| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2018 |
| Session | Specimen |
| Marks | 6 |
| 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 M1 momentum conservation problem requiring application of standard formulas. Part (a) uses conservation of momentum with clearly defined before/after velocities to find k (a simple algebraic equation). Part (b) applies the impulse-momentum theorem directly. While it requires careful sign handling and algebraic manipulation, it involves no novel insight—just methodical application of core mechanics principles that are extensively practiced in M1. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(mu - 2kmu = -\frac{1}{2}mu + kmu\) or \(m\left(\frac{1}{2}u + u\right) = -km(-u - 2u)\) | M1 | Use of CLM or equal and opposite impulses. Need all 4 terms dimensionally correct. Masses and speeds must be paired correctly. Condone sign errors. Condone factor of \(g\) throughout. |
| Unsimplified equation with at most one error | A1 | |
| Correct unsimplified equation | A1 | |
| \(k = \frac{1}{2}\) | A1 | From correct working only |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| For \(P\): \(I = \pm m(\frac{1}{2}u \pm -u)\); For \(Q\): \(I = \pm km(u \pm -2u)\) | M1 | Impulse on \(P\) or impulse on \(Q\). Mass must be used with correct speeds. e.g. \(km \times \frac{1}{2}u\) is M0. If working on \(Q\), allow equation using their \(k\). Terms must be dimensionally correct. Use of \(g\) is M0. |
| \(\frac{3mu}{2}\) | A1 | Only. From correct working only. |
## Question 2:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $mu - 2kmu = -\frac{1}{2}mu + kmu$ or $m\left(\frac{1}{2}u + u\right) = -km(-u - 2u)$ | M1 | Use of CLM or equal and opposite impulses. Need all 4 terms dimensionally correct. Masses and speeds must be paired correctly. Condone sign errors. Condone factor of $g$ throughout. |
| Unsimplified equation with at most one error | A1 | |
| Correct unsimplified equation | A1 | |
| $k = \frac{1}{2}$ | A1 | From correct working only |
### Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| For $P$: $I = \pm m(\frac{1}{2}u \pm -u)$; For $Q$: $I = \pm km(u \pm -2u)$ | M1 | Impulse on $P$ or impulse on $Q$. Mass must be used with correct speeds. e.g. $km \times \frac{1}{2}u$ is M0. If working on $Q$, allow equation using their $k$. Terms must be dimensionally correct. Use of $g$ is M0. |
| $\frac{3mu}{2}$ | A1 | Only. From correct working only. |
---2. Two particles $P$ and $Q$ are moving in opposite directions along the same horizontal straight line. Particle $P$ has mass $m$ and particle $Q$ has mass $k m$. The particles collide directly. Immediately before the collision, the speed of $P$ is $u$ and the speed of $Q$ is $2 u$. 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 $u$ only, the magnitude of the impulse exerted on $Q$ by $P$ in the collision.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2018 Q2 [6]}}