| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2002 |
| Session | January |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Beam suspended by vertical ropes |
| Difficulty | Moderate -0.3 This is a standard M1 moments problem requiring taking moments about a point and resolving vertically. The setup is straightforward with clearly defined forces and positions, though it involves some algebraic manipulation across multiple steps. Slightly easier than average due to being a textbook application of equilibrium principles with no conceptual surprises. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force |
| Answer | Marks | Guidance |
|---|---|---|
| \(150 \downarrow\) \(\omega\) \(\downarrow w\) \(\downarrow 250\) all rest \(\omega\) | B1 | G1 (2) |
| Answer | Marks | Guidance |
|---|---|---|
| [Allow M1 A2, 1,0 for moments eqn at any pt. Then m1 A1 for complete soln \(\Rightarrow T =\) ] | M1 A2,1,0 | M1 A1 (5) |
| Answer | Marks |
|---|---|
| (M1 needs complete soln \(\Rightarrow W\text{R} =\) ) | M1 A1 (2) |
| Answer | Marks |
|---|---|
| By having weight act at centre/mid-pt. | B1 (1) (18) |
## Part (a)
$1\uparrow T$ 4 O 2 $\uparrow 3T$
$150 \downarrow$ $\omega$ $\downarrow w$ $\downarrow 250$ all rest $\omega$ | B1 | G1 (2)
## Part (b)
$M(o): 150.5 + 3T.2 = T.4 + 250.5$
Solve: $T = 250\text{ N}$
[Allow M1 A2, 1,0 for moments eqn at any pt. Then m1 A1 for complete soln $\Rightarrow T =$ ] | M1 A2,1,0 | M1 A1 (5)
## Part (c)
$R(\uparrow)$ $4T = 450 + W$ $\Rightarrow W = 600\text{ N}$
(M1 needs complete soln $\Rightarrow W\text{R} =$ ) | M1 A1 (2)
## Part (d)
By having weight act at centre/mid-pt. | B1 (1) (18)
---\includegraphics{figure_1}
A heavy uniform steel girder $AB$ has length 10 m. A load of weight 150 N is attached to the girder at $A$ and a load of weight 250 N is attached to the girder at $B$. The loaded girder hangs in equilibrium in a horizontal position, held by two vertical steel cables attached to the girder at the points $C$ and $D$, where $AC = 1$ m and $DB = 3$ m, as shown in Fig. 1. The girder is modelled as a uniform rod, the loads as particles and the cables as light inextensible strings. The tension in the cable at $D$ is three times the tension in the cable at $C$.
\begin{enumerate}[label=(\alph*)]
\item Draw a diagram showing all the forces acting on the girder. [2]
\end{enumerate}
Find
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item the tension in the cable at $C$, [5]
\item the weight of the girder. [2]
\item Explain how you have used the fact that the girder is uniform. [1]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2002 Q5 [10]}}