Homework Help: Acceleration of a box pulled up a ramp with friction

1. Oct 7, 2008

M4573R

1. The problem statement, all variables and given/known data
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?

2. Relevant 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

3. 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.

2. Oct 7, 2008

Rake-MC

Well done, it looks good to me.

3. Oct 7, 2008

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.

4. Oct 7, 2008

Rake-MC

I just read over it again and it looks fine.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook