Question

A 136kg crate is at rest on a floor.A man attempts to push it across the floor by applying 412N force horizontally. Taking the coefficient of static friction between the crate and the floor to be 0.37,show that the crate does not move.

Answer 1

pushing force=412
max static frictioni=136*9.8*.37= ...... N

if the pushing force is not greater than the max static friction, it wont move.

Answer 2

M*g = 136*9.8 = 1333 N. = Wt. of crate = Normal force(Fn).
Fs = u*Fn = 0.37 * 1333 = 493 N. = Force of static friction.

F - Fs > M*a.
F - 493 >M*0,
F > 493 N.
So, the min. pushing force (F) must be greater than the force of static friction(Fs).