Three objects on a hanging pulley system

[Koscher]

Homework Statement

Three objects with masses m1 = 37.5 kg, m2 = 19.5 kg, and m3 = 11.1 kg are hanging from ropes that are redirected over pulleys. What is the acceleration of m1? Negative numbers for downward, and positive numbers for upward, please.

There should be a diagram of what the system looks like attached.The attempt at a solution

First I drew a FBD of each of the three masses. I made the tension between mass 2 and 1, the variable T₁₂. I made the tension between mass 1 and 3, the variable T₁₃, just for simplicity sake.

So the equations I got from the FBD were:

T₁₂=m₂a+m₂g
T₁₃=m₃a+m₃g
m₁g-(T₁₂+T₁₃) =m₁a

Then I plugged in the two tension formulas and simply solved for a, which gave me 0.9939 m/s².

I got the question wrong. What I am really wondering is if it just a wrong sign, and the answer is actually -0.9939 m/s². Or is there a mistake in the math somewhere that I can not see.

 

[thiefjack]

Hi,Forces pointing in the positive direction are written first, then subtracted by negatively pointing forces.

 

[Koscher]

I appreciate it. The value was not correct, it was the number that I got, but negative. I left a sign off when doing the math.