Find Friction Force of Box with Mass of 135 kg at 35° Angle

[DaDoctor]

The worker pushes downward and to the left on the box at an angle of 35°. The box has a mass of 135 kg. The box moves horizontally across the floor to the left at a constant velocity. The force applied by the worker is 2030 N∠215°. What is the value of the friction force?Fgravity · sin35° = Fgravityx
Ffriction + Fgravityx = m · a
f = μ · Fssin35° =
Fgravity · sin35° = Fgravityx
m · g · sin35° = Fgravityx
(135 kg)(9.81) sin35° = Fgravityx
759.6 N = Fgravityx

Ffriction + (759.6 N) = (135 kg)(0 m/s2)
Ffriction - 759.6 N = 0 N
Ffriction = 759.6 N

I know that this isn't correct, because my study guide is multiple choice. My options are:
a. 1164 N
b. 1324 N
c. 1663 N
d. 2489 N

I'm really not sure what I'm missing or if I am going the wrong way with finding the value of the friction force. My guess is that c. 1663 N is correct, but that is only a guess. I'd like to be able to prove which answer it is. Thank you for any help!

 

[Student100]

Your guess is right. Your calculations are off quite a bit. What can you conclude about the friction force since the box is moving to the left at a constant velocity?

 

[DaDoctor]

Probably that it is about equal to the Horizontal force, and that the Net Force is 0

 

[DaDoctor]

Your guess is right. Your calculations are off quite a bit. What can you conclude about the friction force since the box is moving to the left at a constant velocity?

Probably that it is about equal to the Horizontal force, and that the Net Force is 0

 

[Student100]

So the forces are balanced right? So to calculate the frictional force on the horizontal plane why are you using sin and fg? What should you do instead?

 

[Student100]

Probably that it is about equal to the Horizontal force, and that the Net Force is 0

Exactly, so what is the Ff in the horizontal direction?

 

[DaDoctor]

Exactly, so what is the Ff in the horizontal direction?

... about 1663 Newtons of force since it is a total of 2030N at a 215 degree angle.

 

[Student100]

... about 1663 Newtons of force since it is a total of 2030N at a 215 degree angle.

Yep. =)

 

[DaDoctor]

Yep. =)

Awesome! Thanks a lot!