# Three objects on a hanging pulley system

1. Feb 5, 2012

### Koscher

The problem statement, all variables and given/known data

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.

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2. Feb 5, 2012

### thiefjack

Hi,

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

Last edited: Feb 5, 2012
3. Feb 5, 2012

### 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.