| Exam Board | WJEC |
|---|---|
| Module | Unit 2 (Unit 2) |
| Year | 2024 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Particle on rough horizontal surface, particle hanging |
| Difficulty | Moderate -0.3 This is a standard connected particles problem requiring application of SUVAT equations and Newton's second law. Part (a) is straightforward kinematics, part (b) involves setting up equations of motion for both masses (routine A-level mechanics), and part (c) tests understanding of modelling assumptions. The multi-step nature and 6 marks for part (b) add some substance, but the techniques are entirely standard with no novel insight required, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03c Newton's second law: F=ma one dimension3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys |
The diagram below shows an object $A$, of mass $2m$ kg, lying on a horizontal table. It is connected to another object $B$, of mass $m$ kg, by a light inextensible string, which passes over a smooth pulley $P$, fixed at the edge of the table. Initially, object $A$ is held at rest so that object $B$ hangs freely with the string taut.
\includegraphics{figure_9}
Object $A$ is then released.
\begin{enumerate}[label=(\alph*)]
\item When object $B$ has moved downwards a vertical distance of 0·4 m, its speed is 1·2 ms$^{-1}$.
Use a formula for motion in a straight line with constant acceleration to show that the magnitude of the acceleration of $B$ is 1·8 ms$^{-2}$. [2]
\item During the motion, object $A$ experiences a constant resistive force of 22 N. Find the value of $m$ and hence determine the tension in the string. [6]
\item What assumption did the word 'inextensible' in the description of the string enable you to make in your solution? [1]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 2 2024 Q9 [9]}}