| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2017 |
| Session | November |
| Marks | 7 |
| 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 standard circular motion problem with a conical pendulum setup. Part (i) requires resolving forces vertically (a routine application of F=ma in circular motion), and part (ii) involves recognizing that contact is lost when the normal force becomes zero. Both parts use straightforward mechanics principles with clear geometric setup and no novel insight required, making it slightly easier than average. |
| Spec | 6.05b Circular motion: v=r*omega and a=v^2/r6.05c Horizontal circles: conical pendulum, banked tracks |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(T\sin60 + R = 0.6g\) | M1 | Resolves vertically |
| \(T\cos60 = 0.6 \times 0.5^2/(0.4\cos60)\) | M1 | Uses Newton's Second Law horizontally |
| \(T = 1.5\) | A1 | |
| \(R = 4.7(0) \text{ N}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(T\sin60 = 0.6g\) (leads to \(T = 6.9282...\)) | M1 | Resolve vertically. Note \(R = 0\) |
| \(6.9282...\cos60 = 0.6\,v^2/(0.4\cos60)\) | M1 | Use Newton's second Law horizontally |
| \(v = 1.07\) | A1 | Greatest value |
## Question 3(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $T\sin60 + R = 0.6g$ | M1 | Resolves vertically |
| $T\cos60 = 0.6 \times 0.5^2/(0.4\cos60)$ | M1 | Uses Newton's Second Law horizontally |
| $T = 1.5$ | A1 | |
| $R = 4.7(0) \text{ N}$ | A1 | |
## Question 3(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $T\sin60 = 0.6g$ (leads to $T = 6.9282...$) | M1 | Resolve vertically. Note $R = 0$ |
| $6.9282...\cos60 = 0.6\,v^2/(0.4\cos60)$ | M1 | Use Newton's second Law horizontally |
| $v = 1.07$ | A1 | Greatest value |
---3\\
\includegraphics[max width=\textwidth, alt={}, center]{8a7016eb-4e76-4104-aa00-fbf09e1d739a-04_305_510_264_813}
One end of a light inextensible string of length 0.4 m is attached to a fixed point $A$ which is above a smooth horizontal surface. A particle $P$ of mass 0.6 kg is attached to the other end of the string. $P$ moves in a circle on the surface with constant speed $v \mathrm {~m} \mathrm {~s} ^ { - 1 }$, with the string taut and making an angle of $60 ^ { \circ }$ with the horizontal (see diagram).\\
(i) Given that $v = 0.5$, calculate the magnitude of the force that the surface exerts on $P$.\\
(ii) Find the greatest possible value of $v$ for which $P$ remains in contact with the surface.\\
\hfill \mbox{\textit{CAIE M2 2017 Q3 [7]}}