| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 15 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Multi-stage motion: particle reaches ground/pulley causing string to go slack |
| Difficulty | Standard +0.3 This is a standard M1 connected particles problem with friction. Parts (a)-(c) involve routine application of Newton's second law and kinematics with given acceleration. Part (d) requires students to recognize the system decouples after Q hits the floor and apply friction deceleration to P, but this is a well-practiced scenario in M1. The multi-part structure and 15 marks indicate moderate length, but each step follows standard procedures without requiring novel insight. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03r Friction: concept and vector form3.03v Motion on rough surface: including inclined planes |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(T - 0.2g = 0.4(1)\) | \(T = 0.4 + 0.2g = 2.36 \text{ N}\) | M1 A1 A1 |
| (b) \(Mg - T = 0.4M\) | \(9.4M = 2.36\) | \(M = 0.251\) |
| (c) \(0.5 = \frac{1}{2} \times 0.4t^2\) | \(t = 1.58 \text{ s}\) | M1 A1 A1 |
| (d) \(P\) has moved \(0.5 \text{ m}\) and has speed \(0.632 \text{ m s}^{-1}\) and acceleration \(-0.2g\), so \(0^2 - 0.632^2 = 2(-0.2g)s\) | \(s = 0.102\) | B1 |
| Comes to rest \(0.75 - (0.5 + 0.102) = 0.148 \text{ m}\) from pulley | M1 A1 | 15 marks |
(a) $T - 0.2g = 0.4(1)$ | $T = 0.4 + 0.2g = 2.36 \text{ N}$ | M1 A1 A1
(b) $Mg - T = 0.4M$ | $9.4M = 2.36$ | $M = 0.251$ | M1 A1 A1
(c) $0.5 = \frac{1}{2} \times 0.4t^2$ | $t = 1.58 \text{ s}$ | M1 A1 A1
(d) $P$ has moved $0.5 \text{ m}$ and has speed $0.632 \text{ m s}^{-1}$ and acceleration $-0.2g$, so $0^2 - 0.632^2 = 2(-0.2g)s$ | $s = 0.102$ | B1 | B1 M1 A1
Comes to rest $0.75 - (0.5 + 0.102) = 0.148 \text{ m}$ from pulley | M1 A1 | **15 marks**A small package $P$, of mass 1 kg, is initially at rest on the rough horizontal top surface of a wooden packing case which is 1.5 m long and 1 m high and stands on a horizontal floor.
The coefficient of friction between $P$ and the case is 0.2.
$P$ is attached by a light inextensible string, which passes over a smooth fixed pulley, to a weight $Q$ of mass $M$ kg which rests against the smooth vertical side of the case.
The system is released from rest with $P$ 0.75 m from the pulley and $Q$ 0.5 m from the pulley.
$P$ and $Q$ start to move with acceleration 0.4 ms$^{-2}$. Calculate
\begin{enumerate}[label=(\alph*)]
\item the tension in the string, in N, [3 marks]
\item the value of $M$, [3 marks]
\item the time taken for $Q$ to hit the floor. [3 marks]
\end{enumerate}
Given that $Q$ does not rebound from the floor,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item calculate the distance of $P$ from the pulley when it comes to rest. [6 marks]
\end{enumerate}
\includegraphics{figure_2}
\hfill \mbox{\textit{Edexcel M1 Q6 [15]}}