| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2015 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Collision with two possible outcomes |
| Difficulty | Standard +0.3 This is a straightforward M1 collision problem requiring conservation of momentum and impulse calculation. Part (a) involves algebraic manipulation to find k, and part (b) is direct application of impulse = change in momentum. The 'show that' structure and clear setup make this slightly easier than average, though it requires careful sign conventions. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance Notes |
| \(2mu - km3u = -2m\frac{1}{2}u + kmv\) | M1 | Conservation of momentum. Must have all four terms but condone sign errors and consistent omission of \(m\) or \(g\) included in all terms |
| \((3u = kv + 3ku)\) | A2,1,0 | \(-1\) for each error. All correct A1A1, one error A1A0, two or more errors A0A0 |
| \(v=(1-k)\dfrac{3u}{k}\) or \(k=\dfrac{3u}{v+3u}\) | A1 | Correct expression for \(v\) or for \(kv\) or for \(k\) |
| \(v > 0 \Rightarrow\) | M1 | Correct inequality for their \(v\) |
| \(\Rightarrow k < 1\) | A1 | Reach given answer correctly |
| Total: (6) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance Notes |
| \(I = 2m(\frac{1}{2}u - {-u})\) | M1 | Impulse \(=\) change in momentum for \(A\) or for \(B\). Condone sign errors |
| A1 | Correct unsimplified expression in terms of \(m\) and \(u\). Allow \(+/-\) | |
| \(= 3mu\) | A1 | Correct answer only |
| Total: (3) |
# Question 2(a):
| Answer/Working | Marks | Guidance Notes |
|---|---|---|
| $2mu - km3u = -2m\frac{1}{2}u + kmv$ | M1 | Conservation of momentum. Must have all four terms but condone sign errors and consistent omission of $m$ or $g$ included in all terms |
| $(3u = kv + 3ku)$ | A2,1,0 | $-1$ for each error. All correct A1A1, one error A1A0, two or more errors A0A0 |
| $v=(1-k)\dfrac{3u}{k}$ or $k=\dfrac{3u}{v+3u}$ | A1 | Correct expression for $v$ or for $kv$ or for $k$ |
| $v > 0 \Rightarrow$ | M1 | Correct inequality for their $v$ |
| $\Rightarrow k < 1$ | A1 | Reach **given answer** correctly |
| **Total: (6)** | | |
---
# Question 2(b):
| Answer/Working | Marks | Guidance Notes |
|---|---|---|
| $I = 2m(\frac{1}{2}u - {-u})$ | M1 | Impulse $=$ change in momentum for $A$ or for $B$. Condone sign errors |
| | A1 | Correct unsimplified expression in terms of $m$ and $u$. Allow $+/-$ |
| $= 3mu$ | A1 | Correct answer only |
| **Total: (3)** | | |
---2. Particle $A$ of mass $2 m$ and particle $B$ of mass $k m$, where $k$ is a positive constant, 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 $A$ is $u$ and the speed of $B$ is $3 u$. The direction of motion of each particle is reversed by the collision. Immediately after the collision the speed of $A$ is $\frac { 1 } { 2 } u$.
\begin{enumerate}[label=(\alph*)]
\item Show that $k < 1$
\item Find, in terms of $m$ and $u$, the magnitude of the impulse exerted on $B$ by $A$ in the collision.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2015 Q2 [9]}}