| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2002 |
| Session | January |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Collision with unchanged direction |
| Difficulty | Standard +0.3 This is a standard M2 collision problem requiring conservation of momentum and Newton's restitution law. Part (a) is routine algebraic manipulation with two equations, part (b) requires the physical constraint that P continues forward (0 < e < 1), part (c) is straightforward KE calculation, and part (d) is trivial recall. The question is slightly easier than average because it's a well-practiced collision setup with clear guidance through each step. |
| Spec | 6.03k Newton's experimental law: direct impact6.03l Newton's law: oblique impacts |
| Answer | Marks | Guidance |
|---|---|---|
| - Solving to \(y = \frac{1}{2}(1+e)u\) (cso) | B1, M1, A1 | M1, B1 |
| Answer | Marks | Guidance |
|---|---|---|
| - \(e < \frac{1}{2}\) (ignore \(e \geq 0\)) | M1, B1 | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| - Final K.E. \(= \frac{1}{2}m(\frac{4}{5}u)^2 + \frac{1}{2}2m(\frac{2}{5}u)^2 = \frac{22}{100}mu^2\) | M1, B1 | M1, B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working: Heat, sound, (work done by) internal forces | G1 | 1 |
## (a)
**Answer/Working:**
- L/M: $mu = mx + 2my$
- N/EL: $x - y = -eu$
- Solving to $y = \frac{1}{2}(1+e)u$ (cso) | B1, M1, A1 | M1, B1 | 5
## (b)
**Answer/Working:**
- Obtaining $x = \frac{1}{2}(1-2e)u$
- Allow angular
- Direction unchanged implies $x > 0$
- $e < \frac{1}{2}$ (ignore $e \geq 0$) | M1, B1 | M1 | B1 | A1 | 4
## (c)
**Answer/Working:**
- $y = \frac{2}{5}u$, $x = \frac{1}{5}u$
- Final K.E. $= \frac{1}{2}m(\frac{4}{5}u)^2 + \frac{1}{2}2m(\frac{2}{5}u)^2 = \frac{22}{100}mu^2$ | M1, B1 | M1, B1 | 4
## (d)
**Answer/Working:** Heat, sound, (work done by) internal forces | G1 | 1
---A smooth sphere $P$ of mass $m$ is moving in a straight line with speed $u$ on a smooth horizontal table. Another smooth sphere $Q$ of mass $2m$ is at rest on the table. The sphere $P$ collides directly with $Q$. After the collision the direction of motion of $P$ is unchanged. The spheres have the same radii and the coefficient of restitution between $P$ and $Q$ is $e$. By modelling the spheres as particles,
\begin{enumerate}[label=(\alph*)]
\item show that the speed of $Q$ immediately after the collision is $\frac{1}{3}(1 + e)u$,
[5]
\item find the range of possible values of $e$.
[4]
\end{enumerate}
Given that $e = \frac{1}{4}$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the loss of kinetic energy in the collision.
[4]
\item Give one possible form of energy into which the lost kinetic energy has been transformed.
[1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2002 Q6 [14]}}