| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2017 |
| Session | October |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Uniform beam on two supports |
| Difficulty | Moderate -0.8 This is a standard M1 moments question requiring straightforward application of equilibrium conditions (sum of moments = 0, sum of forces = 0) with clearly defined geometry. Part (a) involves taking moments about one point to find reactions, while part (b) requires setting up an equation with the given constraint. The calculations are routine with no conceptual challenges beyond basic mechanics principles. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
\includegraphics{figure_1}
A metal girder $AB$, of weight 1080 N and length 6 m, rests in equilibrium in a horizontal position on two supports, one at $C$ and one at $D$, where $AC = 0.5$ m and $BD = 2$ m, as shown in Figure 1. A boy of weight 400 N stands on the girder at $B$ and the girder remains horizontal and in equilibrium. The boy is modelled as a particle and the girder is modelled as a uniform rod.
\begin{enumerate}[label=(\alph*)]
\item Find
\begin{enumerate}[label=(\roman*)]
\item the magnitude of the reaction on the girder at $C$,
\item the magnitude of the reaction on the girder at $D$.
\end{enumerate}
[6]
\end{enumerate}
The boy now stands at a point $E$ on the girder, where $AE = x$ metres, and the girder remains horizontal and in equilibrium. Given that the magnitude of the reaction on the girder at $D$ is now 520 N greater than the magnitude of the reaction on the girder at $C$,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item find the value of $x$.
[5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2017 Q2 [11]}}