Answer to Question #326815 in Mechanics | Relativity for miles

Question

A 30ft ladder weighing 100 lb having its center of the mass one-third of the way up from the bottom rests against a smooth wall so that it makes an angle of  with the ground. If the coefficient of friction between the ground and the ladder is 0.4, how high can a 150-lb man go before the ladder slips?

Answer 1

$mg\frac l3 \cos \alpha +Mgx\cos\alpha=N_l l\sin\alpha,$

$g\cos\alpha (Mx+m\frac l3)=N_l l\sin \alpha,$

$Mx+m\frac l3=\frac{N_l l\tan\alpha}{g} \leqslant \\ \mu(m+M)l \tan\alpha,$

$x\leqslant l(\mu\ tan \alpha(1+\frac mM)-\frac{m}{3M})=28~\text {ft}.$