| Exam Board | OCR |
|---|---|
| Module | Further Mechanics AS (Further Mechanics AS) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions 1 |
| Type | Particle-wall perpendicular collision |
| Difficulty | Moderate -0.8 This is a straightforward application of standard mechanics formulas: coefficient of restitution (e = separation speed / approach speed) and impulse (change in momentum). All three parts require direct substitution into well-known formulas with no problem-solving insight or multi-step reasoning needed. Easier than average A-level mechanics. |
| Spec | 6.03e Impulse: by a force6.03i Coefficient of restitution: e6.03j Perfectly elastic/inelastic: collisions |
| Answer | Marks | Guidance |
|---|---|---|
| \(e = \frac{0 - (-2.8)}{4 - 0} = 0.7\) | B1 [1] | oe e.g. \(\frac{2.8}{4} = 0.7\); B0 for \(-0.7\) |
| Answer | Marks | Guidance |
|---|---|---|
| Impulse on \(P = \Delta mv = \pm(2.5 \times 4 - 2.5 \times (-2.8))\) | M1 | Finding change in \(P\)'s momentum; allow 1 slip but not wrong sign inside brackets |
| \(= 17\) (Ns) | A1 | Do not allow \(-17\) for magnitude |
| in the direction of \(P\)'s final travel oe | B1 [3] | Could be shown on diagram (may be seen in part (a)); away from the wall; ignore "towards P" |
| Answer | Marks | Guidance |
|---|---|---|
| \(17\) (Ns) | B1FT | FT their magnitude of impulse from (b); positive value only, ignore units |
| in the opposite direction (to their previous direction) oe | B1 [2] | Direction of \(P\)'s initial travel; if "left" mentioned in part (a), then accept "right" as opposite direction; NB if \(I = 0\), then award B0B0 |
# Question 1:
## Part (a)
$e = \frac{0 - (-2.8)}{4 - 0} = 0.7$ | **B1** [1] | oe e.g. $\frac{2.8}{4} = 0.7$; B0 for $-0.7$
## Part (b)
Impulse on $P = \Delta mv = \pm(2.5 \times 4 - 2.5 \times (-2.8))$ | **M1** | Finding change in $P$'s momentum; allow 1 slip but not wrong sign inside brackets
$= 17$ (Ns) | **A1** | Do not allow $-17$ for magnitude
in the direction of $P$'s final travel oe | **B1** [3] | Could be shown on diagram (may be seen in part (a)); away from the wall; ignore "towards P"
## Part (c)
$17$ (Ns) | **B1FT** | FT their magnitude of impulse from **(b)**; positive value only, ignore units
in the opposite direction (to their previous direction) oe | **B1** [2] | Direction of $P$'s initial travel; if "left" mentioned in part (a), then accept "right" as opposite direction; NB if $I = 0$, then award B0B0
---1 A particle $P$ of mass 2.5 kg is moving with a constant speed of $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in a straight line on a smooth horizontal plane when it collides directly with a fixed vertical wall.
After the collision $P$ moves away from the wall with a speed of $2.8 \mathrm {~ms} ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Calculate the coefficient of restitution between $P$ and the wall.
\item Find the magnitude and state the direction of the impulse exerted on $P$ by the wall.
\item State the magnitude and direction of the impulse exerted on the wall by $P$.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Mechanics AS 2024 Q1 [6]}}