 m$ and a particle $B$ of mass $m$ are moving along the same straight line on a smooth horizontal surface. The particles are moving in opposite directions towards each other when they collide directly.
\end{enumerate}
Immediately before the collision, the speed of $A$ is $k u$ and the speed of $B$ is $u$. Immediately after the collision, the speed of $A$ is $v$ and the speed of $B$ is $2 v$.
The magnitude of the impulse received by $B$ in the collision is $\frac { 3 } { 2 } m u$.\\
(a) Find $v$ in terms of $u$ only.\\
(b) Find the two possible values of $k$.
\hfill \mbox{\textit{Edexcel FM1 2022 Q1 [8]}}