A crate of oranges on a horizontal floor has a mass of 30 kg. The coefficient of static friction is 0.62. The coefficient of kinetic friction is 0.52. The worker pulls the crate with a force of 200 N.
How do you know if the crate is moving or not? Explain it by comparing the magnitude of the friction with the magnitude of the applied force.

If no external forces are applied in the vertical direction, the weight of the object and the normal force have the same magnitude and point to opposite directions.

The friction force is defined as:

[tex]Fr_k=\mu_k N[/tex]

[tex]Fr_s=\mu_s N[/tex]

Where the subindices k and s are referred as to the kinetic and static friction forces respectively.

The condition for the object to move is that the applied force is greater than the friction force.

The crate of oranges has a mass of 30 Kg, thus its weight is:

W = m.g = 30 * 9.8 = 294 N

The normal force is:

N = W = 294 N

The kinetic friction is calculated as:

[tex]Fr_k=0.52* 294[/tex]

[tex]Fr_k=152.88\ N[/tex]

The static friction is calculated as:

[tex]Fr_s=0.62* 294[/tex]

[tex]Fr_s=182.28\ N[/tex]

The applied force is 200 N and it's greater than both the kinetic and the static friction forces, thus the crate is definitely moving at a certain positive acceleration.