| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Three or more connected particles |
| Difficulty | Standard +0.3 This is a standard M1 connected particles problem requiring Newton's second law applied to a three-body system. Part (a) involves straightforward application of F=ma to particle R, part (b) requires setting up equations for all three particles and solving simultaneously, and part (c) tests understanding of modelling assumptions. While it requires careful bookkeeping across multiple bodies, the techniques are routine for M1 and the question provides significant scaffolding by giving the tension value and asking students to 'show' the acceleration first. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(F = ma\) for R: \(0.5g - 2 = 0.5a\) → \(a = 5.8\) ms\(^{-2}\) | M1 A1 A1 | |
| (b) \(T - 0.1g = 0.1a\) → \(T = 0.58 + 0.98 = 1.56\) N | M1 A1 | |
| \(2 - T = ma\) → \(5.8m = 0.44\) → \(m = 0.0759\) | M1 A1 A1 | |
| (c) String inextensible: if not, accelerations different | B1 B1 | |
| Pulleys smooth: if not, tensions different either side of pulley | B1 B1 | Total: 12 marks |
**(a)** $F = ma$ for R: $0.5g - 2 = 0.5a$ → $a = 5.8$ ms$^{-2}$ | M1 A1 A1 |
**(b)** $T - 0.1g = 0.1a$ → $T = 0.58 + 0.98 = 1.56$ N | M1 A1 |
$2 - T = ma$ → $5.8m = 0.44$ → $m = 0.0759$ | M1 A1 A1 |
**(c)** String inextensible: if not, accelerations different | B1 B1 |
Pulleys smooth: if not, tensions different either side of pulley | B1 B1 | **Total: 12 marks**A particle $P$ of mass $m$ kg, at rest on a smooth horizontal table, is connected to particles $Q$ and $R$, of mass 0.1 kg and 0.5 kg respectively, by strings which pass over fixed pulleys at the edges of the table. The system is released from rest with $Q$ and $R$ hanging freely and it is found that the tension in the section of the string between $P$ and $R$ is 2 N.
\begin{enumerate}[label=(\alph*)]
\item Show that the acceleration of the particles has magnitude 5.8 ms$^{-2}$. \hfill [3 marks]
\item Find the value of $m$. \hfill [5 marks]
\end{enumerate}
Modelling assumptions have been made about the pulley and the strings.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Briefly describe these two assumptions. For each one, state how the mathematical model would be altered if the assumption were not made. \hfill [4 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q4 [12]}}