| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2002 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Conical pendulum – horizontal circle in free space (no surface) |
| Difficulty | Standard +0.3 This is a standard conical pendulum problem requiring resolution of forces and circular motion equations. While it involves multiple steps (resolving vertically for angle, then horizontally for radius/length), the approach is straightforward and commonly practiced in M3. The given tension simplifies the algebra considerably, making this slightly easier than average for this module. |
| Spec | 3.03d Newton's second law: 2D vectors3.03e Resolve forces: two dimensions6.05c Horizontal circles: conical pendulum, banked tracks |
\includegraphics{figure_1}
A metal ball $B$ of mass $m$ is attached to one end of a light inextensible string. The other end of the string is attached to a fixed point $A$. The ball $B$ moves in a horizontal circle with centre $O$ vertically below $A$, as shown in Fig. 1. The string makes a constant angle $\alpha°$ with the downward vertical and $B$ moves with constant angular speed $\sqrt{(2gk)}$, where $k$ is a constant. The tension in the string is $3mg$. By modelling $B$ as a particle, find
\begin{enumerate}[label=(\alph*)]
\item the value of $\alpha$,
[4]
\item the length of the string.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2002 Q2 [9]}}