| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Energy methods for pulley systems |
| Difficulty | Standard +0.3 This is a standard M1 connected particles problem on inclined planes requiring Newton's second law, resolution of forces, and basic kinematics. While it involves multiple steps and careful angle work (30° and 60° planes), it follows a completely routine template taught in all M1 courses with no novel problem-solving required. The modelling assumptions part (d) is pure recall. Slightly easier than average due to its predictable structure. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03l Newton's third law: extend to situations requiring force resolution3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(2g \cos 30° - T = 2a\) and \(T - 3g \cos 60° = 3a\) | M1 A1 A1 | |
| Add: \(g(\sqrt{3} - 1.5) = 5a\) where \(a = 0.455\) ms\(^{-2}\) | M1 A1 | |
| (b) \(T = 3a + 1.5g = 16.1\) N | M1 A1 | |
| (c) \(v^2 = u^2 + 2as = 0 + 2a(0.8) = 0.728\) where \(v = 0.853\) ms\(^{-1}\) | M1 A1 A1 | |
| (d) String inextensible, so acceleration the same for both particles | B1 B1 | |
| Pulley smooth, so tension is constant throughout the string | B1 B1 | Total: 14 marks |
**(a)** $2g \cos 30° - T = 2a$ and $T - 3g \cos 60° = 3a$ | M1 A1 A1 |
Add: $g(\sqrt{3} - 1.5) = 5a$ where $a = 0.455$ ms$^{-2}$ | M1 A1 |
**(b)** $T = 3a + 1.5g = 16.1$ N | M1 A1 |
**(c)** $v^2 = u^2 + 2as = 0 + 2a(0.8) = 0.728$ where $v = 0.853$ ms$^{-1}$ | M1 A1 A1 |
**(d)** String inextensible, so acceleration the same for both particles | B1 B1 |
Pulley smooth, so tension is constant throughout the string | B1 B1 | **Total: 14 marks**Two particles $P$ and $Q$, of masses $3$ kg and $2$ kg respectively, rest on the smooth faces of a wedge whose cross-section is a triangle with angles $30°$, $60°$ and $90°$, as shown. $P$ and $Q$ are connected by a light string, parallel to the lines of greatest slope of the two planes, which passes over a fixed pulley at the highest point of the wedge.
\includegraphics{figure_6}
The system is released from rest with $P$ $0.8$ m from the pulley and $Q$ $1$ m from the bottom of the wedge, and $Q$ starts to move down. Calculate
\begin{enumerate}[label=(\alph*)]
\item the acceleration of either particle, \hfill [5 marks]
\item the tension in the string, \hfill [2 marks]
\item the speed with which $P$ reaches the pulley. \hfill [3 marks]
\end{enumerate}
Two modelling assumptions have been made about the string and the pulley.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item State these two assumptions and briefly describe how you have used each one in your solution. \hfill [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q6 [14]}}