| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2012 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Vertically connected particles, air resistance |
| Difficulty | Moderate -0.3 This is a standard two-part connected particles question requiring basic application of Newton's second law. Part (i) involves straightforward equilibrium (tension equals weight below), and part (ii) requires treating the system as a whole then finding internal tension - both are routine M1 techniques with no novel problem-solving required. |
| Spec | 3.03d Newton's second law: 2D vectors3.03k Connected particles: pulleys and equilibrium |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Tension in \(S_1\) is 30 N | B1 | |
| Tension in \(S_2\) is 50 N | B1 | [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| M1 | For applying Newton's second law to A or to B | |
| \(3g - T - 1.6 = 3a\) (or \(2g + T - 4 = 2a\)) | A1 | |
| \(2g + T - 4 = 2a\) (or \(3g - T - 1.6 = 3a\)) or \((3g+2g)-(1.6+4) = (3+2)a\) | B1 | |
| Acceleration is \(8.88\ \text{ms}^{-2}\) | B1 | |
| Tension is 1.76 N | A1 | [5] |
# Question 5:
**(i)**
| Answer/Working | Mark | Guidance |
|---|---|---|
| Tension in $S_1$ is 30 N | B1 | |
| Tension in $S_2$ is 50 N | B1 | [2] |
**(ii)**
| Answer/Working | Mark | Guidance |
|---|---|---|
| | M1 | For applying Newton's second law to A or to B |
| $3g - T - 1.6 = 3a$ (or $2g + T - 4 = 2a$) | A1 | |
| $2g + T - 4 = 2a$ (or $3g - T - 1.6 = 3a$) or $(3g+2g)-(1.6+4) = (3+2)a$ | B1 | |
| Acceleration is $8.88\ \text{ms}^{-2}$ | B1 | |
| Tension is 1.76 N | A1 | [5] |
SR (max 1/2) for candidates who do not give numerical answers in (i). Allow B1 for Tension in $S_1$ is $3g$ and Tension in $S_2$ is $5g$.
---5\\
\includegraphics[max width=\textwidth, alt={}, center]{fa0e0e0d-b0a6-44e0-8b4f-4923e235c6c6-3_529_195_255_977}
A block $A$ of mass 3 kg is attached to one end of a light inextensible string $S _ { 1 }$. Another block $B$ of mass 2 kg is attached to the other end of $S _ { 1 }$, and is also attached to one end of another light inextensible string $S _ { 2 }$. The other end of $S _ { 2 }$ is attached to a fixed point $O$ and the blocks hang in equilibrium below $O$ (see diagram).\\
(i) Find the tension in $S _ { 1 }$ and the tension in $S _ { 2 }$.
The string $S _ { 2 }$ breaks and the particles fall. The air resistance on $A$ is 1.6 N and the air resistance on $B$ is 4 N .\\
(ii) Find the acceleration of the particles and the tension in $S _ { 1 }$.
\hfill \mbox{\textit{CAIE M1 2012 Q5 [7]}}