| Exam Board | Edexcel |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2020 |
| Session | June |
| Marks | 10 |
| 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 the restitution formula, followed by a straightforward application of restitution at a wall. The multi-step nature and algebraic manipulation elevate it slightly above average, but it follows well-established procedures without requiring novel insight. |
| Spec | 6.03b Conservation of momentum: 1D two particles6.03k Newton's experimental law: direct impact |
| Answer | Marks | Guidance |
|---|---|---|
| KE gain = final KE – initial KE | M1 | KE equation for B. Allow for change in KE |
| \(\frac{48}{25}mu^2 = \frac{1}{2}mw^2 - \frac{1}{2}mu^2\) | A1 | Correct unsimplified equation to find w |
| \(w^2 = \frac{121}{25}u^2\), \(w = \frac{11}{5}u\) | ||
| CLM: \(3m \times 2u + mu = 3mv + mw\) | M1 | All terms required. Condone sign errors |
| \(7mu = 3mv + \frac{11}{5}mu\) \(v = \frac{8}{5}u\) | A1 | Correct unsimplified equation in v and w or their w |
| Impact law: | M1 | Used correctly |
| \(w - v = e(2u - u)\) | A1 | Correct unsimplified equation in v and w or their v and w |
| Solve for e | DM1 | Dependent on the preceding M marks |
| \(\frac{3}{5}u = eu\), \(e = \frac{3}{5}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Impact law: \(fw = v\) | M1 | Condone sign error |
| \(f = \frac{8}{11}\) | A1 | 0.73 or better. Final answer must be positive |
## 7a
KE gain = final KE – initial KE | M1 | KE equation for B. Allow for change in KE
$\frac{48}{25}mu^2 = \frac{1}{2}mw^2 - \frac{1}{2}mu^2$ | A1 | Correct unsimplified equation to find w
$w^2 = \frac{121}{25}u^2$, $w = \frac{11}{5}u$ | |
CLM: $3m \times 2u + mu = 3mv + mw$ | M1 | All terms required. Condone sign errors
$7mu = 3mv + \frac{11}{5}mu$ $v = \frac{8}{5}u$ | A1 | Correct unsimplified equation in v and w or their w
Impact law: | M1 | Used correctly
$w - v = e(2u - u)$ | A1 | Correct unsimplified equation in v and w or their v and w
Solve for e | DM1 | Dependent on the preceding M marks
$\frac{3}{5}u = eu$, $e = \frac{3}{5}$ | A1 |
(8)
## 7b
Impact law: $fw = v$ | M1 | Condone sign error
$f = \frac{8}{11}$ | A1 | 0.73 or better. Final answer must be positive
(2)
[10]
---7. Particle $A$ of mass $3 m$ is moving in a straight line with speed $2 u$ on a smooth horizontal surface. Particle $A$ collides directly with particle $B$ of mass $m$, which is moving along the same straight line and in the same direction as $A$.
Immediately before the collision, the speed of $B$ is $u$.\\
As a result of the collision, the direction of motion of $B$ is unchanged and the kinetic energy gained by $B$ is $\frac { 48 } { 25 } m u ^ { 2 }$
\begin{enumerate}[label=(\alph*)]
\item Find the coefficient of restitution between $A$ and $B$.\\
(8)
After the collision, $B$ hits a smooth fixed vertical wall that is perpendicular to the direction of motion of $B$. The coefficient of restitution between $B$ and the wall is $f$.
Given that the speed of $B$ immediately after first hitting the wall is equal to the speed of $A$ immediately after its first collision with $B$,
\item find the value of $f$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M2 2020 Q7 [10]}}