| Exam Board | OCR |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Forces, equilibrium and resultants |
| Type | Smooth ring on string |
| Difficulty | Moderate -0.3 This is a standard M1 equilibrium problem with three forces on a particle. Part (i) tests understanding of smooth rings (1 mark recall), part (ii) requires resolving forces in two directions to find tension (routine technique), and part (iii) uses the result to find mass. The geometry is straightforward and all steps follow standard procedures with no novel insight required, making it slightly easier than average. |
| Spec | 3.03m Equilibrium: sum of resolved forces = 03.03n Equilibrium in 2D: particle under forces |
\includegraphics{figure_1}
A light inextensible string has its ends attached to two fixed points $A$ and $B$. The point $A$ is vertically above $B$. A smooth ring $R$ of mass $m$ kg is threaded on the string and is pulled by a force of magnitude $1.6$ N acting upwards at $45°$ to the horizontal. The section $AR$ of the string makes an angle of $30°$ with the downward vertical and the section $BR$ is horizontal (see diagram). The ring is in equilibrium with the string taut.
\begin{enumerate}[label=(\roman*)]
\item Give a reason why the tension in the part $AR$ of the string is the same as that in the part $BR$. [1]
\item Show that the tension in the string is $0.754$ N, correct to 3 significant figures. [3]
\item Find the value of $m$. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q1 [7]}}