| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Three or more connected particles |
| Difficulty | Standard +0.3 This is a straightforward two-particle pulley problem requiring basic application of Newton's second law. Students must identify equal tensions and accelerations, draw force diagrams, and solve simultaneous equations—all standard M1 techniques with no novel problem-solving required. Slightly easier than average due to the guided structure and explicit prompts. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03l Newton's third law: extend to situations requiring force resolution |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Horizontal: \(10 - 8\sin 50°\) | M1 | Resolving horizontally, correct trig |
| \(= 10 - 6.128... = 3.87\) N (i) component | A1 | |
| Vertical: \(-8\cos 50°\) | M1 | Resolving vertically |
| \(= -5.14\) N (j) component | A1 | |
| \(\mathbf{F} = 3.87\mathbf{i} - 5.14\mathbf{j}\) | A1 | Both components correct to 3 s.f. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \( | \mathbf{F} | = \sqrt{3.87^2 + 5.14^2}\) |
| \(= 6.43\) N | A1 | |
| Angle with upward vertical: \(\tan\theta = \frac{3.87}{5.14}\) | M1 | Correct method for angle |
| \(\theta = 36.9°\) (from upward vertical) | A1 |
# Question 2:
## Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Horizontal: $10 - 8\sin 50°$ | M1 | Resolving horizontally, correct trig |
| $= 10 - 6.128... = 3.87$ N (i) component | A1 | |
| Vertical: $-8\cos 50°$ | M1 | Resolving vertically |
| $= -5.14$ N (j) component | A1 | |
| $\mathbf{F} = 3.87\mathbf{i} - 5.14\mathbf{j}$ | A1 | Both components correct to 3 s.f. |
## Part (ii)
| Answer | Marks | Guidance |
|--------|-------|----------|
| $|\mathbf{F}| = \sqrt{3.87^2 + 5.14^2}$ | M1 | |
| $= 6.43$ N | A1 | |
| Angle with upward vertical: $\tan\theta = \frac{3.87}{5.14}$ | M1 | Correct method for angle |
| $\theta = 36.9°$ (from upward vertical) | A1 | |
---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]{9a79f274-1a3f-4d11-9775-313d82075035-002_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 Q2}}