Day: December 1, 2022

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202212011713 Solution to 1974-HL-PHY-I-2

A uniform ladder 6\,\mathrm{m} long and weighing 390\,\mathrm{N} rests with one end on the rough ground and the other end against a smooth wall. The ladder makes an angle of 60^\circ with the ground, and the coefficient of friction between the ladder and ground is 0.8.

(a) Draw a diagram to indicate the forces acting on the ladder.
(b) How far can a man weighing 980\,\mathrm{N} go up the ladder before the ladder begins to slip?

Roughwork.

(a)

Taking moment about the lower end of the ladder:

\begin{aligned} \textrm{Torque}_\textrm{clockwise}\,(\tau_{\circlearrowright}) & = \textrm{Torque}_\textrm{anticlockwise}\,(\tau_{\circlearrowleft}) \\ (W\cos\theta )(d/2) & = (N_2\sin\theta )(d) \\ \end{aligned}

whereas about its upper tip:

\begin{aligned} (N_1\cos\theta )(d) & =(W\cos\theta )(d/2) + (f\sin\theta )(d) \\ \end{aligned}

we have two equations.

(b)

This part is not to be attempted.