Tension/bucket problem

1. Oct 21, 2006

chocolatecello

Allright, so I'm stuck on this problem:

"One 3.0-kg paint bucket is hanging by a massless cord from another 3.0-kg paint bucket, also hanging by a massless cord. a) If the buckets are at rest, what is the tension in each cord?"

Here's what I have so far:

I drew a free-body diagram with tension (T) pointing upwards and weight (W) pointing downwards on both buckets.
Then I tried to solve it like this:

Fnet=ma
sum of forces=W-T

W=mg
W=30(9.8)
W=294

T=ma
T=30a

so sum of F=294-30a
but now I have two variables and I'm not sure what to do. I think I'm missing something obvious here, so could somebody help point me in the right direction? Thanks :)

2. Oct 21, 2006

Fermat

Since the bodies are at rest, then there is no movement, hence no acceleration, hence no need to use newton's 2nd law.
Since the bodies are at rest, then they are in equlibrium with each other, which means that all forces acting cancel each other out (i.e. there is no net force).
Since the forces balance, then any upward force must equal the downwards force.

3. Oct 22, 2006

QuantumCrash

This is actually quite a simple problem and it is quite unnecessary to get so complicated in your calculations. In your free body diagram, you have to realise that your forces are in equilibrium. Perhaps it helps if you sort of have an idea where the net acceleration will be when drawing a free body diagram, which is not downwards as your equations suggest (though in this case it is actually non-existent). This will help you in more complicated problems like pulleys later on.