| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Conical pendulum – horizontal circle in free space (no surface) |
| Difficulty | Moderate -0.3 This is a standard conical pendulum problem requiring resolution of forces and application of circular motion formulas (T cos θ = mg, T sin θ = mrω²). While it involves multiple steps and simultaneous equations, it follows a well-established method taught directly in M3 with no novel problem-solving required, making it slightly easier than average. |
| Spec | 6.05c Horizontal circles: conical pendulum, banked tracks |
A particle $P$ of mass 0.5 kg is attached to one end of a light inextensible string of length 1.5 m. The other end of the string is attached to a fixed point $A$. The particle is moving, with the string taut, in a horizontal circle with centre $O$ vertically below $A$. The particle is moving with constant angular speed 2.7 rad s$^{-1}$. Find
\begin{enumerate}[label=(\alph*)]
\item the tension in the string, [4]
\item the angle, to the nearest degree, that $AP$ makes with the downward vertical. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2005 Q1 [7]}}