Find acceleration of this system with friction

[lax1113]

Homework Statement

Body A weighs 102 N, Body B weighs 32 N. The coefficeints of friction between A and the incline are .56 for static, .25 for kinetic. Angle is 40 degrees. Find the acceleration of the system when block A is at rest... when it is moving up the incline, and when it is moving down the incline.

(Block A is on the ramp attached to a string that goes up to the top of the ramp, down a pulley that attaches block B)

Homework Equations

Fnet=MA
Ff=Fnormal(coefficient of friction)
Fnet=T-Ff
Fnormal=Mgy

The Attempt at a Solution

I have done problems just the same as this very recently, but for some reason, I cannot think of how to get the tension in the string/rope. I don't know why, but it just seems to be escaping me, and after getting T, the rest of the problem is already solved. I have the friction, equal to mgy multiped by the coefficient. So the acceleration would be the T-friction, all divided by the mass of the system.

 

[heth]

You have three cases - block A at rest, moving up, and moving down.

Each will have a different free body diagram. You'll need to treat each case separately, rather than trying to lump them together with the same equations.

 

[lax1113]

hey heth,
Yeah i just stared at this for some reason and didn't even think about it.
I took a little break and revisited it and got something that looked like this...
(just for A not in motion)

Fnet=mg_ax+ff-T
Fnet=T-mg_b

so mg_ax+ff-T=T-mg_b

solved for T

T=(mg_ax+mg_b+Ff)/2

then take this tension find the unbalanced force, and divide it by the systems mass.