| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2007 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find impulse magnitude |
| Difficulty | Moderate -0.8 This is a straightforward M1 momentum question requiring direct application of conservation of momentum (with clear before/after states), impulse-momentum theorem, and Newton's second law. All parts follow standard textbook procedures with no problem-solving insight needed—just careful substitution into familiar formulas with attention to sign conventions. |
| Spec | 3.03c Newton's second law: F=ma one dimension6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) CLM: \(0.3u = 0.3 \times (-2) + 0.6 \times 5\) → \(u = 8\) | M1 A1 | 4 marks |
| (b) \(I = 0.6 \times 5 = 3\) (Ns) | M1 A1 | 2 marks |
| (c) \(v = u + at ⇒ 5 = a \times 1.5\) (\(a = \frac{10}{3}\)) | M1 A1 | N2L: \(R = 0.6 \times \frac{10}{3} = 2\) |
**(a)** CLM: $0.3u = 0.3 \times (-2) + 0.6 \times 5$ → $u = 8$ | M1 A1 | 4 marks
**(b)** $I = 0.6 \times 5 = 3$ (Ns) | M1 A1 | 2 marks
**(c)** $v = u + at ⇒ 5 = a \times 1.5$ ($a = \frac{10}{3}$) | M1 A1 | N2L: $R = 0.6 \times \frac{10}{3} = 2$ | M1 A1 | 4 marks | 10 marks total
---A particle $P$ of mass 0.3 kg is moving with speed $u$ m s$^{-1}$ in a straight line on a smooth horizontal table. The particle $P$ collides directly with a particle $Q$ of mass 0.6 kg, which is at rest on the table. Immediately after the particles collide, $P$ has speed 2 m s$^{-1}$ and $Q$ has speed 5 m s$^{-1}$. The direction of motion of $P$ is reversed by the collision. Find
\begin{enumerate}[label=(\alph*)]
\item the value of $u$, [4]
\item the magnitude of the impulse exerted by $P$ on $Q$. [2]
\end{enumerate}
Immediately after the collision, a constant force of magnitude $R$ newtons is applied to $Q$ in the direction directly opposite to the direction of motion of $Q$. As a result $Q$ is brought to rest in 1.5 s.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the value of $R$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2007 Q4 [10]}}