You're still in a redecorating mood and want to move a 35kg bookcase to a different place in the living room. You exert 58 N on it which makes it move at 0.12 m/s^2. Find the coefficient of kinetic friction between the bookcase and the carpet

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