On a horizontal surface is located an object of mass 20 kg and it is observed that
To set it in motion, a
80 N force, whereas if the object is
in motion, only one
40 N force, to keep it at speed
constant. Determine the values of the coefficients
static and kinetic friction, respectively.
(g = 10 m / s2).
A) 0.32; 0.11
B) 0.36; 0.15
C) 0.40; 0.2
D) 0.45; 0.22

By Newton's second law, the net vertical force acting on the object is 0, so that

n - w = 0

where n = magnitude of the normal force of the surface pushing up on the object, and w = weight of the object. Hence n = w = mg = 196 N, where m = 20 kg and g = 9.80 m/s².

The force of static friction exerts up to 80 N on the object, since that's the minimum required force needed to get it moving, which means the coefficient of static friction µ is such that

80 N = µ (196 N)   →   µ = (80 N)/(196 N) ≈ 0.408

Moving at constant speed, there is a kinetic friction force of 40 N opposing the object's motion, so that the coefficient of kinetic friction ν is

40 N = ν (196 N)   →   ν = (40 N)/(196 N) ≈ 0.204

And so the closest answer is C.

(Note: µ and ν are the Greek letters mu and nu)

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