| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| 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 three-particle pulley system requiring force diagrams and Newton's second law applied to connected particles. While it involves multiple bodies and two tensions, the setup is straightforward (smooth surfaces, light strings), and the solution follows a routine method of writing equations for each mass and solving simultaneously. Slightly above average due to the three-body system, but still a textbook exercise. |
| Spec | 3.03a Force: vector nature and diagrams3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys |
# Question 1
## (i)
B1: Diagrams for both 2 and 9 kg blocks. The tensions must be different from each other. No extra forces.
B1: Tensions on 6 kg block. The tensions must be different from each other. No extra forces.
B1: $6g$ and $R$ on 6 kg block. No extra forces.
**Special Case:** When the tensions are given as $T_1, T_2, T_3, T_4$ (or equivalent) award up to SC1 SC0 for the first two marks.
## (ii)
M1: First equation correct: $9g - T_2 = 9a$
M1: Both the remaining two equations correct: $T_2 - T_1 = 6a$ and $T_1 - 2g = 2a$
Do not give this mark if both tensions are shown as the same.
A1: $a = \frac{7}{17}g = 4.04 \text{ (m s}^{-2}\text{)}$
A1: $T_1 = 27.7 \text{ (N)}$
A1: $T_2 = 51.9 \text{ (N)}$
The final three marks are dependent on both M marks. $a$, $T_1$ and $T_2$ may be found in any order and FT should be allowed from the first of these found.
## (ii) Alternative: Whole system
M1: $9g - 2g = 17a$
A1: $a = \frac{7g}{17} = 4.04$
M1: $T_1 - 2g = 2a$ and $9g - T_2 = 9a$ — Both equations correct. Or equivalent.
A1: $T_1 = 27.7 \text{ (N)}$
A1: $T_2 = 51.9 \text{ (N)}$
The final two marks are dependent on both M marks. $T_1$ and $T_2$ may be found in either order and FT should be allowed from their value for $a$.
**Note:** Follow through between parts of Question 2 should be allowed for values found in parts (ii) and (iii) providing the questions are not simplified.1 Fig. 2 shows a 6 kg block on a smooth horizontal table. It is connected to blocks of mass 2 kg and 9 kg by two light strings which pass over smooth pulleys at the edges of the table. The parts of the strings attached to the 6 kg block are horizontal.
\begin{figure}[h]
\begin{center}
\includegraphics[alt={},max width=\textwidth]{9bff41e0-7be0-4932-ae50-a612abb3fe19-1_345_1141_364_480}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{center}
\end{figure}
(i) Draw three separate diagrams showing all the forces acting on each of the blocks.\\
(ii) Calculate the acceleration of the system and the tension in each string.
\hfill \mbox{\textit{OCR MEI M1 Q1 [8]}}