Angle on ramp with cart and weights on rope at end

[jskrzypi]

Homework Statement

A 250g cart with 250g of weight is on a ramp. Rope attached to right side going over pulley with a 50g weight on end. Calculate angle ramp needs to be at to maintain cart stationary

edit: track is frictionless

Relevant Equations

Fnetx=nx+Tx+(FG)x=0
Fnety=ny+Ty+(FG)y=0

I believe the nx, Ty, and (fs)y are all 0. I could solve for theta if I could figure out (fs)x or ny.

edit: Track is frictionless, so delete (fs) forces.

 

[TSny]

You wrote $(F_G)_x$ as $Mg\cos\theta$ and $(F_G)_y$ as $Mg\sin\theta$. Check your trig functions here. Also, shouldn't $(F_G)_x$ and $(F_G)_y$ both be negative?

 

[jskrzypi]

I just caught the cos/sin issue. And I wasn't sure about them being negative. Obviously they are, but I may be getting it confused. Class said g is just a scalar of 9.8 m/s^2, and we need to add in the signs so it would be +(-g). I just don't know when/where to add the negatives.

 

[haruspex]

don't know when/where to add the negatives.

First, you need to define which way you are taking as positive for each variable. It doesn’t matter what you choose as long as you are consistent.
I would take positive as downslope for the cart and vertically down for the suspended mass.