| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Momentum and Collisions |
| Type | Direct collision, find mass |
| Difficulty | Standard +0.3 This is a standard M1 collision question requiring conservation of momentum and impulse calculation. The setup is straightforward with clearly defined before/after velocities. Part (a) involves a single momentum equation to solve for k, and part (b) is direct application of impulse = change in momentum. While it requires careful sign handling, it's a routine textbook exercise with no novel problem-solving required. |
| Spec | 6.03a Linear momentum: p = mv6.03b Conservation of momentum: 1D two particles6.03e Impulse: by a force6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| \(\text{cons. of mom: } m(3u) - km(2u) = m(\frac{3}{2}u) + km(u)\) | M1 A1 | |
| \(3mu + \frac{3}{2}mu = kmu + 2kmu\) | M1 | |
| \(\frac{9}{2}mu = 3kmu \therefore k = \frac{3}{2}\) | A1 | |
| \(\text{impulse} = \Delta \text{ mom} = m[(-\frac{3}{2}u) - 3u] = -\frac{9}{2}mu \therefore \text{mag.} = \frac{9}{2}mu\) | M2 A1 | (7 marks) |
$\text{cons. of mom: } m(3u) - km(2u) = m(\frac{3}{2}u) + km(u)$ | M1 A1 |
$3mu + \frac{3}{2}mu = kmu + 2kmu$ | M1 |
$\frac{9}{2}mu = 3kmu \therefore k = \frac{3}{2}$ | A1 |
$\text{impulse} = \Delta \text{ mom} = m[(-\frac{3}{2}u) - 3u] = -\frac{9}{2}mu \therefore \text{mag.} = \frac{9}{2}mu$ | M2 A1 | (7 marks)Two particles $P$ and $Q$, of mass $m$ and $km$ respectively, are travelling in opposite directions on a straight horizontal path with speeds $3u$ and $2u$ respectively. $P$ and $Q$ collide and, as a result, the direction of motion of both particles is reversed and their speeds are halved.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $k$. [4 marks]
\item Write down an expression in terms of $m$ and $u$ for the magnitude of the impulse which $P$ exerts on $Q$ during the collision. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q1 [7]}}