Question

A person is pushing an object of mass m along the ground with a force F . The coefficient of kinetic friction between the object and the ground is ${\mu }_k$ . The object is accelerating, but then the person stops pushing and the object slides to a halt. The person then starts pushing on the object again with a force F , but the object doesn't budge. The maximum coefficient of static friction between the object and the ground is ${\mu }_s$. Which of the following statements is true?

• A. $F>\frac{{\mu }_k}{{\mu }_s}$
• B. ${\mu }_k>{\mu }_s$
• C. ${\mu }_{k}mg<F\le {\mu }_{s}mg$
• D. ${\mu }_{s}mg=F$
• E. The scenario described is physically impossible

Answer 1

Answer: (C)

${\mu }_{k}mg<F\le {\mu }_{s}mg$

When the person is pushing on the moving box, the box accelerates, meaning that F is greater than the force of kinetic friction, ${\mu }_k$. When the box is at rest, the person is unable to make the box move, which means that the maximum force of static friction, ${\mu }_s$, is greater than or equal to F .You may be tempted by D : the box isnt moving, so the force of static friction perfectly balances out the pushing force exerted by the person. However, ${\mu }_s$ is the maximum coefficient of static friction. The force of static friction is always only enough to resist the pushing force, so its possible that the person could apply a greater force and still not make the object budge. Also, note that B states a physical impossibility.The coefficient of static friction is always greater than the coefficient of kinetic friction.