| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Beam suspended by vertical ropes |
| Difficulty | Standard +0.3 This is a standard M1 statics problem requiring equilibrium of forces and moments about a point. The setup is straightforward with clearly defined masses and positions, requiring only routine application of ΣF=0 and taking moments. The constraint that T_P = 2T_Q simplifies the algebra considerably. While it has multiple parts and 9 marks total, each step follows a standard textbook method with no novel insight required, making it slightly easier than average. |
| Spec | 3.04b Equilibrium: zero resultant moment and force3.04c Use moments: beams, ladders, static problems |
| Answer | Marks | Guidance |
|---|---|---|
| (a) | resolve ↑: \(3T = 180g\) | M1 |
| \(T = 60g\), so tension in cable at \(P = 120g\) | A1 | |
| (b) | moments about \(P\): \(100gx + 60g(1.25) + 20g(1.5) = 3T\) | M2 A1 |
| \(100gx = 75g\), so \(x = 0.75\) and hence \(BP = 0.75\)m | M1 A1 | |
| (c) | (i) weight acts at middle of platform | B1 |
| (ii) platform doesn't bend | B1 | (9) |
(a) | resolve ↑: $3T = 180g$ | M1 |
| $T = 60g$, so tension in cable at $P = 120g$ | A1 |
(b) | moments about $P$: $100gx + 60g(1.25) + 20g(1.5) = 3T$ | M2 A1 |
| $100gx = 75g$, so $x = 0.75$ and hence $BP = 0.75$m | M1 A1 |
(c) | (i) weight acts at middle of platform | B1 |
| (ii) platform doesn't bend | B1 | (9) |\includegraphics{figure_1}
Figure 1 shows two window cleaners, Alan and Baber, of mass 60 kg and 100 kg respectively standing on a platform $PQ$ of length 3 metres and mass 20 kg. The platform is suspended by two vertical cables attached to the ends $P$ and $Q$. Alan is standing at the point $A$, 1.25 metres from $P$, Baber is standing at the point $B$ and the tension in the cable at $P$ is twice the tension in the cable at $Q$.
Modelling the platform as a uniform rod and Alan and Baber as particles,
\begin{enumerate}[label=(\alph*)]
\item find the tension in the cable at $P$, [2 marks]
\item find the distance $BP$. [5 marks]
\item State how you have used the modelling assumptions that
\begin{enumerate}[label=(\roman*)]
\item the platform is uniform,
\item the platform is a rod.
\end{enumerate}
[2 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q3 [9]}}