| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2010 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Newton's laws and connected particles |
| Type | Two inclined planes, pulley at top |
| Difficulty | Standard +0.3 This is a standard connected particles problem requiring Newton's second law applied to two masses on an inclined plane. The question guides students through the solution by asking them to find tension first, then use it to find the coefficient of friction. While it involves multiple forces and components, the setup is conventional and the method is routine for M1 students who have practiced connected particles problems. Slightly easier than average due to the structured approach and standard techniques. |
| Spec | 3.03k Connected particles: pulleys and equilibrium3.03o Advanced connected particles: and pulleys3.03t Coefficient of friction: F <= mu*R model |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(0.36g\sin60° - T = 0.36 \times 0.25\) | B1 | |
| Tension is 3.03 N | B1 | AG |
| [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(T \pm F - 0.24g\sin60° = 0.24 \times 0.25\) | M1 | For applying Newton's second law to B |
| \(F = 3.03 - 0.24g\sin60° - 0.24 \times 0.25\) | A1 | |
| \((F = 0.889)\) | A1 | |
| \(R = 0.24g\cos60°\quad (R = 1.2)\) | B1 | |
| M1 | For using \(\mu = F/R\) | |
| Coefficient is 0.74 | A1 | |
| [6] |
## Question 4:
### Part (i):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $0.36g\sin60° - T = 0.36 \times 0.25$ | B1 | |
| Tension is 3.03 N | B1 | AG |
| **[2]** | | |
### Part (ii):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $T \pm F - 0.24g\sin60° = 0.24 \times 0.25$ | M1 | For applying Newton's second law to B |
| $F = 3.03 - 0.24g\sin60° - 0.24 \times 0.25$ | A1 | |
| $(F = 0.889)$ | A1 | |
| $R = 0.24g\cos60°\quad (R = 1.2)$ | B1 | |
| | M1 | For using $\mu = F/R$ |
| Coefficient is 0.74 | A1 | |
| **[6]** | | |
---4\\
\includegraphics[max width=\textwidth, alt={}, center]{dafc271d-a77b-4401-9170-e13e484d6e5f-3_499_567_260_788}
The diagram shows a vertical cross-section of a triangular prism which is fixed so that two of its faces are inclined at $60 ^ { \circ }$ to the horizontal. One of these faces is smooth and one is rough. Particles $A$ and $B$, of masses 0.36 kg and 0.24 kg respectively, are attached to the ends of a light inextensible string which passes over a small smooth pulley fixed at the highest point of the cross-section. $B$ is held at rest at a point of the cross-section on the rough face and $A$ hangs freely in contact with the smooth face (see diagram). $B$ is released and starts to move up the face with acceleration $0.25 \mathrm {~m} \mathrm {~s} ^ { - 2 }$.\\
(i) By considering the motion of $A$, show that the tension in the string is 3.03 N , correct to 3 significant figures.\\
(ii) Find the coefficient of friction between $B$ and the rough face, correct to 2 significant figures.
\hfill \mbox{\textit{CAIE M1 2010 Q4 [8]}}