| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2017 |
| Session | June |
| Marks | 7 |
| 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 conservation problem requiring standard application of conservation of momentum to find final velocity, then calculating impulse using change in momentum. All steps are routine with no conceptual challenges or novel problem-solving required—easier than the typical A-level question which would involve more steps or less obvious setup. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \(8mu - 9mu = -2mV + 3mu\) | M1 A1 | M1 for CLM with correct no. of terms, dimensionally correct; A1 for correct equation |
| \(V = 2u\) | A1 (3) | Must be positive since speed is required |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| (Direction of \(P\) has been) reversed | B1 (1) | Only available if correct velocity obtained in (a); B0 for 'changed', 'direction has changed', 'yes' |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| For \(Q\): \(I = 3m(u - -3u) = 12mu\) | M1 A1, A1 (3) | M1 for Impulse = change in momentum of \(Q\) (must have \(3m\) in both terms); A1 for \(3m(u--3u)\); A1 for \(12mu\) (must be positive) |
| OR For \(P\): \(I = 2m(2u - -4u) = 12mu\) | M1 A1, A1 (3) | M1 for Impulse = change in momentum of \(P\) (must have \(2m\) in both terms); A1 for \(2m(2u--4u)\); A1 for \(12mu\) |
# Question 2:
## Part (a):
| Working/Answer | Marks | Guidance |
|---|---|---|
| $8mu - 9mu = -2mV + 3mu$ | M1 A1 | M1 for CLM with correct no. of terms, dimensionally correct; A1 for correct equation |
| $V = 2u$ | A1 (3) | Must be positive since speed is required |
## Part (b):
| Working/Answer | Marks | Guidance |
|---|---|---|
| (Direction of $P$ has been) reversed | B1 (1) | Only available if correct velocity obtained in (a); B0 for 'changed', 'direction has changed', 'yes' |
## Part (c):
| Working/Answer | Marks | Guidance |
|---|---|---|
| For $Q$: $I = 3m(u - -3u) = 12mu$ | M1 A1, A1 (3) | M1 for Impulse = change in momentum of $Q$ (must have $3m$ in both terms); A1 for $3m(u--3u)$; A1 for $12mu$ (must be positive) |
| OR For $P$: $I = 2m(2u - -4u) = 12mu$ | M1 A1, A1 (3) | M1 for Impulse = change in momentum of $P$ (must have $2m$ in both terms); A1 for $2m(2u--4u)$; A1 for $12mu$ |
---2. Two particles, $P$ and $Q$, have masses $2 m$ and $3 m$ respectively. They are moving towards each other in opposite directions on a smooth horizontal plane when they collide directly. Immediately before they collide the speed of $P$ is $4 u$ and the speed of $Q$ is $3 u$. As a result of the collision, $Q$ has its direction of motion reversed and is moving with speed $u$.
\begin{enumerate}[label=(\alph*)]
\item Find the speed of $P$ immediately after the collision.
\item State whether or not the direction of motion of $P$ has been reversed by the collision.
\item Find the magnitude of the impulse exerted on $P$ by $Q$ in the collision.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2017 Q2 [7]}}