m = mass of the book = 35 kg
F = force applied on the book = 58 N
f = frictional force acting on the book is opposite direction of applied force = ?
a = acceleration of the bookcase = 0.12 m/s
along the direction of applied force , the force equation for the motion of he bookcase is given as
F - f = ma
inserting the values
58 - f = (35) (0.12)
f = 53.8 N
weight of the bookcase is given as
W = m g = 35 x 9.8 = 343 N
F' = normal force acting on the bookcase in upward direction by the carpet
the normal force in upward direction balances the weight of the bookcase
hence F' = W
F' = 343 N
Coefficient of kinetic friction is given as
μ = f/F'
μ = 53.8/343
μ = 0.16
