Question

A 60.0-kg mass person wishes to push a 120-kg mass box across a level floor. The coefficient of static friction between the person's shoes and the floor is 0.700. What is the maximum coefficient of static friction between the box and the floor such that the person can push horizontally on the box and cause it to start moving?

Answer 1

Answer:

μ = 0.350

Explanation:

For the person to able to move the box, the force exerted by the person on the box must equal the force exerted by the box:

$F_{p} = F_{b}$

In this case, force can be calculated as a product of mass (m) by the acceleration of gravity (g) and the coefficient of static friction (μ):

$m_{p}*g*\mu_{p}=m_{b}*g*\mu_{b}\\m_{p}*\mu_{p}=m_{b}*\mu_{b}\\60*0.7=120*\mu_{b}\\\mu_{b}= 0.35$

Therefore, for the person to be able to push the box horizontally, the coefficient of static friction between the box and the floor should not be higher than 0.350.