| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2022 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find impulse magnitude |
| Difficulty | Moderate -0.8 This is a straightforward M1 impulse question requiring only the impulse-momentum equation (Impulse = change in momentum) applied once, with clear given values. It involves basic algebraic manipulation and sign conventions but no problem-solving insight or multi-step reasoning beyond choosing the correct direction convention. |
| Spec | 6.03e Impulse: by a force6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(-4mu = 3m(v-2u)\) or \(4mu = 3m(-v+2u)\) or \(-4mu = 3m(-v-2u)\) or \(4mu = 3m(v+2u)\) | M1A1 | Impulse-momentum equation, dimensionally correct, correct no. of terms; condone sign errors but must be attempting a difference of momenta. Allow if they use \(m\) instead of \(3m\) |
| Speed is \(\frac{2}{3}u\), \(0.67u\) or better | A1 | cao (must be positive) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Same as its original direction / direction is unchanged / 'same direction' / 'it is the same' / 'opposite to \(P\)'s original direction' / 'towards \(P\)' | DB1 | Dependent on obtaining either \(\frac{2}{3}u\) or \(-\frac{2}{3}u\) for \(v\) in (a). Allow 'east' or 'to the left' etc. 'motion of \(Q\) is unchanged' is B0 |
# Question 1:
## Part 1(a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $-4mu = 3m(v-2u)$ **or** $4mu = 3m(-v+2u)$ **or** $-4mu = 3m(-v-2u)$ **or** $4mu = 3m(v+2u)$ | M1A1 | Impulse-momentum equation, dimensionally correct, correct no. of terms; condone sign errors but must be attempting a difference of momenta. Allow if they use $m$ instead of $3m$ |
| Speed is $\frac{2}{3}u$, $0.67u$ or better | A1 | cao (must be positive) |
## Part 1(b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| Same as its original direction / direction is unchanged / 'same direction' / 'it is the same' / 'opposite to $P$'s original direction' / 'towards $P$' | DB1 | Dependent on obtaining either $\frac{2}{3}u$ or $-\frac{2}{3}u$ for $v$ in (a). Allow 'east' or 'to the left' etc. 'motion of $Q$ is unchanged' is B0 |
---\begin{enumerate}
\item Two particles, $P$ and $Q$, are moving towards each other in opposite directions along the same straight line when they collide directly. Immediately before the collision the speed of $Q$ is $2 u$. The mass of $Q$ is $3 m$ and the magnitude of the impulse exerted by $P$ on $Q$ in the collision is $4 m u$.
\end{enumerate}
Find\\
(a) the speed of $Q$ immediately after the collision,\\
(b) the direction of motion of $Q$ immediately after the collision.
\hfill \mbox{\textit{Edexcel M1 2022 Q1 [4]}}