| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2012 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Two particles over pulley, vertical strings |
| Difficulty | Moderate -0.8 This is a standard textbook pulley problem requiring only direct application of Newton's second law to two connected masses. Students apply F=ma to each mass, recognize the tension is equal in both strings and accelerations have equal magnitude, then solve two simultaneous equations—a routine procedure practiced extensively in M1 with no novel problem-solving required. |
| Spec | 3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Let tension in string be \(T\) N and acceleration be \(a\) m s\(^{-2}\) | M1 | One correct equation which must involve \(a\) and a weight |
| 3 kg block: \(T - 3g = 3a\) | M1 | A second correct equation; this one must involve \(a\), \(T\) and a weight |
| 5 kg block: \(5g - T = 5a\) | ||
| \(2g = 8a\) | M1 | Elimination of both \(T\) and \(a\) from their equations or substitution of their \(a\) in their 3-term equation |
| \(a = g/4 = 2.45\) (m s\(^{-2}\)) | A1 | Cao dependent on at least one of the first two M marks |
| \(T = 36.75\) (N) | A1 | Cao dependent on at least one of the first two M marks |
| [5] |
## Question 1:
| Answer | Mark | Guidance |
|--------|------|----------|
| Let tension in string be $T$ N and acceleration be $a$ m s$^{-2}$ | M1 | One correct equation which must involve $a$ and a weight |
| 3 kg block: $T - 3g = 3a$ | M1 | A second correct equation; this one must involve $a$, $T$ and a weight |
| 5 kg block: $5g - T = 5a$ | | |
| $2g = 8a$ | M1 | Elimination of both $T$ and $a$ from their equations or substitution of their $a$ in their 3-term equation |
| $a = g/4 = 2.45$ (m s$^{-2}$) | A1 | Cao dependent on at least one of the first two M marks |
| $T = 36.75$ (N) | A1 | Cao dependent on at least one of the first two M marks |
| | **[5]** | |
---1 Fig. 1 shows two blocks of masses 3 kg and 5 kg connected by a light string which passes over a smooth, fixed pulley.
Initially the blocks are held at rest but then they are released.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{0330185f-d79d-4a78-9fa2-29ec345c2856-2_490_303_520_881}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{center}
\end{figure}
Find the acceleration of the blocks when they start to move, and the tension in the string.
\hfill \mbox{\textit{OCR MEI M1 2012 Q1 [5]}}