How Do You Calculate Tension in a Rope Pulling a Box with Friction and an Angle?

[Balsam]

1. Homework Statement
You are pulling a 39kg box on a level floor by a rope attached to the box. The rope makes an angle of 21 degrees with the horizontal. The coefficient of kinetic frictions between the box and the floor is 0.23. Calculate the magnitude of the tension in the rope needed to keep the box moving at a constant velocity?

Homework Equations

fnet=ma

The Attempt at a Solution

I have pictures of my attempted solution attached. I stopped solving it because I realized that my Ft variables would cancel out and I would have nothing to solve for. Also, what I did makes no sense but I was trying to solve it like you solve other forces problems where you find set up your equations and find a variable present in each equation and set those equations equal to each other. I don't think that works here. My steps are numbered. The attached picture is the first one and the picture at the top is the second one.

 

[CWatters]

I agree with your starting equation for the vertical sum of forces but I think you have a sine error in the horizontal equation. You appear to have friction acting in the same direction as the tension force (eg both positive).

 

[Balsam]

I agree with your starting equation for the vertical sum of forces but I think you have a sine error in the horizontal equation. You appear to have friction acting in the same direction as the tension force (eg both positive).

Is there another way to solve this problem?

 

[CWatters]

I think you are on the right track. I don't think F_T will cancel.

PS: it's midnight where I live so I'm off to bed.

 

[haruspex]

@Balsam, I strongly urge you to develop the habit of working entirely algebraically until the final step. It has many advantages (see section 1 of https://www.physicsforums.com/insights/frequently-made-errors-equation-handling/).
As CWatters (almost) posted, your final equation is correct except for a sign (not sine) that is wrong.

 

[CWatters]

+1

Sorry yes I meant sign not sine.