| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find impulse magnitude |
| Difficulty | Moderate -0.3 This is a straightforward M1 mechanics question applying conservation of momentum and basic friction calculations. Part (a) uses impulse = change in momentum with given values, part (b) applies Newton's third law or momentum conservation directly, and part (c) uses standard work-energy or SUVAT with friction. All steps are routine applications of standard formulae with no conceptual challenges, making it slightly easier than average. |
| Spec | 3.03v Motion on rough surface: including inclined planes6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) mag. of impulse is same as cannon on shell; impulse \(= \Delta \text{mom} = 3(200 - 0) = 600 \text{ Ns}\) (towards cannon) | B1 M1 A1 | |
| (b) for cannon: \(mv - mu = 600\); \(600v = 600\) so \(v = 1 \text{ ms}^{-1}\) | M1 A1 | |
| (c) \(R = mg\); \(F = ma\) | M1 | |
| but \(F = \mu R\) \(\therefore a = \frac{-\mu R}{m} = \frac{-\mu mg}{m} = -\mu g\) | M1 A1 | |
| use with \(u = 1\), \(v = 0\): \(v^2 = u^2 + 2as\), so \(0 = 1 - 2(0.75)(9.8)s\) | M1 M1 | |
| \(s = 0.0680 \text{ m} = 7 \text{ cm}\) (nearest cm) | A1 | (11) |
**(a)** mag. of impulse is same as cannon on shell; impulse $= \Delta \text{mom} = 3(200 - 0) = 600 \text{ Ns}$ (towards cannon) | B1 M1 A1 |
**(b)** for cannon: $mv - mu = 600$; $600v = 600$ so $v = 1 \text{ ms}^{-1}$ | M1 A1 |
**(c)** $R = mg$; $F = ma$ | M1 |
but $F = \mu R$ $\therefore a = \frac{-\mu R}{m} = \frac{-\mu mg}{m} = -\mu g$ | M1 A1 |
use with $u = 1$, $v = 0$: $v^2 = u^2 + 2as$, so $0 = 1 - 2(0.75)(9.8)s$ | M1 M1 |
$s = 0.0680 \text{ m} = 7 \text{ cm}$ (nearest cm) | A1 | (11)3. A cannon of mass 600 kg lies on a rough horizontal surface and is used to fire a 3 kg shell horizontally at $200 \mathrm {~ms} ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Find the impulse which the shell exerts on the cannon.
\item Find the speed with which the cannon recoils.
Given that the coefficient of friction between the cannon and the surface is 0.75 ,
\item calculate, to the nearest centimetre, the distance that the cannon travels before coming to rest.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q3 [11]}}