Question #210999

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?


1
Expert's answer
2021-06-28T17:18:03-0400

{μ2mgcosa0=mgsinal2+Mgsinad=μ1mgsinal,μ1mgsina0=Mgsina(ld)+mgsinal2+μ2mgcosag,\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}

{ml2+Md=μ1ml,0=Msina(ld)+msinal2+μ2mcosal,\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=lml2μ1ml+msinal2μ2mcosal2M+mcosa0.23l=11.5 ft.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.


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