Simple Forces question I cannot seem to get

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To determine the minimum force required to move a 620N couch across the floor with a static friction coefficient of 0.31, the force of friction must be calculated. The force of friction (Ff) is found using the equation Ff = μFn, where Fn equals the weight of the couch (620N). This results in Ff = 0.31 * 620N, yielding a force of 192N. The solution confirms that an applied force of 192N is necessary to overcome static friction and initiate movement. The calculation is correct, although finding the mass of the couch was unnecessary for this problem.
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Homework Statement


A couch weighing 620N is to be pushed to a new location across the room. The coefficent 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: Fg=620N
μs=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?
 
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Element1674 said:

Homework Statement


A couch weighing 620N is to be pushed to a new location across the room. The coefficent 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: Fg=620N
μs=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.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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