| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2022 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find impulse magnitude |
| Difficulty | Moderate -0.3 This is a straightforward momentum conservation problem requiring standard application of impulse-momentum theorem. Part (a) uses conservation of momentum with clearly defined before/after states, and part (b) is direct calculation of impulse from change in momentum. The setup is clear with no geometric complexity or novel insight required, making it slightly easier than average. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| CLM: \(km \times 3u - mu = -km \times \frac{3}{2}u + m \times \frac{1}{2}u\) | M1 A1 A1 | M1: correct no. of terms, dimensionally correct, condone sign errors; A1 correct equation with one error; A1 correct equation |
| \(k = \frac{1}{3}\) | A1 | Allow 0.33 or better |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(I = m\left(\frac{1}{2}u - {-u}\right)\) OR \(I = \frac{1}{3}m\left(\frac{3}{2}u - {-3u}\right)\) | M1 A1 | Must have masses and speeds paired correctly; must attempt difference of momenta; Allow M1 if \(k\) not substituted; M0 if \(g\) included |
| \(I = \frac{3}{2}mu\), must be positive | A1 | cao; allow change of negative expression to positive |
## Question 2:
**Part (a):**
| Answer/Working | Marks | Guidance |
|---|---|---|
| CLM: $km \times 3u - mu = -km \times \frac{3}{2}u + m \times \frac{1}{2}u$ | M1 A1 A1 | M1: correct no. of terms, dimensionally correct, condone sign errors; A1 correct equation with one error; A1 correct equation |
| $k = \frac{1}{3}$ | A1 | Allow 0.33 or better |
**Part (b):**
| Answer/Working | Marks | Guidance |
|---|---|---|
| $I = m\left(\frac{1}{2}u - {-u}\right)$ **OR** $I = \frac{1}{3}m\left(\frac{3}{2}u - {-3u}\right)$ | M1 A1 | Must have masses and speeds paired correctly; must attempt difference of momenta; Allow M1 if $k$ not substituted; M0 if $g$ included |
| $I = \frac{3}{2}mu$, must be positive | A1 | cao; allow change of negative expression to positive |
---2. A particle $P$ has mass $k m$ and a particle $Q$ has mass $m$. The particles are moving towards each other in opposite directions along the same straight line when they collide directly.
Immediately before the collision, $P$ has speed $3 u$ and $Q$ has speed $u$.\\
As a result of the collision, the direction of motion of each particle is reversed and the speed of each particle is halved.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $k$.
\item Find, in terms of $m$ and $u$, the magnitude of the impulse exerted on $Q$ in the collision.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2022 Q2 [7]}}