consider a ladder with a painter climbing up it. the mass of the uniform ladder is 12.0 kg , and the mass of the painter is 55.0 kg . if the ladder begins to slip at its base when the painter's feet are 70 % of the way up the length of the ladder, what is the coefficient of static friction between the ladder and the floor? assume the wall is frictionless.

Question

16-12-2022
Physics

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consider a ladder with a painter climbing up it. the mass of the uniform ladder is 12.0 kg , and the mass of the painter is 55.0 kg . if the ladder begins to slip at its base when the painter's feet are 70 % of the way up the length of the ladder, what is the coefficient of static friction between the ladder and the floor? assume the wall is frictionless.

Answer :

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kumargaurav1012000 kumargaurav1012000 · Answer 1 · 2022-12-22T00:09:38-05:00

The things that are creating friction determine the coefficient of static friction value. Its value typically ranges from 0 to 1, although it can also be higher than 1.

The term "static friction" refers to friction between two or more stationary solid objects. Static friction, for instance, can stop an object from rolling down a sloped surface. The coefficient of kinetic friction is typically lower than the coefficient of static friction, commonly abbreviated as s. Static friction is the resistance people feel when they try to move a stationary object over a surface without actually moving their bodies in relation to the surface.

We need to check that before ladder slips the length of ladder the painter can climb.

So we need to satisfy the equilibrium conditions.

So for ∑Fx=0, ∑Fy=0 and ∑M=0

We have,

At the base of ladder, two components N₁ acting vertical and f₁ acting horizontal

At the top of ladder, N₂ acting horizontal

And Between somewhere we have the weight of painter acting downward equal to= mg

So, we have N₁=mg

and also mg*d*cosФ= N₂*l*sin∅

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