| Exam Board | SPS |
|---|---|
| Module | SPS ASFM (SPS ASFM) |
| Year | 2020 |
| Session | May |
| Marks | 6 |
| Topic | Work done and energy |
| Type | Particle on smooth curved surface |
| Difficulty | Standard +0.3 This is a standard circular motion energy conservation problem with straightforward application of formulas. Part (a) requires direct use of energy conservation to find speed at a given angle, and part (b) asks whether the bead reaches the top—both are routine A-level mechanics exercises with clear methods and minimal problem-solving insight required. |
| Spec | 6.02i Conservation of energy: mechanical energy principle6.05d Variable speed circles: energy methods |
\includegraphics{figure_7}
A smooth wire is shaped into a circle of radius 2.5 m which is fixed in a vertical plane with its centre at a point $O$. A small bead $B$ is threaded onto the wire. $B$ is held with $OB$ vertical and is then projected horizontally with an initial speed of $8.4 \mathrm{ms}^{-1}$ (see diagram).
\begin{enumerate}[label=(\alph*)]
\item Find the speed of $B$ at the instant when $OB$ makes an angle of 0.8 radians with the downward vertical through $O$. [3]
\item Determine whether $B$ has sufficient energy to reach the point on the wire vertically above $O$. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS ASFM 2020 Q7 [6]}}