Question

A 21 kg chair initially at rest on a horizontal
floor requires a 166 N horizontal force to set
it in motion. Once the chair is in motion, a
133 N horizontal force keeps it moving at a
constant velocity.
The acceleration of gravity is 9.81 m/s
2
.
a) What is the coefficient of static friction
between the chair and the floor?

Answer 1

Static friction is a force that keeps an object at rest. It must be overcome to start moving the object. On a horizontal  surface, the normal force on an object is $F_{\eta}=mg.$ The maximum force of static friction is $F_s^{max}=\mu_s \cdot F_{\eta}$ . This must be overcome by horizontal force in order to set the chair in motion.

Using this, the coefficient of static friction is $\mu_s =\frac{F_s^{max}}{F_{\eta}}=\frac{166 N }{21 kg \cdot 9.81 m/s^2}=0.806$

Answer: The coefficient of static friction between the chair and the floor is $0.806$