Acceleration of a box pulled up a ramp with friction

[M4573R]

Homework Statement

A 160kg box is on a plane with an incline of 35 degrees. A rope is attached to the box and a pulley at the top of the ramp and has a tension of 1240 N. The static coefficient of friction is 0.45. Will the box move up the ramp? If so, what is its acceleration?

Homework Equations

Total force on box = m*a
Is Force of tension >= Force of friction + Force of gravity down ramp(?)

Force of static friction = umg*cos(theta) = 0.45*160.0*9.81*cos(35) = 579 N
Force of gravity down ramp = mg*sin(theta) = 160.0*9.81*sin(35) = 900 N

The Attempt at a Solution

Force Total = m * a
1240 N >= 579 N - 900 N
1240 N >= 1479 N -> No it won't slide up the ramp.

I hope this is correct, I'm not sure if using the force acting down the ramp is correct or not.

 

[Rake-MC]

Well done, it looks good to me.

 

[M4573R]

The next problem implies the box reaches the top of the ramp and we are given a coefficient of kinetic friction, So I want to make extra sure.

 

[Rake-MC]

I just read over it again and it looks fine.