| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2009 |
| Session | January |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Collision with two possible outcomes |
| Difficulty | Moderate -0.3 This is a straightforward M1 momentum conservation problem with clearly defined before/after states. Part (a) requires direct application of conservation of momentum, part (b) involves sign interpretation, and part (c) is a standard impulse calculation. While multi-part, each step follows routine mechanics procedures without requiring problem-solving insight or novel approaches. |
| Spec | 6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \(2u \rightarrow \quad \leftarrow 4u \qquad km(2u) - 4mu = -kmu + mv\) | M1 A1 | |
| \(u(3k - 4) = v\) | A1 | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \(k > 2 \Rightarrow v > 0 \Rightarrow\) direction of motion reversed | M1A1A1 cso | (3) |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| For \(B\): \(m(u(3k-4)) - (-4u)\) | M1 A1 f.t. | |
| \(= 7mu\) | A1 | (3) [9] |
## Question 3:
### Part (a):
| Working/Answer | Marks | Guidance |
|---|---|---|
| $2u \rightarrow \quad \leftarrow 4u \qquad km(2u) - 4mu = -kmu + mv$ | M1 A1 | |
| $u(3k - 4) = v$ | A1 | **(3)** |
### Part (b):
| Working/Answer | Marks | Guidance |
|---|---|---|
| $k > 2 \Rightarrow v > 0 \Rightarrow$ direction of motion reversed | M1A1A1 cso | **(3)** |
### Part (c):
| Working/Answer | Marks | Guidance |
|---|---|---|
| For $B$: $m(u(3k-4)) - (-4u)$ | M1 A1 f.t. | |
| $= 7mu$ | A1 | **(3) [9]** |
---3. Two particles $A$ and $B$ are moving on a smooth horizontal plane. The mass of $A$ is $k m$, where $2 < k < 3$, and the mass of $B$ is $m$. The particles are moving along the same straight line, but in opposite directions, and they collide directly. Immediately before they collide the speed of $A$ is $2 u$ and the speed of $B$ is $4 u$. As a result of the collision the speed of $A$ is halved and its direction of motion is reversed.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $k$ and $u$, the speed of $B$ immediately after the collision.
\item State whether the direction of motion of $B$ changes as a result of the collision, explaining your answer.
Given that $k = \frac { 7 } { 3 }$,
\item find, in terms of $m$ and $u$, the magnitude of the impulse that $A$ exerts on $B$ in the collision.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2009 Q3 [9]}}