| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 13 |
| 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 applied to two connected particles, followed by a straightforward vector addition to find the force on the pulley. Part (a) is a 'show that' requiring equation setup and solving, parts (b-c) are routine calculations, and part (d) tests conceptual understanding. Slightly above average due to the multi-part nature and the need to handle vector components in part (c), but all techniques are standard M1 fare with no novel problem-solving required. |
| Spec | 3.03b Newton's first law: equilibrium3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| (a) eqn. of motion for Dermot: \(54g - T = 54(1)\) | M1 A1 | |
| eqn. of motion for Corinne (mass \(M\)): \(T - Mg = M(1)\) | M1 A1 | |
| \(54g - Mg = 54 + M\) | M1 | |
| \(M(1 + g) = 54(g - 1)\) | M1 | |
| mass of Corinne = 44 kg | A1 | |
| (b) \(T = 44(1 + 9.8)\) (from eqn. of motion of Corinne) | M2 | |
| \(T = 475.2 \text{ N}\) | A1 | |
| (c) force on pulley = \(2T = 950.4 \text{ N}\) | M1 A1 | |
| (d) e.g. rough branch will mean lower (possibly zero) acc\(^n\) | B1 | (13) |
(a) eqn. of motion for Dermot: $54g - T = 54(1)$ | M1 A1 |
eqn. of motion for Corinne (mass $M$): $T - Mg = M(1)$ | M1 A1 |
$54g - Mg = 54 + M$ | M1 |
$M(1 + g) = 54(g - 1)$ | M1 |
mass of Corinne = 44 kg | A1 |
(b) $T = 44(1 + 9.8)$ (from eqn. of motion of Corinne) | M2 |
$T = 475.2 \text{ N}$ | A1 |
(c) force on pulley = $2T = 950.4 \text{ N}$ | M1 A1 |
(d) e.g. rough branch will mean lower (possibly zero) acc$^n$ | B1 | (13) |6. Corinne and her brother Dermot are lifted by their parents onto the two ends of a rope which is slung over a large, horizontal branch. When their parents let go of them Dermot, whose mass is 54 kg , begins to descend with an acceleration of $1 \mathrm {~ms} ^ { - 2 }$.
By modelling the children as a pair of particles connected by a light inextensible string, and the branch as a smooth pulley,
\begin{enumerate}[label=(\alph*)]
\item show that Corinne's mass is 44 kg ,
\item calculate the tension in the rope,
\item find the force on the branch.
In a more sophisticated model, the branch is assumed to be rough.
\item Explain what effect this would have on the initial acceleration of the children.\\
(1 mark)
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q6 [13]}}