| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2019 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Particle on table with string above |
| Difficulty | Moderate -0.3 This is a straightforward circular motion problem requiring standard application of Newton's second law and geometry. Students must find the radius using Pythagoras (0.4m), calculate centripetal force (T sin θ = mrω²), then resolve vertically for the normal reaction. All steps are routine with no novel insight required, making it slightly easier than average. |
| Spec | 3.03b Newton's first law: equilibrium6.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| \(r = 0.4\) m | B1 | Use Pythagoras's theorem |
| \(T\cos\theta = 0.4 \times 5^2 \times 0.4\) | M1 | Use Newton's Second Law |
| \(T \times \frac{0.4}{0.5} = 4,\ T = 5\text{N}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| \(R = 0.4g - T\sin\theta\) | M1 | Resolve vertically. Allow for their \(T\) for M1 |
| \(R = 1\text{N}\) | A1 |
## Question 3(i):
| $r = 0.4$ m | B1 | Use Pythagoras's theorem |
| $T\cos\theta = 0.4 \times 5^2 \times 0.4$ | M1 | Use Newton's Second Law |
| $T \times \frac{0.4}{0.5} = 4,\ T = 5\text{N}$ | A1 | |
## Question 3(ii):
| $R = 0.4g - T\sin\theta$ | M1 | Resolve vertically. Allow for their $T$ for M1 |
| $R = 1\text{N}$ | A1 | |
---3 A particle $P$ of mass 0.4 kg is attached to a fixed point $A$ by a light inextensible string of length 0.5 m . The point $A$ is 0.3 m above a smooth horizontal surface. The particle $P$ moves in a horizontal circle on the surface with constant angular speed $5 \mathrm { rad } \mathrm { s } ^ { - 1 }$.\\
(i) Calculate the tension in the string.\\
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(ii) Find the magnitude of the force exerted by the surface on $P$.\\
\hfill \mbox{\textit{CAIE M2 2019 Q3 [5]}}