| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | June |
| Marks | 6 |
| 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 momentum question requiring direct application of impulse formula (change in momentum) and conservation of momentum. Both parts involve standard calculations with clearly given values and no conceptual challenges or problem-solving insight needed—easier than average A-level. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks |
|---|---|
| For \(P\): \(-I = 3(1-4)\) | M1 A1 |
| \(I = 9\) Ns | A1 |
| (3) |
| Answer | Marks |
|---|---|
| For \(Q\): \(9 = m(1.5 - -3)\) | M1 A1 |
| \(m = 2\) | A1 |
| Answer | Marks |
|---|---|
| \(12 - 3m = 3 + 1.5m\) | M1 A1 |
| \(m = 2\) | A1 |
| (3) | |
| [6] |
## Part (a)
For $P$: $-I = 3(1-4)$ | M1 A1
$I = 9$ Ns | A1
| (3)
## Part (b)
For $Q$: $9 = m(1.5 - -3)$ | M1 A1
$m = 2$ | A1
**OR**
$12 - 3m = 3 + 1.5m$ | M1 A1
$m = 2$ | A1
| (3)
| [6]
**Notes for Question 1:**
- M1 for attempt at Impulse = difference in momenta for particle $P$ (must be considering one particle i.e. have same mass in both terms) (M0 if $g$ is included or if mass omitted)
- First A1 for $\pm 3(1-4)$
- Second A1 for 9 (Must be positive). Allow change of sign at end to obtain magnitude.
- N.B. For M1 they may use CLM to find a value for $m$ first and then use it when considering the change in momentum of $Q$ to find the impulse.
**EITHER**
- M1 for attempt at their Impulse from (a) = difference in momenta for particle $Q$ (must be considering one particle) (M0 if $g$ is included or if mass omitted)
- First A1 for $9 = m(1.5 - -3)$ oe
- Second A1 for $m = 2$
**OR**
- M1 for attempt at CLM equation, with correct no. of terms, dimensionally correct. Allow consistent extra $g$'s and sign errors.
- First A1 for a correct equation i.e. $12 - 3m = 3 + 1.5m$ oe
- Second A1 for $m = 2$
---Particle $P$ has mass 3 kg and particle $Q$ has mass $m$ kg. The particles are moving in opposite directions along a smooth horizontal plane when they collide directly. Immediately before the collision, the speed of $P$ is $4 \text{ m s}^{-1}$ and the speed of $Q$ is $3 \text{ m s}^{-1}$. In the collision the direction of motion of $P$ is unchanged and the direction of motion of $Q$ is reversed. Immediately after the collision, the speed of $P$ is $1 \text{ m s}^{-1}$ and the speed of $Q$ is $1.5 \text{ m s}^{-1}$.
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of the impulse exerted on $P$ in the collision. [3]
\item Find the value of $m$. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2013 Q1 [6]}}