Answer to Question #219089 in Physics for ran

Question

3. A 27.0 kg object is being pulled east across the ground with a horizontal force of 110 N. If the acceleration of the box is 2.82 m/s ^ 2 , what is the coefficient of kinetic friction? (Ensure you draw a free body diagram.)

Answer 1

The Newton's second law says

$$ma=F-F_f$$

Hence, the friction force

$$F_f=F-ma\\ =110\:\rm N-27.0\; kg*2.82\: m/s^2=33.9\:\rm N$$

The coefficient of kinetic friction

$$\mu_k=\frac{F_f}{N}=\frac{F_f}{mf}\\ =\frac{33.9\:\rm N}{27.0\:\rm kg*9.81\:\rm m/s^2}=0.128$$