| Exam Board | SPS |
|---|---|
| Module | SPS FM Mechanics (SPS FM Mechanics) |
| Year | 2022 |
| Session | January |
| Marks | 9 |
| Topic | Circular Motion 1 |
| Type | Particle on cone surface – with string attached to vertex or fixed point |
| Difficulty | Challenging +1.2 This is a standard Further Maths mechanics problem combining elastic strings (Hooke's law) with circular motion on a cone. Part (i) is straightforward application of T = λx/l. Part (ii) requires resolving forces in a conical pendulum setup and using circular motion equations, which is a well-practiced FM technique. The geometry is given explicitly (cone dimensions), making this a multi-step but routine application of standard methods rather than requiring novel insight. |
| Spec | 6.02g Hooke's law: T = k*x or T = lambda*x/l6.05c Horizontal circles: conical pendulum, banked tracks |
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=(\roman*)]
\item Find the tension in the string.
[2]
\item Find the speed of P.
[7]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Mechanics 2022 Q5 [9]}}