Question

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

Answer 1

Answer: 0.16

Explanation:

Newton's second law states that the resultant of the forces exerted on the bookcase is equal to the product between the mass (m) and the acceleration (a):

$F-F_f = ma$

where

F = 58 N is the force applied

Ff is the frictional force

Substituting, we find the frictional force

$F_f = F-ma=58 N-(35 kg)(0.12 m/s^2)=53.8 N$

The frictional force has the form:

$F_f = \mu mg$

where $\mu$ is the coefficient of kinetic friction. Re-arranging the formula, we can find the coefficient:

$\mu=\frac{F_f}{mg}=\frac{53.8 N}{(35 kg)(9.8 m/s^2)}=0.16$