| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2003 |
| Session | January |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Particle on smooth horizontal surface, particle hanging |
| Difficulty | Standard +0.3 This is a standard M1 pulley problem with connected particles. Part (a) requires setting up Newton's second law for both particles and solving simultaneous equations (routine). Part (b) uses constant acceleration equations (standard). Part (c) adds friction but follows the same method with an additional force term. All techniques are textbook exercises with no novel insight required, making it slightly easier than average. |
| 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 |
|---|---|---|
| A: \(T = 0.8a\) | B1 | |
| B: \(1.2g - T = 1.2a\) | M1 A1 | |
| Solve: \(T = 0.48g = 4.7\) N | M1 A1 | (5 marks) |
| Answer | Marks | Guidance |
|---|---|---|
| \(a = 0.6g = 5.88\) | M1 | |
| Hence \(0.6 = \frac{1}{2} \times 0.6g \times t^2\) | M1 | |
| \(t = 0.45\) or \(0.452\) s | A1 | (3 marks) |
| \(F = \mu R = \frac{1}{5} \times 0.8g\) | B1 | |
| A: \(T' - F = 0.8a'\) | M1 A1 | |
| B: \(1.2g - T' = 1.2a'\) | B1 | |
| Solve: \(a' = 0.52g\) | M1 A1 | |
| \(0.6 = \frac{1}{2} \times 0.52g \times t^2\) | M1 | |
| \(t = 0.49\) or \(0.485\) s | A1 | (8 marks) |
## Part (a)
A: $T = 0.8a$ | B1 |
B: $1.2g - T = 1.2a$ | M1 A1 |
Solve: $T = 0.48g = 4.7$ N | M1 A1 | (5 marks)
## Part (b)
$a = 0.6g = 5.88$ | M1 |
Hence $0.6 = \frac{1}{2} \times 0.6g \times t^2$ | M1 |
$t = 0.45$ or $0.452$ s | A1 | (3 marks)
$F = \mu R = \frac{1}{5} \times 0.8g$ | B1 |
A: $T' - F = 0.8a'$ | M1 A1 |
B: $1.2g - T' = 1.2a'$ | B1 |
Solve: $a' = 0.52g$ | M1 A1 |
$0.6 = \frac{1}{2} \times 0.52g \times t^2$ | M1 |
$t = 0.49$ or $0.485$ s | A1 | (8 marks)
**Total: 16 marks**\includegraphics{figure_4}
A particle $A$ of mass 0.8 kg rests on a horizontal table and is attached to one end of a light inextensible string. The string passes over a small smooth pulley $P$ fixed at the edge of the table. The other end of the string is attached to a particle $B$ of mass 1.2 kg which hangs freely below the pulley, as shown in Fig. 4. The system is released from rest with the string taut and with $B$ at a height of 0.6 m above the ground. In the subsequent motion $A$ does not reach $P$ before $B$ reaches the ground. In an initial model of the situation, the table is assumed to be smooth. Using this model, find
\begin{enumerate}[label=(\alph*)]
\item the tension in the string before $B$ reaches the ground, [5]
\item the time taken by $B$ to reach the ground. [3]
\end{enumerate}
In a refinement of the model, it is assumed that the table is rough and that the coefficient of friction between $A$ and the table is $\frac{1}{4}$. Using this refined model,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item find the time taken by $B$ to reach the ground. [8]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2003 Q8 [16]}}