| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Multi-stage motion: changing surface conditions or external intervention |
| Difficulty | Standard +0.3 This is a standard M1 connected particles problem with friction. Part (a) is trivial impulse-momentum application (1 mark). Part (b) tests understanding of modeling assumptions. Parts (c-d) require setting up equations of motion with friction and tension, then solving for time and distance - all routine M1 techniques with no novel insight needed. The 7 marks for part (c) suggests multiple steps, but these are standard: resolve forces, apply F=ma, solve equations. Slightly easier than average due to straightforward setup and well-signposted parts. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03v Motion on rough surface: including inclined planes6.03e Impulse: by a force6.03f Impulse-momentum: relation |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(5m = 2mv\) → \(v = 2.5\) | B1 | |
| (b) Smooth pulley | B1 | |
| (c) \(F = ma\) for each sphere: \(T + \frac{2}{3}(2mg) = 2ma\), \(mg - T = ma\) | M1 A1 A1 | |
| Add: \(3ma = \frac{11}{7}mg\) → \(a = \frac{11}{21} = 5.13\) ms\(^{-2}\) | M1 A1 | |
| (d) \(v^2 = u^2 + 2as: 0 = 2.5^2 - 10.27s\) → \(s = 0.609\) m | M1 A1 M1 A1 | 13 marks |
**(a)** $5m = 2mv$ → $v = 2.5$ | B1 |
**(b)** Smooth pulley | B1 |
**(c)** $F = ma$ for each sphere: $T + \frac{2}{3}(2mg) = 2ma$, $mg - T = ma$ | M1 A1 A1 |
Add: $3ma = \frac{11}{7}mg$ → $a = \frac{11}{21} = 5.13$ ms$^{-2}$ | M1 A1 |
**(d)** $v^2 = u^2 + 2as: 0 = 2.5^2 - 10.27s$ → $s = 0.609$ m | M1 A1 M1 A1 | 13 marks |Two smooth spheres $A$ and $B$, of masses $2m$ and $m$ respectively, are connected by a light inextensible string which passes over a smooth fixed pulley as shown. $A$ is initially at rest on the rough horizontal surface of a table, the coefficient of friction between $A$ and the table being $\frac{2}{7}$. $B$ hangs freely on the end of the vertical portion of the string.
\includegraphics{figure_5}
$A$ is now given an impulse, directed away from the pulley, of magnitude $5m$ Ns.
\begin{enumerate}[label=(\alph*)]
\item Show that the system starts to move with speed $2.5 \text{ ms}^{-1}$. [1 mark]
\item State which modelling assumption ensures that the tensions in the two sections of the string can be taken to be equal. [1 mark]
\end{enumerate}
Given that $A$ comes to rest before it reaches the edge of the table and before $B$ hits the pulley,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the time taken for the system to come to rest. [7 marks]
\item Find the distance travelled by $A$ before it first comes to rest. [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q5 [13]}}