Buoyancy of sphere in water

1. Jan 25, 2009

dnp33

1. The problem statement, all variables and given/known data

A hollow plastic sphere is held below the surface of a fresh water lake by a cord anchored to the bottom of the lake. The sphere has a volume of 0.65 m^3 and the tension in the cord is 842 N. What is the mass of the sphere, in kg? Enter your answer using 3 decimal places, don't enter the units

2. Relevant equations

$$\rho *V*g=F$$
F=mg

3. The attempt at a solution

because the system is in equilibrium
F tension + Force of gravity = Buoyant Force.
842N + (9.81m/s^2)m = (1000kg/m^3)(0.65m^3)(9.81m/s^2)
the answer turns out to be 564kg, unless i'm doing something really stupid.
but that seems to be really high for a hollow plastic sphere.

2. Jan 25, 2009

Delphi51

Re: buoyancy/equilibrium

Your calc looks correct! And your physical intuition. I guess whoever made up the question estimated the mass rather high.

3. Jan 25, 2009

dnp33

Re: buoyancy/equilibrium

yeah i can't think of anything that i'm doing wrong, it just seems really weird that the mass would be so high.
when i worked out the density of the ball it was lower than that of water so it should float it just seems weird thinking about something that heavy floating.

4. Jan 26, 2009

nvn

dnp33: Your answer is correct. Let's say the hollow sphere in your given problem is made of polyvinyl chloride (PVC) plastic, has a wall thickness of t = 148.12 mm, and contains air at atmospheric pressure. The density of polyvinyl chloride is rhop = 1400 kg/m^3. Can you compute the mass of this sphere? Neglect the density of air.