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What is the magnitude?

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 μk=0.20. The coefficient of static friction between the box and the surface is μs=0.60. What's the magnitude of the force of friction acting on the box during the push?
 
Answer: 60 N

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John M. | John - Algebra TutorJohn - Algebra Tutor
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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. 
 
 
 
Amarjeet K. | Professional Engineer for Math and Science TuroringProfessional Engineer for Math and Scien...
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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.
 
:)