What is the magnitude?

Question

A 20 kg box remains at rest on a horizontal surface while a person pushes directly to the right on the box with a force of 60 N. The coefficient of kinetic friction between the box and the surface is μ_k=0.20. The coefficient of static friction between the box and the surface is μ_s=0.60. What's the magnitude of the force of friction acting on the box during the push?

 

Answer: 60 N

Answer 1

The problem tells us that the box remains at rest. 

 

The force due to friction must equal the force from the person, or else the box moves.   

 

Since the question did not ask direction, we only need to know the magnitude of the friction force, which is 60N. 

 

 

 

Answer 2

Static friction = .6 x 20 = 12N

Kinetic friction = .2 x 20 = 4N

 

If 60N force is applied the box will move with a net force of 60-4=56N

 

To begin with when 60 N force is applied the static friction increases from 0 to 12 N in the direction opposite to the applied force.

 

When external force applied increase more than 12 N and box begins to move the frcition reduces to kinetic friction = 4N again in the direction opposite to the applied force.

 

Therefore magnitude of friction increases from 0 to 12 and then reduces to 4 N during the push and stays constant i.e. 4 N after the body begines to move.

 

:)