Calculate Force to Move Crate at Steady Speed

[goluigi2196]

1. If the coefficient of kinetic friction between a 30 kg crate and the floor is 0.26, what horizontal force is required to move the crate at a steady speed across the floor?F_p is the pushing force.

2. Homework Equations
ΣF_x=ma_x
ΣF_y=0
F_f=μ_kF_n

solving for F_p I get...
F_p=ma_x+F_f

The Attempt at a Solution

F_p=ma_x+F_f
F_p=30a_x+F_f

ok..there aren't enough known components...

F_f=μ_kF_n
F_f=μ_kmg
F_f=(0.26)(30)(9.8)
F_f=76.44

There's the friction variable . Plug that into the other equation...

F_p=30a_x+76.44

I still have 2 variables missing. I need the acceleration. How do I find that?

 

[Haru Yo Koi]

Acceleration is the change in velocity. In this case, do you have a change in velocity or is the velocity remaining constant?

 

[goluigi2196]

Well it did say there's a steady speed. Wait...that means a_x=0 right? Because if the velocity is constant that means that the acceleration is 0...I think...

 

[Haru Yo Koi]

Yes, exactly.

 

[goluigi2196]

oh wow. I guess I wasn't thinking there.

 

[goluigi2196]

and that means Fp=76.44 N..right? Because the ax cancels out and 30(0)=0.

 

[Haru Yo Koi]

Indeed.

 

[goluigi2196]

Ok thanks.