| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find impulse magnitude |
| Difficulty | Standard +0.3 This is a standard M1 momentum conservation problem with straightforward application of impulse-momentum theorem. Part (a) is a 'show that' using conservation of momentum with clear setup. Parts (b) and (c) involve direct substitution into standard formulas (impulse = change in momentum, friction deceleration). Slightly above average due to multi-part structure and sign conventions, but requires no novel insight—pure textbook application. |
| Spec | 3.03r Friction: concept and vector form6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(3M(3) - 2M(5) = 3Mv + 2Mv\) | M1 A1 | |
| \(M = Mv\) i.e. \(v = 1 \text{ ms}^{-1}\) | M1 A1 | |
| (b) \( | 3M(1 - 3) | = 24\) |
| \(M = 2\) | A1 | |
| (c) \(R = 6g\) \(F = ma\) | M2 | |
| but \(F = \mu R\) so \(a = \frac{-\mu R}{m} = \frac{-0.1 \times 6g}{6} = -0.98 \text{ ms}^{-2}\) | M1 A1 | |
| \(u = 1, v = 0, a = -0.98\); use \(v = u + at\) | M1 | |
| \(0 = 1 - 0.98t\) i.e. \(t = 1.02\) seconds | M1 A1 | (14) |
(a) $3M(3) - 2M(5) = 3Mv + 2Mv$ | M1 A1 |
$M = Mv$ i.e. $v = 1 \text{ ms}^{-1}$ | M1 A1 |
(b) $|3M(1 - 3)| = 24$ | M1 A1 |
$M = 2$ | A1 |
(c) $R = 6g$ $F = ma$ | M2 |
but $F = \mu R$ so $a = \frac{-\mu R}{m} = \frac{-0.1 \times 6g}{6} = -0.98 \text{ ms}^{-2}$ | M1 A1 |
$u = 1, v = 0, a = -0.98$; use $v = u + at$ | M1 |
$0 = 1 - 0.98t$ i.e. $t = 1.02$ seconds | M1 A1 | (14) |
**Total: (75)**7. Two particles $A$ and $B$, of mass $3 M \mathrm {~kg}$ and $2 M \mathrm {~kg}$ respectively, are moving towards each other on a rough horizontal track. Just before they collide, $A$ has speed $3 \mathrm {~ms} ^ { - 1 }$ and $B$ has speed $5 \mathrm {~ms} ^ { - 1 }$. Immediately after the impact, the direction of motion of both particles has been reversed and they are both travelling at the same speed, $v$.
\begin{enumerate}[label=(\alph*)]
\item Show that $v = 1 \mathrm {~ms} ^ { - 1 }$.
The magnitude of the impulse exerted on $A$ during the collision is 24 Ns.
\item Find the value of $M$.
Given that the coefficient of friction between $A$ and the track is 0.1 ,
\item find the time taken from the moment of impact until $A$ comes to rest.
END
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q7 [14]}}