| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Heavier particle hits ground, lighter continues upward - vertical strings |
| Difficulty | Standard +0.3 This is a standard M1 pulley problem with a common extension where one particle hits the ground. Part (i) requires routine application of Newton's second law to connected particles. Parts (ii) and (iii) involve straightforward energy calculations and kinematics with constant acceleration. The 'string becomes slack then taut again' scenario is a textbook exercise requiring students to find when A reaches maximum height and returns, but involves no novel insight—just careful application of standard SUVAT equations. |
| Spec | 3.02d Constant acceleration: SUVAT formulae3.03k Connected particles: pulleys and equilibrium6.02a Work done: concept and definition6.02d Mechanical energy: KE and PE concepts6.02e Calculate KE and PE: using formulae |
7 Loads $A$ and $B$, of masses 1.2 kg and 2.0 kg respectively, are attached to the ends of a light inextensible string which passes over a fixed smooth pulley. $A$ is held at rest and $B$ hangs freely, with both straight parts of the string vertical. $A$ is released and starts to move upwards. It does not reach the pulley in the subsequent motion.\\
(i) Find the acceleration of $A$ and the tension in the string.\\
(ii) Find, for the first 1.5 metres of $A$ 's motion,
\begin{enumerate}[label=(\alph*)]
\item A's gain in potential energy,
\item the work done on $A$ by the tension in the string,
\item A's gain in kinetic energy.
B hits the floor 1.6 seconds after $A$ is released. $B$ comes to rest without rebounding and the string becomes slack.\\
(iii) Find the time from the instant the string becomes slack until it becomes taut again.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2011 Q7 [11]}}