| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2001 |
| Session | June |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Two strings, two fixed points |
| Difficulty | Standard +0.3 This is a standard M3 circular motion problem with vertical axis rotation. Part (a) is simple trigonometry, part (b) requires resolving forces in two directions and applying F=mrω², and part (c) involves algebraic manipulation of inequalities. All techniques are routine for M3 students, making this slightly easier than average. |
| Spec | 6.05c Horizontal circles: conical pendulum, banked tracks |
\includegraphics{figure_4}
A particle $P$ of mass $m$ is attached to two light inextensible strings. The other ends of the string are attached to fixed points $A$ and $B$. The point $A$ is a distance $h$ vertically above $B$. The system rotates about the line $AB$ with constant angular speed $\omega$. Both strings are taut and inclined at $60°$ to $AB$, as shown in Fig. 4. The particle moves in a circle of radius $r$.
\begin{enumerate}[label=(\alph*)]
\item Show that $r = \frac{\sqrt{3}}{2}h$. [2]
\item Find, in terms of $m$, $g$, $h$ and $\omega$, the tension in $AP$ and the tension in $BP$. [8]
\end{enumerate}
The time taken for $P$ to complete one circle is $T$.
\begin{enumerate}[label=(\alph*)]\setcounter{enumi}{2}
\item Show that $T < \pi\sqrt{\left(\frac{2h}{g}\right)}$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2001 Q6 [14]}}