Standard +0.8 This is a challenging statics problem requiring resolution of forces in two directions, taking moments about a strategic point, applying friction laws at two surfaces simultaneously, and solving the resulting system of equations. The limiting equilibrium at both contacts adds significant complexity beyond standard ladder problems, requiring careful algebraic manipulation across multiple equations to find x.
A uniform ladder \(AB\) of mass 35 kg and length 7 m rests with its end \(A\) on rough horizontal ground and its end \(B\) against a rough vertical wall. The ladder is inclined at an angle of \(45°\) to the horizontal. A man of mass 70 kg is standing on the ladder at a point \(C\), which is \(x\) metres from \(A\). The coefficient of friction between the ladder and the wall is \(\frac{1}{4}\) and the coefficient of friction between the ladder and the ground is \(\frac{1}{2}\).
The system is in limiting equilibrium.
Find \(x\). [8]
A uniform ladder $AB$ of mass 35 kg and length 7 m rests with its end $A$ on rough horizontal ground and its end $B$ against a rough vertical wall. The ladder is inclined at an angle of $45°$ to the horizontal. A man of mass 70 kg is standing on the ladder at a point $C$, which is $x$ metres from $A$. The coefficient of friction between the ladder and the wall is $\frac{1}{4}$ and the coefficient of friction between the ladder and the ground is $\frac{1}{2}$.
The system is in limiting equilibrium.
Find $x$. [8]
\hfill \mbox{\textit{OCR H240/03 2017 Q14 [8]}}