Answer to Question #210999 in Classical Mechanics for Syed

Question

A uniform ladder of length 50 feet, rests against a vertical wall with which it makes an angle of

60 degree, the coefficient of friction between wall and ladder and ground respectively being 1/2 and 3/5. If a man whose weight is one-fourth to the ladder ascends the ladder, how high will

be he when ladder slips?

Answer 1

$\begin{cases} \mu_2mg\cos a\cdot 0=mg\sin a\frac l2+Mg\sin a d=\mu_1 mg \sin a l, \\ \mu_1 mg \sin a\cdot 0=Mg\sin a(l-d)+mg\sin a\frac l2+\mu_2 mg\cos ag, \end{cases}$

$\begin{cases} m\frac l2+Md=\mu_1ml,\\ 0=M\sin a(l-d)+m\sin a\frac l2+\mu_2m\cos al, \end{cases}$

$d=l-\frac{ml-2\mu_1ml+m\sin a\frac l2-\mu_2 m\cos al}{2M+m\cos a}\approx 0.23l=11.5~ft.$