You need to move a 132 kg sofa to a different location in the room. It takes a force of 125 N to start it uniformly. What is the coefficient of static friction between the
sofa and the carpet?

Let w denote the weight of the sofa, n the magnitude of the normal force, and f the magnitude of the friction force. The sofa is in equilibrium, so by Newton's second law,

n - w = 0

125 N - f = 0

The sofa has a weight of

w = (132 kg) g = 1293.6 N

where g = 9.80 m/s² is the magnitude of the acceleration due to gravity. Since n = w, the normal force has the same magnitude.

The friction force is proportional to the normal force by a factor of the coefficient of static friction µ, such that

f = µ n

Our second equation tells us f = 125 N, so solve for µ :

125 N = µ (1293.6 N)

µ ≈ 0.0966