| Exam Board | OCR |
|---|---|
| Module | Further Mechanics (Further Mechanics) |
| Year | 2021 |
| Session | June |
| Marks | 9 |
| Topic | Circular Motion 2 |
| Type | Conical pendulum (horizontal circle) |
| Difficulty | Standard +0.8 This is a Further Mechanics conical pendulum problem requiring resolution of forces in 3D (tension, normal reaction, weight) with the constraint that the particle moves on the cone's surface. Students must find the geometry (angle from vertical using cone dimensions), apply Hooke's law for tension, then use circular motion dynamics with F=mrω². While systematic, it requires careful geometric reasoning and coordination of multiple concepts beyond standard A-level, placing it moderately above average difficulty. |
| Spec | 6.02h Elastic PE: 1/2 k x^26.02i Conservation of energy: mechanical energy principle6.05c Horizontal circles: conical pendulum, banked tracks |
3 A right circular cone $C$ of height 4 m and base radius 3 m has its base fixed to a horizontal plane. One end of a light elastic string of natural length 2 m and modulus of elasticity 32 N is fixed to the vertex of $C$. The other end of the string is attached to a particle $P$ of mass 2.5 kg .\\
$P$ moves in a horizontal circle with constant speed and in contact with the smooth curved surface of $C$. The extension of the string is 1.5 m .
\begin{enumerate}[label=(\alph*)]
\item Find the tension in the string.
\item Find the speed of $P$.
\end{enumerate}
\hfill \mbox{\textit{OCR Further Mechanics 2021 Q3 [9]}}