| 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 | Standard +0.3 This is a standard conical pendulum problem with straightforward application of circular motion principles and Newton's second law. Part (i) requires resolving forces and using F=mv²/r with given values. Part (ii) involves recognizing that contact is lost when normal reaction becomes zero. The geometry is given, calculations are routine, and no novel insight is required—slightly easier than average A-level mechanics. |
| 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 | |
| \(R = 4.70\) N | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(T\sin60 = 0.6g\), leads to \(T = 6.9282...\) | M1 | Resolve vertically. Note \(R = 0\) |
| \(6.9282...\cos60 = 0.6v^2/(0.4\cos60)\) | 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 | |
| $R = 4.70$ N | A1 | |
## Question 3(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $T\sin60 = 0.6g$, leads to $T = 6.9282...$ | M1 | Resolve vertically. Note $R = 0$ |
| $6.9282...\cos60 = 0.6v^2/(0.4\cos60)$ | M1 | Use Newton's Second Law horizontally |
| $v = 1.07$ | A1 | Greatest value |
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\includegraphics[max width=\textwidth, alt={}, center]{2e4e6e32-eafc-4196-aaa8-42909cc2078e-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]}}