| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2009 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Given impulse, find velocity or mass |
| Difficulty | Moderate -0.3 This is a straightforward M1 mechanics question requiring direct application of the impulse-momentum theorem to each particle separately. The impulse magnitude is given, eliminating the need to use conservation of momentum or coefficient of restitution. Students simply apply Δp = I with careful attention to signs, making this slightly easier than average for A-level. |
| Spec | 6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03f Impulse-momentum: relation |
| Answer | Marks |
|---|---|
| (a) For \(A\): \(-\frac{7mu}{2} = 2m(v_A - 2u)\) | M1 A1 |
| \(v_A = \frac{u}{4}\) | A1 |
| (3) | |
| (b) For \(B\): \(\frac{7mu}{2} = m(v_B - 3u)\) | M1 A1 |
| \(v_B = \frac{u}{2}\) | A1 |
| OR CLM: \(4mu - 3mu = 2m\frac{u}{4} + mv_B\) | M1 A1 |
| \(v_B = \frac{u}{2}\) | A1 |
| (3) | |
| Total: [6] |
**(a)** For $A$: $-\frac{7mu}{2} = 2m(v_A - 2u)$ | M1 A1 |
$v_A = \frac{u}{4}$ | A1 |
| **(3)** |
**(b)** For $B$: $\frac{7mu}{2} = m(v_B - 3u)$ | M1 A1 |
$v_B = \frac{u}{2}$ | A1 |
**OR CLM:** $4mu - 3mu = 2m\frac{u}{4} + mv_B$ | M1 A1 |
$v_B = \frac{u}{2}$ | A1 |
| **(3)** |
| **Total: [6]** |Two particles $A$ and $B$ are moving on a smooth horizontal plane. The mass of $A$ is $2m$ and the mass of $B$ is $m$. The particles are moving along the same straight line but in opposite directions and they collide directly. Immediately before they collide the speed of $A$ is $2u$ and the speed of $B$ is $3u$. The magnitude of the impulse received by each particle in the collision is $\frac{7mu}{2}$.
Find
\begin{enumerate}[label=(\alph*)]
\item the speed of $A$ immediately after the collision, [3]
\item the speed of $B$ immediately after the collision. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2009 Q3 [6]}}