| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2016 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Particle on table with string above |
| Difficulty | Standard +0.3 This is a standard circular motion problem requiring resolution of tension forces and application of F=mv²/r. Part (i) involves straightforward calculation using Pythagoras and circular motion equation. Part (ii) requires recognizing that maximum tension occurs when the ball is about to lose contact with the table (normal reaction = 0), then solving for angular speed - a common extension but still routine for M2 level. |
| 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 |
| \(\theta (= \tan^{-1}0.45/0.6 = 36.87...) = 36.9°\) | B1 | Or \(\tan\theta = 3/4\) |
| \(0.4v^2/0.6 = 5\cos\theta\) | M1 | |
| \(v = 2.45\text{ ms}^{-1}\) | A1 | Total: 3 marks; Or \(\sqrt{6}\) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(T\sin\theta = 0.4g\) | M1 | |
| \(T = 6.67\) N | A1 | Accept \(0.66,\; 6\frac{2}{3},\; 20/3\) |
| \(0.4\omega^2 \times 0.6 = 6.67\cos\theta\) | M1 | |
| \(\omega = 4.71\text{ rad s}^{-1}\) | A1 | Total: 4 marks; Accept \(4.72\text{ rad s}^{-1}\) |
## Question 5:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\theta (= \tan^{-1}0.45/0.6 = 36.87...) = 36.9°$ | B1 | Or $\tan\theta = 3/4$ |
| $0.4v^2/0.6 = 5\cos\theta$ | M1 | |
| $v = 2.45\text{ ms}^{-1}$ | A1 | Total: 3 marks; Or $\sqrt{6}$ |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $T\sin\theta = 0.4g$ | M1 | |
| $T = 6.67$ N | A1 | Accept $0.66,\; 6\frac{2}{3},\; 20/3$ |
| $0.4\omega^2 \times 0.6 = 6.67\cos\theta$ | M1 | |
| $\omega = 4.71\text{ rad s}^{-1}$ | A1 | Total: 4 marks; Accept $4.72\text{ rad s}^{-1}$ |
---5 A small ball $B$ of mass 0.4 kg moves in a horizontal circle with centre $O$ and radius 0.6 m on a smooth horizontal surface. One end of a light inextensible string is attached to $B$; the other end of the string is attached to a fixed point 0.45 m vertically above $O$.\\
(i) Given that the tension in the string is 5 N , calculate the speed of $B$.\\
(ii) Find the greatest possible tension in the string for the motion, and the corresponding angular speed of $B$.
\hfill \mbox{\textit{CAIE M2 2016 Q5 [7]}}