Answer to Question #201965 in Physics for Nique

Question

A student pushes a desk 1.3 m across the floor at constant velocity. What is the mass of the desk if the coefficient of friction is 0.19 and the student did 49.4 J of work on the desk? 

 

 

 

 

Answer 1

Let's first find the pushing force:

$$W=F_{p}d,$$ $$F_p=\dfrac{W}{d}=\dfrac{49.4\ J}{1.3\ m}=38\ N.$$

Since the desk moves across the floor at constant velocity there is no acceleration:

$$F_p-F_{fr}=0,$$ $$F_p=F_{fr}=\mu mg,$$ $$m=\dfrac{F_p}{\mu g}=\dfrac{38\ N}{0.19\cdot9.8\ \dfrac{m}{s^2}}=20.4\ kg.$$