Simple Forces question I cannot seem to get

[Element1674]

Homework Statement

A couch weighing 620N is to be pushed to a new location across the room. The coefficient of static friction between the couch and the floor is 0.31. What is the minimum force required to set the couch into motion.

Homework Equations

See below

The Attempt at a Solution

Given: F_g=620N
μ_s=0.31
Required: Force applied
Analysis: In order for the couch to begin moving, the applied force must be equal to the force of friction. Therefore finding the force of friction will indirectly find the minimum force applied.
Solution: Find the mass of the couch by using Fg=mg=620N
mg=620N
m=620N/9.81m/s^2
m=63.2...kg (keep all the decimals)

then find Ff using Ff=μFn; since there is no vertical acceleration, Fg=mg. The question gave mg (620N) so...
Ff=(0.31)(620N)
Ff=192N [backwards]
Fa=192N [forwards]

Therefore 192N of force are required.

Is this solution correct?

 

[Dick]

Homework Statement

A couch weighing 620N is to be pushed to a new location across the room. The coefficient of static friction between the couch and the floor is 0.31. What is the minimum force required to set the couch into motion.

Homework Equations

See below

The Attempt at a Solution

Given: F_g=620N
μ_s=0.31
Required: Force applied
Analysis: In order for the couch to begin moving, the applied force must be equal to the force of friction. Therefore finding the force of friction will indirectly find the minimum force applied.
Solution: Find the mass of the couch by using Fg=mg=620N
mg=620N
m=620N/9.81m/s^2
m=63.2...kg (keep all the decimals)

then find Ff using Ff=μFn; since there is no vertical acceleration, Fg=mg. The question gave mg (620N) so...
Ff=(0.31)(620N)
Ff=192N [backwards]
Fa=192N [forwards]

Therefore 192N of force are required.

Is this solution correct?

Looks ok to me. But you didn't need to to find m.