| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2013 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Particle inside smooth hollow cylinder |
| Difficulty | Standard +0.3 This is a straightforward circular motion problem requiring application of F=mv²/r for the horizontal force, then Pythagoras to find the resultant with the normal reaction balancing weight. The setup is clear, calculations are routine, and part (ii) explicitly guides students to the final answer. Slightly above average due to the two-component force resolution, but still a standard M2 exercise. |
| Spec | 6.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(F = 0.4 \times 1.5^2 / (0.6/2)\) | M1 | \(\text{Acc}^n = v^2/r\) (accept 0.6 as r) |
| \(F = 3\) N | A1 [2] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(R^2 = 3^2 + (0.4g)^2\) | M1 | Uses Pythagoras with normal force from base and answer (i) |
| \(R = 5\) | A1 (AG) [4] | From \(g = 10\) only |
## Question 1:
### Part (i)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $F = 0.4 \times 1.5^2 / (0.6/2)$ | M1 | $\text{Acc}^n = v^2/r$ (accept 0.6 as r) |
| $F = 3$ N | A1 [2] | |
### Part (ii)
| Answer/Working | Mark | Guidance |
|---|---|---|
| $R^2 = 3^2 + (0.4g)^2$ | M1 | Uses Pythagoras with normal force from base and answer (i) |
| $R = 5$ | A1 (AG) [4] | From $g = 10$ only |
---1 A small sphere of mass 0.4 kg moves with constant speed $1.5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in a horizontal circle inside a smooth fixed hollow cylinder of diameter 0.6 m . The axis of the cylinder is vertical, and the sphere is in contact with both the horizontal base and the vertical curved surface of the cylinder.\\
(i) Calculate the magnitude of the force exerted on the sphere by the vertical curved surface of the cylinder.\\
(ii) Hence show that the magnitude of the total force exerted on the sphere by the cylinder is 5 N .
\hfill \mbox{\textit{CAIE M2 2013 Q1 [4]}}