| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Applied force in addition to weights |
| Difficulty | Standard +0.3 This is a standard two-part pulley problem with friction requiring straightforward application of Newton's laws and limiting equilibrium conditions. Part (i) involves basic force balance with friction opposing motion, while part (ii) adds an applied force but still follows routine mechanics procedures. The calculations are direct with no conceptual surprises, making it slightly easier than average for M1. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03t Coefficient of friction: F <= mu*R model3.03u Static equilibrium: on rough surfaces |
| Answer | Marks |
|---|---|
| 4 | (i) |
| (ii) | T = 0.2g and T = F |
| Answer | Marks |
|---|---|
| X = 2.8 | M1 |
| Answer | Marks |
|---|---|
| A1 ft 3 | For resolving forces vertically |
| Answer | Marks | Guidance |
|---|---|---|
| Page 3 | Mark Scheme | Syllabus |
| A AND AS LEVEL – JUNE 2005 | 9709 | 4 |
Question 4:
4 | (i)
(ii) | T = 0.2g and T = F
µ
R = 0.3g and 0.2g = R
Coefficient is 2/3
F = 2/3(0.3g – 1.8) (= 0.8)
X = 2.8 | M1
A1
M1
A1 4
B1
B1ft
M1
A1 ft 3 | For resolving forces vertically
on A and horizontally on B
For resolving forces vertically
µ
on B and using F = R
SR (max 1 / 4) for candidates
who do not use a = 0
µ
0.2g – 0.3 g = 0.5a
µ
ft wrong
For using X = T + F (correct
signs needed)
ft incorrect values of T(from part
(i)) and/or µ
Page 3 | Mark Scheme | Syllabus | Paper
A AND AS LEVEL – JUNE 2005 | 9709 | 4\includegraphics{figure_4}
Particles $A$ and $B$, of masses $0.2 \text{ kg}$ and $0.3 \text{ kg}$ respectively, are connected by a light inextensible string. The string passes over a smooth pulley at the edge of a rough horizontal table. Particle $A$ hangs freely and particle $B$ is in contact with the table (see diagram).
\begin{enumerate}[label=(\roman*)]
\item The system is in limiting equilibrium with the string taut and $A$ about to move downwards. Find the coefficient of friction between $B$ and the table.
[4]
\end{enumerate}
A force now acts on particle $B$. This force has a vertical component of $1.8 \text{ N}$ upwards and a horizontal component of $X \text{ N}$ directed away from the pulley.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item The system is now in limiting equilibrium with the string taut and $A$ about to move upwards. Find $X$.
[3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2005 Q4 [7]}}