There is a block of wood floating on the surface of a body of water, with a ball attached to the bottom of the block by a string. I am asked to find the volume of the ball given the tension in the string. We also know the volume of the wood block from an earlier problem if applicable (I don't think it is needed for this problem but I may be wrong).
B = mg = ρfluidgVobject
∑F = ma
ρV = m
The Attempt at a Solution
I started out with a fbd and summed the forces on the ball:
∑F = T + B - mballg = 0.
Substituted in the buoyancy equation:
∑F = T + ρwatergVball - mballg = 0.
Then rearranging and substituting in ρV = m for the ball:
T + ρwatergVball = ρballVg.
Finally rearranging for the volume of the ball:
Vball = T / ((ρball - ρwater)g).
Alas, this did not result in the correct answer and I am not sure where I went wrong. I think it is somewhere with my forces, buoyancy has always confused me and its exact function as a force. Any help appreciated!