A ladder of mass 10 kg rests against a frictionless wall at an angle of 75° from

Question

A ladder of mass 10 kg rests against a frictionless wall at an angle of 75° from the ground. A 80 kg man stands on the ladder ¾ of the distance from the bottom. How much force does the top of the ladder exert on the wall? The coefficient of static friction between the ladder and the floor is 0.85. A ladder of mass 10 kg rests against a frictionless wall at an angle of 75° from the ground. A 80 kg man stands on the ladder ¾ of the distance from the bottom. How much force does the top of the ladder exert on the wall? The coefficient of static friction between the ladder and the floor is 0.85. A ladder of mass 10 kg rests against a frictionless wall at an angle of 75° from the ground. A 80 kg man stands on the ladder ¾ of the distance from the bottom. How much force does the top of the ladder exert on the wall? The coefficient of static friction between the ladder and the floor is 0.85.

Explanation / Answer

Given that,

Mass of the ladder = m = 10 kg ; theta = 75 degrees ;

mass of the person = M = 80 kg ; mu = 0.85

let us conider L be the length of the ladder. Then the person is at 3L/4.

Let N be the normal reaction of the wall. There will be three forces acting, the weight of the ladder at L/2, the weight of the person at 3L/4 and and the normal reaction of the wall. Sum of all the forces acting should be zero.

m g L / 2 cos(theta) + 3 M g L cos(theta) / 4 - N L sin(theta) = 0

taking L common and dividing the eqn by cos theta we get

mg/2 + 3Mg/4 - N tan(theta) = 0

Simplifying the above we get

N = [mg/2 + 3 Mg/4]/tan(theta) = [0.5 x 10 x 9.8 + 0.75 x 80 x 9.8 ] / tan(75) = 170.7 Newtons

Hence, N = 170.7 N

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