Question

A uniform ladder whose length is 5.0 m and whose weight is 400 N leans against a frictionless vertical wall. The coefficient of static friction between the level ground and the foot of the ladder is 0.46. What is the greatest distance the foot of the ladder can be placed from the base of the wall without the ladder immediately slipping?

Answer 1

F_a is the normal force at A

Fr is the frictional force

F_b is the reaction force at B

Its a frictionless wall so there are no vertical forces at B

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Consider all forces in y direction

F_a -400 =0

F_a =400 N

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Consider all Forces in x direction

Fr -F_b =0

F_r =F_b

We know that Frictional force =Normal Force * coefficient of friction

F_b =F_a =0.46*400 =184N

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Take Moment about A

F_b*h -400*b/2 =0

184*h =200b

h =1.087b

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Consider the right triangle

ANSWER= 3.4m

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