| Exam Board | OCR MEI |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2008 |
| Session | January |
| Marks | 18 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Uniform beam on two supports |
| Difficulty | Standard +0.3 This is a standard M2 moments/equilibrium question with multiple parts building on each other. Part (i) is straightforward moment calculation (shown), part (ii) uses basic equilibrium equations, part (iii) involves resolving moments with the beam at an angle. While it requires careful bookkeeping across several parts and understanding of perpendicular distances when the beam is tilted, all techniques are routine for M2 students with no novel problem-solving required. Slightly easier than average due to the scaffolded structure and standard methods throughout. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force6.04e Rigid body equilibrium: coplanar forces |
Fig. 4.1 shows a uniform beam, CE, of weight 2200 N and length 4.5 m. The beam is freely pivoted on a fixed support at D and is supported at C. The distance CD is 2.75 m.
\includegraphics{figure_4}
The beam is horizontal and in equilibrium.
\begin{enumerate}[label=(\roman*)]
\item Show that the anticlockwise moment of the weight of the beam about D is 1100 N m.
Find the value of the normal reaction on the beam of the support at C. [6]
\end{enumerate}
The support at C is removed and spheres at P and Q are suspended from the beam by light strings attached to the points C and R. The sphere at P has weight 440 N and the sphere at Q has weight $W$ N. The point R of the beam is 1.5 m from D. This situation is shown in Fig. 4.2.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item The beam is horizontal and in equilibrium. Show that $W = 1540$. [3]
\end{enumerate}
The sphere at P is changed for a lighter one with weight 400 N. The sphere at Q is unchanged. The beam is now held in equilibrium at an angle of 20° to the horizontal by means of a light rope attached to the beam at E. This situation (but without the rope at E) is shown in Fig. 4.3.
\includegraphics{figure_5}
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{2}
\item Calculate the tension in the rope when it is
\begin{enumerate}[label=(\Alph*)]
\item at 90° to the beam, [6]
\item horizontal. [3]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{OCR MEI M2 2008 Q4 [18]}}