| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2019 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Circular Motion 2 |
| Type | Ratio of tensions/forces |
| Difficulty | Challenging +1.2 This is a standard Further Maths circular motion problem requiring application of Newton's second law at two points, energy conservation between A and B, and solving simultaneous equations. While it involves multiple steps and careful angle geometry, the techniques are well-practiced in FM2 and the 'show that' format guides students to the answer. The algebraic manipulation is moderate but systematic. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.05d Variable speed circles: energy methods6.05e Radial/tangential acceleration |
2 A particle $P$ of mass $m$ is attached to one end of a light inextensible string of length $a$. The other end of the string is attached to a fixed point $O$. The particle $P$ is moving in a complete vertical circle about $O$. The points $A$ and $B$ are on the circle, at opposite ends of a diameter, and such that $O A$ makes an acute angle $\alpha$ with the upward vertical through $O$. The speed of $P$ as it passes through $A$ is $\frac { 3 } { 2 } \sqrt { } ( a g )$. The tension in the string when $P$ is at $B$ is four times the tension in the string when $P$ is at $A$.\\
(i) Show that $\cos \alpha = \frac { 3 } { 4 }$.\\
(ii) Find the tension in the string when $P$ is at $B$.\\
\hfill \mbox{\textit{CAIE FP2 2019 Q2 [8]}}