| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Bullet penetration with resistance |
| Difficulty | Standard +0.3 This is a standard two-part mechanics question combining conservation of momentum (routine application) with friction/kinematics (straightforward calculation). The setup is clear, the methods are direct textbook applications, and part (b) is a 'show that' which guides students to the answer. Slightly above average difficulty due to unit conversion and two-stage problem, but no novel insight required. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03v Motion on rough surface: including inclined planes6.03b Conservation of momentum: 1D two particles6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) cons. of mom.: \(0.05(400) = (0.05 + 4.95)v\) | M2 | |
| \(20 = 5v\) \(\therefore v = 4 \text{ ms}^{-1}\) | A1 | |
| (b) \(R = mg\); \(F = ma\) | M1 | |
| but \(F = \mu R\) \(\therefore a = \frac{\mu R}{m} = \frac{\mu mg}{m} = \mu g\) | M1 A1 | |
| use with \(u = 4, v = 0, s = 4\) | M1 | |
| \(v^2 = u^2 + 2as\), so \(0 = 16 - 8\mu g\) | M1 | |
| \(\mu = \frac{16}{8g} = \frac{3}{5}\) | A1 | (9) |
**(a)** cons. of mom.: $0.05(400) = (0.05 + 4.95)v$ | M2 |
$20 = 5v$ $\therefore v = 4 \text{ ms}^{-1}$ | A1 |
**(b)** $R = mg$; $F = ma$ | M1 |
but $F = \mu R$ $\therefore a = \frac{\mu R}{m} = \frac{\mu mg}{m} = \mu g$ | M1 A1 |
use with $u = 4, v = 0, s = 4$ | M1 |
$v^2 = u^2 + 2as$, so $0 = 16 - 8\mu g$ | M1 |
$\mu = \frac{16}{8g} = \frac{3}{5}$ | A1 | (9)4. A bullet of mass 50 g is fired horizontally at a wooden block of mass 4.95 kg which is lying at rest on a rough horizontal surface. The bullet enters the block at $400 \mathrm {~ms} ^ { - 1 }$ and becomes embedded in the block.
\begin{enumerate}[label=(\alph*)]
\item Find the speed with which the block begins to move.
Given that the block decelerates uniformly to rest over a distance of 4 m ,
\item show that the coefficient of friction is $\frac { 2 } { g }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [9]}}