| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2021 |
| Session | January |
| 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 standard M1 impulse-momentum question requiring straightforward application of impulse = change in momentum and conservation of momentum. The two-part structure and given impulse magnitude make it slightly easier than average, as students follow a clear mechanical procedure without needing problem-solving insight. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| For \(P\): \(-5mu = 2m(v - 3u)\) | M1A1 | Dimensionally correct impulse-momentum equation (M0 if \(g\) included), must be difference of momenta, equation in \(v\) only |
| \(v = \frac{1}{2}u\) | A1 | Must be positive |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| For \(Q\): \(5mu = m(w - (-2u))\) | M1A1 | Dimensionally correct impulse-momentum equation (M0 if \(g\) included), must be difference of momenta, equation in \(w\) only |
| \(w = 3u\) | A1 | Must be positive |
| OR CLM: \(2m \times 3u - m \times 2u = 2m \times \frac{1}{2}u + mw\) | M1A1 | Dimensionally correct CLM (allow consistent extra \(g\)'s or cancelled \(m\)'s), equation in \(w\) only |
| \(w = 3u\) | A1 | Mark parts (a) and (b) together if necessary |
# Question 2:
## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| For $P$: $-5mu = 2m(v - 3u)$ | M1A1 | Dimensionally correct impulse-momentum equation (M0 if $g$ included), must be difference of momenta, equation in $v$ only |
| $v = \frac{1}{2}u$ | A1 | Must be positive |
## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| For $Q$: $5mu = m(w - (-2u))$ | M1A1 | Dimensionally correct impulse-momentum equation (M0 if $g$ included), must be difference of momenta, equation in $w$ only |
| $w = 3u$ | A1 | Must be positive |
| **OR** CLM: $2m \times 3u - m \times 2u = 2m \times \frac{1}{2}u + mw$ | M1A1 | Dimensionally correct CLM (allow consistent extra $g$'s or cancelled $m$'s), equation in $w$ only |
| $w = 3u$ | A1 | Mark parts (a) and (b) together if necessary |
---2. Two particles, $P$ and $Q$, have masses $2 m$ and $m$ respectively. The particles are moving towards each other in opposite directions along the same straight line on a smooth horizontal plane. The particles collide directly.
Immediately before the collision, the speed of $P$ is $3 u$ and the speed of $Q$ is $2 u$.
The magnitude of the impulse exerted on $Q$ by $P$ in the collision is 5mu.
Find
\begin{enumerate}[label=(\alph*)]
\item the speed of $P$ immediately after the collision,
\item the speed of $Q$ immediately after the collision.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2021 Q2 [6]}}