Let <em>w</em> denote the weight of the sofa, <em>n</em> the magnitude of the normal force, and <em>f</em> the magnitude of the friction force. The sofa is in equilibrium, so by Newton's second law,
<em>n</em> - <em>w</em> = 0
125 N - <em>f</em> = 0
The sofa has a weight of
<em>w</em> = (132 kg) <em>g</em> = 1293.6 N
where <em>g</em> = 9.80 m/s² is the magnitude of the acceleration due to gravity. Since <em>n</em> = <em>w</em>, 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 <em>µ</em>, such that
<em>f</em> = <em>µ</em> <em>n</em>
Our second equation tells us <em>f</em> = 125 N, so solve for <em>µ</em> :
125 N = <em>µ</em> (1293.6 N)
<em>µ</em> ≈ 0.0966
