| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2008 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 2 |
| Type | String through hole/bead on string |
| Difficulty | Standard +0.3 This is a standard circular motion problem with a bead on a string requiring resolution of forces and application of F=ma in circular motion. The geometry is given explicitly, making it straightforward to find angles and apply tension equations. Part (i) is a 'show that' which guides students to the answer, and part (ii) follows directly from standard circular motion formula. Slightly above average due to 3D geometry and two-part structure, but well within typical M2 scope. |
| Spec | 3.03d Newton's second law: 2D vectors3.03e Resolve forces: two dimensions6.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \([T\sin ORC + T\sin ORD = mg]\) | M1 | For resolving forces on R vertically |
| \(Tx1.6/2 + Tx0.5/1.3 = 0.2x10\) | A1 | |
| Tension is 1.69N | A1 | Subtotal: 3 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \([T\cos ORC + T\cos ORD = mv^2/r]\) | M1 | For using Newton's second law horizontally |
| \(Tx1.2/2 + Tx1.2/1.3 = 0.2v^2/1.2\) | A1 | |
| \(v = 3.93\) | A1 | Subtotal: 3. Total: 6 |
## Question 3:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $[T\sin ORC + T\sin ORD = mg]$ | M1 | For resolving forces on R vertically |
| $Tx1.6/2 + Tx0.5/1.3 = 0.2x10$ | A1 | |
| Tension is 1.69N | A1 | **Subtotal: 3** |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $[T\cos ORC + T\cos ORD = mv^2/r]$ | M1 | For using Newton's second law horizontally |
| $Tx1.2/2 + Tx1.2/1.3 = 0.2v^2/1.2$ | A1 | |
| $v = 3.93$ | A1 | **Subtotal: 3. Total: 6** |
---3\\
\includegraphics[max width=\textwidth, alt={}, center]{36259e2a-aa9b-4655-b0c2-891f96c3f5a4-3_637_572_264_788}
One end of a light inextensible string is attached to a point $C$. The other end is attached to a point $D$, which is 1.1 m vertically below $C$. A small smooth ring $R$, of mass 0.2 kg , is threaded on the string and moves with constant speed $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$ in a horizontal circle, with centre at $O$ and radius 1.2 m , where $O$ is 0.5 m vertically below $D$ (see diagram).\\
(i) Show that the tension in the string is 1.69 N , correct to 3 significant figures.\\
(ii) Find the value of $v$.
\hfill \mbox{\textit{CAIE M2 2008 Q3 [6]}}