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

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To calculate the tension in a rope pulling a 39kg box at a 21-degree angle with a coefficient of kinetic friction of 0.23, it's essential to analyze the forces acting on the box. The net force equation, fnet = ma, is applicable, but care must be taken with the direction of friction and tension forces in the equations. Some participants noted errors in the setup, particularly regarding the signs of the forces in the horizontal equation. It is recommended to solve the problem algebraically before substituting values to avoid confusion. The discussion emphasizes the importance of correctly identifying force directions and maintaining clarity in calculations.
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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.
 

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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).
 
CWatters said:
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?
 
I think you are on the right track. I don't think FT will cancel.

PS: it's midnight where I live so I'm off to bed.
 
+1

Sorry yes I meant sign not sine.
 
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