   Chapter 8, Problem 79AP

Chapter
Section
Textbook Problem

A uniform ladder of length L and weight w is leaning against a vertical wall. The coefficient of static friction between the ladder and the floor is the same as that between the ladder and the wall. If this coefficient of static friction is μs = 0.500, determine the smallest angle the ladder can make with the floor without slipping.

To determine
The smallest angle the ladder can make with the floor without slipping.

Explanation

Given info: The co-efficient of static friction is 0.500 .

Explanation: The normal force by the wall is Fx=0=f1n2n2=f1=μsn1 and the normal force by the floor is Fy=0=n1w+μsn2=0n1=w/1+μs2 .

The following diagram shows the free body diagram of ladder.

The torque about the lower end of the ladder is τ=0 yields such that

w(L/2)cosθ+n2(Lsinθ)+f2(Lcosθ)=0 and by making the substitution of n2 and f2=

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