| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| 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 involving moments and equilibrium. Part (a) requires taking moments about a point and resolving vertically with a light rod (routine textbook exercise). Part (b) adds the complication of a uniform rod and a given ratio of tensions, requiring algebraic manipulation but still following standard procedures. The multi-part structure and need to set up moment equations makes it slightly above average difficulty, but it's a very typical M1 question with no novel insight required. |
| Spec | 3.04b Equilibrium: zero resultant moment and force3.04c Use moments: beams, ladders, static problems |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(T_P + T_Q = 22g\) | \(M(A): 1.5(5g) + 3.5(8g) = 4.5T_Q\) | \(T_Q = 37g + 4.5 = 80.6 \text{ N}\) |
| (b) \(2.5T_Q = 22g + mg\) | \(M(A): mg(2.25) + 9g + 28g = 4.5T_Q\) | \(2.25m + 37 = 39.6 + 1.8m\) |
(a) $T_P + T_Q = 22g$ | $M(A): 1.5(5g) + 3.5(8g) = 4.5T_Q$ | $T_Q = 37g + 4.5 = 80.6 \text{ N}$ | $T_P = 22g - T_Q = 135 \text{ N}$ | B1 M1 A1 M1 A1 A1
(b) $2.5T_Q = 22g + mg$ | $M(A): mg(2.25) + 9g + 28g = 4.5T_Q$ | $2.25m + 37 = 39.6 + 1.8m$ | $0.45m = 2.6$ | $m = 5.78$ | B1 M1 A1 M1 A1 A1 | **12 marks**In a theatre, three lights $A$, $B$ and $C$ are suspended from a horizontal beam $XY$ of length 4.5 m. $A$ and $C$ are each of mass 8 kg and $B$ is of mass 6 kg. The beam $XY$ is held in place by vertical ropes $PX$ and $QY$, as shown.
\includegraphics{figure_8}
In a simple mathematical model of this situation, $XY$ is modelled as a light rod.
\begin{enumerate}[label=(\alph*)]
\item Calculate the tension in each of $PX$ and $QY$. [6 marks]
\end{enumerate}
In a refined model, $XY$ is modelled as a uniform rod of mass $m$ kg.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item If the tension in $PX$ is 1.5 times that in $QY$, calculate the value of $m$. [6 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q8 [12]}}