Question

What force must the worker exert to get the box moving & what force must the worker exert to accelerate the box at 0.1 meters per second squared to the south?

Answer 1

Since static friction is the minimum force required to just start the motion of a stationary object.

Here if we need to start an object from rest then we required F = 700 N

So for the first part of the above problem Force will be F = 700 N

Now if the box is already moving then we will have to use kinetic friction force between box and floor

now we can write the equation of net force as

$F - F_k = m*a$

here

$F_k = kinetic friction = 220 N$

$m = mass = 500 kg$

$a = acceleration = 0.1 m/s^2$

now we will have

$F - 220 = 500* 0.1$

$F = 220 + 50 = 270 N$