A horizontal force is applied to a box on a leveled floor, what is the magnitude of the friction force on the box?

Question

Problem:

When a horizontal force of 274 N is applied to a 89 kg box on a leveled floor, the box slides with constant velocity. What is the magnitude of the friction force on the box?

Additional Questions (if u have time, please explain):

1) I am struggling with understanding if "magnitude of friction force" represents Fs or Fk. So I dont really know which formulas to apply or the order to apply them.

2) When a force is applied, should I assume im looking for Fk?

3) Additional explanations / advice welcome!

Answer 1

The notation F_k must represent a friction force when the box is in motion (k for kinetic). The notation F_s probably represents a friction force when the box is at rest (s for static). In this problem since the box is moving the notation F_k is appropriate (for most materials F_ks ).

Paraphrasing Newton's First Law:

A body moving at a constant velocity has no acceleration and the forces acting on that body do so to keep the body at that velocity (including zero). The forces cancel each other to keep the body in equilibrium. When a body is in equilibrium, the sum of the forces acting on it are zero.

So if we assume the box is moving from left to right, we can assume forces acting in that direction are positive. So the 274 N is acting to the right (it doesn't matter if it's pushing or pulling) is positive. Now a friction force always opposes motion so it acts in the opposite direction. The sum of the forces acting on the box in the horizontal direction are zero means:

274 N - F_k = 0

F_k = 274 N

The mass of the box was given but it's not needed. That's because the box is not accelerating (if it was, then the force balance would have been 274 - F_k = ma). In real world problems we often know things that don't enter into the problem solution. We have to understand the physics in order to know what to ignore!

Now about the term magnitude...

Forces are represented with vectors having magnitude and direction. But if a problem is only in one dimension, as this one is, the direction is obvious and we only have to deal with magnitudes. In this problem, we summed the forces acting in the horizontal direction in order to find the magnitude of the friction force. We know the friction force is pointing to the left. It has to be in order to prevent the box from accelerating.

Had we been asked to find the coefficient of kinetic friction, μ_k, we could have used the mass to calculate it since F_k=μ_kW where W =mg is the weight.

μ_k = F_k/(mg) = 274N/[(89 kg)(9.81 m/sec²)] = 0.31

I hope this helps.