A crate of mass 100 kg is at rest on a horizontal floor. The coefficient of static friction between the crate and the floor is 0.4, and the coefficient of kinetic friction is 0.3 . A force F of magnitude 344 N is then applied to the crate, parallel to the floor. Which of the following is true ?

Options

A. The crate will accelerate across the floor at `0.5 m//s^(2)`.
B. The static friction force, which is the reaction force to F as guaranteed by Newton 's Third Law, will also have a magnitude of 344 N.
C. The crate will slide across the floor at a constant speed of `0.5 m//s`.
D. The crate will not move.

Answer

D

Explanation

The maximum force that static friction can exert on the crate is `mu_(s)F_(N)= mu_(s)F_(w)= mu_(s) mg= (0.4)(100 kg)(10 N//kg)=400 N`. Since the force applied to the crate is only 344 N, static friction is able to apply that same magnitude of force on the crate, keeping it stationary. [Choice (B) is incorrect because the static friction force is not the reaction force to F, both F and `F_(f("static"))` act on the same object (the crate) and therefore cannot form an action / reaction pair.]