| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2021 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Pulley systems |
| Type | Variable mass or unknown mass |
| Difficulty | Standard +0.3 This is a standard two-particle pulley problem requiring Newton's second law applied to both masses (finding m from given tension) and then kinematics or energy methods (finding final speed). The setup is straightforward with clearly stated conditions, requiring routine application of F=ma to a connected system and basic SUVAT/energy calculations. Slightly easier than average due to the direct nature of both parts and standard pulley mechanics. |
| Spec | 3.03k Connected particles: pulleys and equilibrium6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks |
|---|---|
| 2(a) | 0.1 kg particle T −0.1g =0.1a |
| Answer | Marks | Guidance |
|---|---|---|
| System mg−0.1g =( m+0.1 ) a | M1 | Apply Newton’s 2nd law to either the 0.1 kg particle, the m kg |
| Answer | Marks |
|---|---|
| A1 | Two correct equations |
| Answer | Marks | Guidance |
|---|---|---|
| Solve for m a=5 | M1 | From 2 equations with the correct number of relevant terms |
| m=0.3 | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
| Answer | Marks | Guidance |
|---|---|---|
| 2(b) | v2 =0+2×5×0.9 | M1 |
| v=3 m s–1 | A1 FT | FT on 1.8a |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 2:
--- 2(a) ---
2(a) | 0.1 kg particle T −0.1g =0.1a
m kg particle mg−T =ma
System mg−0.1g =( m+0.1 ) a | M1 | Apply Newton’s 2nd law to either the 0.1 kg particle, the m kg
particle or to the system, correct number of terms
A1 | Two correct equations
[ ]
Solve for m a=5 | M1 | From 2 equations with the correct number of relevant terms
m=0.3 | A1
4
Question | Answer | Marks | Guidance
--- 2(b) ---
2(b) | v2 =0+2×5×0.9 | M1 | Use of v2 =u2 +2as with u=0, s=0.9 and their a≠±g
v=3 m s–1 | A1 FT | FT on 1.8a
2
Question | Answer | Marks | Guidance\includegraphics{figure_2}
Two particles $A$ and $B$ have masses $m$ kg and 0.1 kg respectively, where $m > 0.1$. The particles are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley and the particles hang vertically below it. Both particles are at a height of 0.9 m above horizontal ground (see diagram). The system is released from rest, and while both particles are in motion the tension in the string is 1.5 N. Particle $B$ does not reach the pulley.
\begin{enumerate}[label=(\alph*)]
\item Find $m$. [4]
\item Find the speed at which $A$ reaches the ground. [2]
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2021 Q2 [6]}}