| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Bullet penetration with resistance |
| Difficulty | Moderate -0.3 This is a straightforward two-part mechanics question requiring standard application of conservation of momentum (part a) and uniform acceleration equations with Newton's second law (part b). Both parts are routine M1 calculations with no conceptual challenges or problem-solving insight required, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae6.03b Conservation of momentum: 1D two particles |
| Answer | Marks | Guidance |
|---|---|---|
| (a) cons. of mom.: \(2u = 0.03(100)\) \(u = 1.5 \text{ ms}^{-1}\) | M2, A1 | |
| (b) \(v^2 = u^2 + 2as\) so \(0 = 6400 + 2a(0.02)\) \(a = 160000 \text{ ms}^{-2}\) so \(F = 0.03(160000) = 4800 \text{ N}\) (opp. dir" to bullet) | M1 A1, M1 A1 | (7) |
| (a) cons. of mom.: $2u = 0.03(100)$ $u = 1.5 \text{ ms}^{-1}$ | M2, A1 | |
| (b) $v^2 = u^2 + 2as$ so $0 = 6400 + 2a(0.02)$ $a = 160000 \text{ ms}^{-2}$ so $F = 0.03(160000) = 4800 \text{ N}$ (opp. dir" to bullet) | M1 A1, M1 A1 | (7) |2. During trials of a bullet-proof vest, a shotgun of mass 2 kg is used to fire a bullet of mass 30 g horizontally at the vest. The initial speed of the bullet is $100 \mathrm {~ms} ^ { - 1 }$.
\begin{enumerate}[label=(\alph*)]
\item Calculate the initial speed of recoil of the gun.
The bullet hits the vest horizontally at a speed of $80 \mathrm {~ms} ^ { - 1 }$ and is brought uniformly to rest in a distance of 2 cm .
\item Find the magnitude of the force exerted by the vest on the bullet in bringing it to rest.\\
(4 marks)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q2 [7]}}