| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2024 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Collision followed by wall impact |
| Difficulty | Standard +0.3 This is a standard M2 collision problem requiring conservation of momentum and Newton's restitution law, followed by analysis of a second collision condition. While it involves multiple stages (particle collision, wall impact, condition for second collision), each step uses routine mechanics formulas with straightforward algebraic manipulation. The inequality work in part (b) is typical for this topic level. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03i Coefficient of restitution: e6.03j Perfectly elastic/inelastic: collisions6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance Notes |
| Use of CLM (or equal and opposite impulses) | M1 | Correct no. of terms, dim correct, condone sign errors |
| \(mu = -mv + 2mw\) | A1 | Or equivalent |
| Use of NEL | M1 | Correct way round, condone sign errors |
| \(eu = v + w\) | A1 | Or equivalent |
| Solve for \(v\) | DM1 | Dependent on both preceding M marks |
| \(v = \frac{u(2e-1)}{3}\) | A1 | Or equivalent |
| Total: 6 marks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance Notes |
| NEL at the wall: \(x = \frac{1}{3}w\) | B1 | Allow \(+/-\): they might be working with velocities |
| \(w = \frac{u(e+1)}{3}\) | B1 | Or equivalent expression for \(w\) |
| \(\frac{1}{3} \times \frac{u(e+1)}{3} > \frac{u(2e-1)}{3}\) | M1 | Use of their \(x >\) their \(v\) |
| \(e < \frac{4}{5}\) | A1 | cao |
| \(\frac{1}{2} < e < \frac{4}{5}\) | A1 | cao |
| Total: 5 marks |
## Question 5(a):
| Answer/Working | Mark | Guidance Notes |
|---|---|---|
| Use of CLM (or equal and opposite impulses) | M1 | Correct no. of terms, dim correct, condone sign errors |
| $mu = -mv + 2mw$ | A1 | Or equivalent |
| Use of NEL | M1 | Correct way round, condone sign errors |
| $eu = v + w$ | A1 | Or equivalent |
| Solve for $v$ | DM1 | Dependent on both preceding M marks |
| $v = \frac{u(2e-1)}{3}$ | A1 | Or equivalent |
| **Total: 6 marks** | | |
## Question 5(b):
| Answer/Working | Mark | Guidance Notes |
|---|---|---|
| NEL at the wall: $x = \frac{1}{3}w$ | B1 | Allow $+/-$: they might be working with velocities |
| $w = \frac{u(e+1)}{3}$ | B1 | Or equivalent expression for $w$ |
| $\frac{1}{3} \times \frac{u(e+1)}{3} > \frac{u(2e-1)}{3}$ | M1 | Use of their $x >$ their $v$ |
| $e < \frac{4}{5}$ | A1 | cao |
| $\frac{1}{2} < e < \frac{4}{5}$ | A1 | cao |
| **Total: 5 marks** | | |
---\begin{enumerate}
\item A particle $P$ of mass $m$ and a particle $Q$ of mass $2 m$ are at rest on a smooth horizontal plane.
\end{enumerate}
Particle $P$ is projected with speed $u$ along the plane towards $Q$ and the particles collide. The coefficient of restitution between the particles is $e$.
As a result of the collision, the direction of motion of $P$ is reversed.\\
(a) Find, in terms of $u$ and $e$, the speed of $P$ after the collision.
After the collision, $Q$ goes on to hit a vertical wall which is fixed at right angles to the direction of motion of $Q$. The coefficient of restitution between $Q$ and the wall is $\frac { 1 } { 3 }$ Given that there is a second collision between $P$ and $Q$\\
(b) find the full range of possible values of $e$.
\hfill \mbox{\textit{Edexcel M2 2024 Q5 [11]}}