| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Three or more connected particles |
| Difficulty | Standard +0.3 This is a standard two-particle pulley system requiring straightforward application of Newton's second law to both masses. While it involves multiple parts including conceptual understanding (part i) and setting up equations (parts ii-iii), the mathematical steps are routine: draw force diagrams, write F=ma for each particle, solve simultaneous equations. The setup is simpler than typical three-particle systems, making it slightly easier than average. |
| Spec | 3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| The pulleys are smooth and the string is inextensible | E1 | Accept only 'the pulley is smooth' |
| E1 | ||
| Total: 2 |
| Answer | Marks | Guidance |
|---|---|---|
| Diagrams | B1 | All forces present with labels and arrows. Acc not reqd. |
| Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| For X, N2L upwards: \(T - 2g = 2a\) | M1 | N2L. Allow \(F = mga\). All forces present. Award for equation for X or Y or combined |
| A1 | Any form | |
| For Y, N2L downwards: \(4g - T = 4a\) | A1 | Any form |
| Solve for \(a\) and \(T\) | ||
| \(a = \frac{g}{3}\) (3.27 (3 s. f.)) | A1 | |
| \(T = \frac{8}{3}g\) (26.1 (3 s. f.)) | F1 | FT second answer |
| Total: 5 |
**Part (i)**
| The pulleys are smooth and the string is inextensible | E1 | Accept only 'the pulley is smooth' |
| | E1 | |
| | | **Total: 2** |
**Part (ii)**
| Diagrams | B1 | All forces present with labels and arrows. Acc not reqd. |
| | | **Total: 1** |
**Part (iii)**
| For X, N2L upwards: $T - 2g = 2a$ | M1 | N2L. Allow $F = mga$. All forces present. Award for equation for X or Y or combined |
| | A1 | Any form |
| For Y, N2L downwards: $4g - T = 4a$ | A1 | Any form |
| Solve for $a$ and $T$ | | |
| $a = \frac{g}{3}$ (3.27 (3 s. f.)) | A1 | |
| $T = \frac{8}{3}g$ (26.1 (3 s. f.)) | F1 | FT second answer |
| | | **Total: 5** |
---2 Particles of mass 2 kg and 4 kg are attached to the ends $X$ and $Y$ of a light, inextensible string. The string passes round fixed, smooth pulleys at $\mathrm { P } , \mathrm { Q }$ and R , as shown in Fig. 2. The system is released from rest with the string taut.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{c84a748a-a6f4-48c5-b864-fe543569bdf5-2_478_397_1211_872}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}
\begin{enumerate}[label=(\roman*)]
\item State what information in the question tells you that\\
(A) the tension is the same throughout the string,\\
(B) the magnitudes of the accelerations of the particles at X and Y are the same.
The tension in the string is $T \mathrm {~N}$ and the magnitude of the acceleration of the particles is $a \mathrm {~ms} ^ { - 2 }$.
\item Draw a diagram showing the forces acting at X and a diagram showing the forces acting at Y .
\item Write down equations of motion for the particles at X and at Y . Hence calculate the values of $T$ and $a$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI M1 2005 Q2 [8]}}