| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| 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 equilibrium conditions (sum of forces = 0, sum of moments = 0) with straightforward algebra. The given relationship between tensions simplifies the solution significantly, making it slightly easier than average for mechanics questions, though it requires careful setup of the moment equation. |
| Spec | 3.04a Calculate moments: about a point3.04b Equilibrium: zero resultant moment and force3.04c Use moments: beams, ladders, static problems |
| Answer | Marks |
|---|---|
| 2 | T 3T |
Question 2:
2 | T 3T
40g 20g
(a) R(↑): T + 3T = 40g + 20g M1
T = 15g, so tension at C is 45g or 441 N or 440 N A1
(2)
(b) M(B) 15g x 3 + 45g x d = 40g x 1.5 M1 A2,1,0√
↓
Solve: d = 1/3 or 0.33 or 0.333 m M1 A1
(5)
_________________________________________________________________\includegraphics{figure_1}
A plank $AB$ has mass 40 kg and length 3 m. A load of mass 20 kg is attached to the plank at $B$. The loaded plank is held in equilibrium, with $AB$ horizontal, by two vertical ropes attached at $A$ and $C$, as shown in Figure 1. The plank is modelled as a uniform rod and the load as a particle. Given that the tension in the rope at $C$ is three times the tension in the rope at $A$, calculate
\begin{enumerate}[label=(\alph*)]
\item the tension in the rope at $C$, [2]
\item the distance $CB$. [5]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2005 Q2 [7]}}