A painter of mass 76.8 kg is 1.46 m from the top of a 6.50-m ladder. The ladder

Question

A painter of mass 76.8 kg is 1.46 m from the top of a 6.50-m ladder. The ladder rests ageinst a wall. Friction between the ladder and the wall is negligible. The ladder's mass is S.2S kg. Assume the ladder is set up according to Occupational Safety and Health Administration standards so that it makes a 7s.s angle with the noor. (a) What is the minimum coefficient of static friction required for the painter's safety? (b) Would rubber ladder tips on dry concrete be safe? (Assume that the coefficient of friction between rubber and dry concrete is 0.8.) No

Explanation / Answer

a)
As the ladder is in equilibrium, net force and net torque acting on it must be zero.

let Fw is the force exerted by the wall on the ladder.

Apply net torque about bottom = 0

5.25*9.8*3.25*sin(90-75.5) + 76.8*9.8*(6.5 - 1.46)*sin(90-75.5) - Fw*6.5*sin(75.5) = 0

==> Fw = 157.6 N

let N is normal force acting on the ladder.

now apply, Fnety = 0

N - 76.8*9.8 - 5.25*9.8 = 0

N = 804.1 N

now apply, Fnetx = 0

Fx - Fw = 0

mue_s*N - Fw = 0

mue_s = Fw/N

= 157.6/804.1

= 0.196 <<<<<<<<<<------------------------Answer

b) yes.

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