| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2017 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Elastic string – horizontal circle on surface |
| Difficulty | Moderate -0.5 This is a straightforward circular motion problem requiring direct application of standard formulas (v = rω to find radius, then Hooke's law with centripetal force). Both parts involve single-step calculations with clearly given data and no conceptual challenges beyond recalling the basic relationships. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Notes |
| \((4 = 5r)\) \(r = 0.8\) m | B1 | Uses \(v = r\omega\) |
| Total: 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Notes |
| \(T = 0.2 \times 5^2 \times 0.8\) | M1 | Uses Newton's Second Law horizontally |
| \(T = 4\) N | A1 FT | FT with their radius from part (i) |
| \(4 = \lambda(0.8 - 0.6)/0.6\) | M1 | Uses \(T = \frac{\lambda x}{L}\) |
| \(\lambda = 12\) | A1 | |
| Total: 4 |
## Question 1:
**Part (i)**
| Answer | Marks | Notes |
|--------|-------|-------|
| $(4 = 5r)$ $r = 0.8$ m | B1 | Uses $v = r\omega$ |
| **Total: 1** | | |
**Part (ii)**
| Answer | Marks | Notes |
|--------|-------|-------|
| $T = 0.2 \times 5^2 \times 0.8$ | M1 | Uses Newton's Second Law horizontally |
| $T = 4$ N | A1 FT | FT with their radius from part (i) |
| $4 = \lambda(0.8 - 0.6)/0.6$ | M1 | Uses $T = \frac{\lambda x}{L}$ |
| $\lambda = 12$ | A1 | |
| **Total: 4** | | |
---1 A particle $P$ of mass 0.2 kg moves with speed $4 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and angular speed $5 \mathrm { rad } \mathrm { s } ^ { - 1 }$ in a horizontal circle on a smooth surface. $P$ is attached to one end of a light elastic string of natural length 0.6 m . The other end of the string is attached to the point on the surface which is the centre of the circular motion of $P$.\\
(i) Find the radius of this circle.\\
(ii) Find the modulus of elasticity of the string.\\
\hfill \mbox{\textit{CAIE M2 2017 Q1 [5]}}