| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | June |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Force on pulley from string |
| Difficulty | Standard +0.3 This is a standard M1 pulley problem requiring Newton's second law for connected particles with friction. Students must write equations for both particles, account for friction (μR), and solve simultaneously for tension and acceleration. The pulley force part (b) requires vector addition at 90°, which is routine at this level. Slightly easier than average due to straightforward setup and clean numbers. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03m Equilibrium: sum of resolved forces = 03.03o Advanced connected particles: and pulleys3.03t Coefficient of friction: F <= mu*R model3.03v Motion on rough surface: including inclined planes3.04a Calculate moments: about a point |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \(F = \frac{1}{5}R\) | M1 | First M1 for use of \(F = \frac{1}{5}R\) in an equation |
| \(R = 1.5g\) | B1 | B1 for \(R = 1.5g\) |
| \(T - F = 1.5a\) | M1 A1 | Second M1 resolving horizontally; First A1 correct equation. Note: whole system \(3g - F = 4.5a\) acceptable |
| \(3g - T = 3a\) | M1 A1 | Third M1 resolving vertically; Second A1 correct equation |
| \(T = 1.2g\) or \(11.8\text{ N}\) or \(12\text{ N}\) | DM1 A1 | Fourth M1 (dependent on M1, M1, M1) solving for \(T\); Third A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Working/Answer | Marks | Guidance |
| \(R = \sqrt{T^2 + T^2}\) or \(2T\cos 45°\) or \(\dfrac{T}{\cos 45°}\) | M1 A1 | First M1 complete method for magnitude (M0 if different tensions used); First A1 |
| \(= 16.6\text{ (N)}\) or \(17\text{ (N)}\) or \(\dfrac{6g\sqrt{2}}{5}\) | A1 | Second A1 |
| Direction is \(45°\) below the horizontal | B1 | B1 for \(45°\) below horizontal or correct diagram. Ignore subsequent wrong answers e.g. bearing of \(225°\) (scores B0). Total: 12 |
## Question 8(a):
| Working/Answer | Marks | Guidance |
|---|---|---|
| $F = \frac{1}{5}R$ | M1 | First M1 for use of $F = \frac{1}{5}R$ in an equation |
| $R = 1.5g$ | B1 | B1 for $R = 1.5g$ |
| $T - F = 1.5a$ | M1 A1 | Second M1 resolving horizontally; First A1 correct equation. Note: whole system $3g - F = 4.5a$ acceptable |
| $3g - T = 3a$ | M1 A1 | Third M1 resolving vertically; Second A1 correct equation |
| $T = 1.2g$ or $11.8\text{ N}$ or $12\text{ N}$ | DM1 A1 | Fourth M1 (dependent on M1, M1, M1) solving for $T$; Third A1 | **(8)** |
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## Question 8(b):
| Working/Answer | Marks | Guidance |
|---|---|---|
| $R = \sqrt{T^2 + T^2}$ or $2T\cos 45°$ or $\dfrac{T}{\cos 45°}$ | M1 A1 | First M1 complete method for magnitude (M0 if different tensions used); First A1 |
| $= 16.6\text{ (N)}$ or $17\text{ (N)}$ or $\dfrac{6g\sqrt{2}}{5}$ | A1 | Second A1 |
| Direction is $45°$ below the horizontal | B1 | B1 for $45°$ below horizontal or correct diagram. Ignore subsequent wrong answers e.g. bearing of $225°$ (scores B0). **Total: 12** | **(4)** |8.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{d408dd83-c5b2-4e55-b5c1-3e7f3faadbcb-14_460_981_274_475}
\captionsetup{labelformat=empty}
\caption{Figure 3}
\end{center}
\end{figure}
Two particles $P$ and $Q$ have masses 1.5 kg and 3 kg respectively. The particles are attached to the ends of a light inextensible string. Particle $P$ is held at rest on a fixed rough horizontal table. The coefficient of friction between $P$ and the table is $\frac { 1 } { 5 }$. The string is parallel to the table and passes over a small smooth light pulley which is fixed at the edge of the table. Particle $Q$ hangs freely at rest vertically below the pulley, as shown in Figure 3. Particle $P$ is released from rest with the string taut and slides along the table.
Assuming that $P$ has not reached the pulley, find
\begin{enumerate}[label=(\alph*)]
\item the tension in the string during the motion,
\item the magnitude and direction of the resultant force exerted on the pulley by the string.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2016 Q8 [12]}}