HW problem with force and friction

[cjknowland]

Homework Statement

A sledge loaded with bricks has a total mass of 17.4 kg and is pulled at constant speed by a rope inclined at 19.2° above the horizontal. The sledge moves a distance of 20.0 m on a horizontal surface. The coefficient of kinetic friction between the sledge and surface is 0.500.

(a) What is the tension in the rope?

(b) How much work is done by the rope on the sledge?

(c) What is the mechanical energy lost due to friction?

Homework Equations

The Attempt at a Solution

I am having trouble finding the normal force with the pull at 19.2 degrees. If anyone could help in solving this problem it would be greatly appreciated.

 

[cjknowland]

I believe the key is that the acceleration is zero but I do not know how to apply it...

 

[cjknowland]

F-fk=MA but in order to find fk, I need to use fk=(coefficient of friction)(normal force) but i do not know how to find the normal force with the information given.

 

[cjknowland]

okay I got an answer of 76.76... I don't know if its correct

 

[Zyxer22]

Solving for T, I got 76.97 N

I'm willing to bet the discrepancy is rounding.
To be sure, I used
mg-Tsin(θ) = N
friction = (mg-Tsin(θ))μ
Tcos(θ)=friction = (mg-Tsin(θ))μ

T(cos(θ) + sin(θ)μ) = mgμ

so, T =mgμ/(cos(θ) + sin(θ)μ)

 

[cjknowland]

thank you so much =]