An 85 kg clock initially at rest on a horizontal floor requires a 680 N horizontal force to set it in motion. After the clock is in motion, a horizontal force of 540 N keeps it moving with a constant velocity. Find μs and μk between the clock and the floor.

A force of 680 N is required to get the clock moving, so the maximum static friction is also f ˢ = 680 N. The clock is at rest, so the net vertical force acting on it is 0, and by Newton's second law,

n - mg = 0

where

n = magnitude of the normal force

m = 85 kg = mass of the clock

g = 9.8 m/s² = magnitude of the acceleration due to gravity

So we have

n = mg = (85 kg) (9.8 m/s²) = 833 N

which means the static friction f ˢ is such that

f ˢ = µ ˢ n

Solving for the coefficient of static friction gives

µ ˢ = (680 N) / (833 N) ≈ 0.82

After it starts moving, a force of 540 N is required to keep the clock going at a constant speed, so the kinetic friction is also f ᵏ = 540 N. Then

f ᵏ = µ ᵏ n

and solving for the coefficient of kinetic friction yields

µ ᵏ = (540 N) / (833 N) ≈ 0.65