Tension and acceleration problem

[freshcoast]

1. Problem statement/ given data
The weights of the objects are 200N and 300N. The pulleys are essentially frictionless and massless. Pulley P1 has a stationary axle, but pulley P2 is free to move up and down. Find the tensions FT1 and FT2 and the acceleration of each body.

2. Homework Equations .
F=ma

3. Attempt.
I drew a FBD for each mass with m1 going down with down as the positive and m2 going up with up as the positive direction. I know that in this system the tension for mass 2 is twice the tension of mass 1 and that the acceleration for mass 2 is half of mass 1. I have the answer and the explained solution but I don't know how I'm getting a different answer than they are. Can someone check what I am not seeing here? I know if I find the right acceleration I just have to plug that into find the tensions.

The answer in the book is a= 1.78m/s^2

 

[TSny]

It looks to me that your second equation has a sign error.

 

[freshcoast]

For mass 2? Since that mass is going up shouldn't the upwards be the positive direction? So it would be T - mg ?

 

[TSny]

Yes, that's right. I should have been clearer. I was referring to the second line of your equations where you wrote for m₁: F_T1 = m₁a_y + m₁g. Check the signs in this equation.

 

[freshcoast]

Oh I see it now, got it thanks!