| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2002 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Multi-stage motion: particle reaches ground/pulley causing string to go slack |
| Difficulty | Standard +0.3 This is a standard M1 pulley system question with connected particles and friction. Parts (a)-(c) involve routine application of Newton's second law and friction formulas with straightforward algebra. Part (d) requires using equations of motion after the string slackens, which is a common extension but still follows standard procedures. The multi-part structure and 16 marks indicate moderate length, but no novel insight is required—it's a textbook exercise testing standard mechanics techniques. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03l Newton's third law: extend to situations requiring force resolution3.03r Friction: concept and vector form3.03t Coefficient of friction: F <= mu*R model |
| Answer | Marks | Guidance |
|---|---|---|
| \(Q: 5mg - T = 5ma\) | M1 A1 | M1 A1 (4) |
| Answer | Marks | Guidance |
|---|---|---|
| \(a = 0.49\) | M1 A1 (4) | M1 A1 (4) |
| Answer | Marks |
|---|---|
| \(\Rightarrow T = 3mg\) | M1 A1 (2) |
| Answer | Marks | Guidance |
|---|---|---|
| Dist of P: \(3mf = 1.8mg \Rightarrow s = \frac{2}{3}h\) | M1 A1 (V) | M1 A1 (6) (16) |
## Part (a)
$P: T - F = 3ma$
$Q: 5mg - T = 5ma$ | M1 A1 | M1 A1 (4)
## Part (b)
$F = 0.6 \times 3mg$ $(= 1.8mg)$
Hence $5mg - 1.8mg = 8ma$
$a = 0.49$ | M1 A1 (4) | M1 A1 (4)
## Part (c)
Sub: $T = 3ma + F$ or $5mg - 5ma$
$\Rightarrow T = 3mg$ | M1 A1 (2)
## Part (d)
Speed when Q hits floor: $v^2 = 2 \times 0.49 \times h$
$= \frac{4}{5}gh$
Decel of P: $3mf = 1.8mg \Rightarrow f = 0.49$
Dist of P: $3mf = 1.8mg \Rightarrow s = \frac{2}{3}h$ | M1 A1 (V) | M1 A1 (6) (16)\includegraphics{figure_4}
Two particles $P$ and $Q$ have masses $3m$ and $5m$ respectively. They are connected by a light inextensible string which passes over a small smooth light pulley fixed at the edge of a rough horizontal table. Particle $P$ lies on the table and particle $Q$ hangs freely below the pulley, as shown in Fig. 4. The coefficient of friction between $P$ and the table is 0.6. The system is released from rest with the string taut. For the period before $Q$ hits the floor or $P$ reaches the pulley,
\begin{enumerate}[label=(\alph*)]
\item write down an equation of motion for each particle separately, [4]
\item find, in terms of $g$, the acceleration of $Q$, [4]
\item find, in terms of $m$ and $g$, the tension in the string. [2]
\end{enumerate}
When $Q$ has moved a distance $h$, it hits the floor and the string becomes slack. Given that $P$ remains on the table during the subsequent motion and does not reach the pulley,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item find, in terms of $h$, the distance moved by $P$ after the string becomes slack until $P$ comes to rest. [6]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2002 Q8 [16]}}