A ladder of weight W leans against a wall. The ladder has rollers at the top so

Question

A ladder of weight W leans against a wall. The ladder has rollers at the top so that the wall exerts a normal force only on the top of the ladder. A person of weight Wp slowly climbs the ladder A free-body diagram for the ladder is shown. F, (friction) A. As the person ascends the ladder, the force from the wall (Fwall) stays the same B. Increases C. Decreases Suppose in the previous problem the man has mass 75 kg, the ladder has mass 25 kg and the angle at base is 65 degrees, if the man ascends to the middle of the ladder the force from the wall is A. 490 Newton B. 230 Newton C. 620 Newton D. 330 Newton

Explanation / Answer

balancimg moment,

M = (d Wp cos(theta)) + (L/2 WL cos(theta)) - (L Fwall sin(theta)) = 0

Fwall is directly propotional to the distance d.

d increases so Fwall also increases.

Ans: (B)

M = (L/2 x 75 x 9.81 x cos65) + (L/2 x 25 x 9.81 x cos65) - (L F sin65) = 0

F = (100 x 9.81 x cos65)/( 2 sin65)

F = 229 N

Ans(B) 230 N

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