Acceleration of a box pulled up a ramp with friction

AI Thread Summary
A 160kg box on a 35-degree incline is analyzed for movement when a tension of 1240 N is applied via a rope. The static friction force calculated is 579 N, while the gravitational force acting down the ramp is 900 N. The total force comparison shows that the tension is insufficient to overcome the combined forces of friction and gravity, resulting in the conclusion that the box will not slide up the ramp. The discussion confirms the calculations and expresses a desire for clarity on the next problem involving kinetic friction. Overall, the analysis indicates that the box remains stationary on the incline.
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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.
 
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Well done, it looks good to me.
 
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.
 
I just read over it again and it looks fine.
 
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