# Balloon buoyancy

1. Dec 2, 2009

### gmorrill

1. The problem statement, all variables and given/known data
An empty rubber balloon has a mass of 0.0122 kg. The balloon is filled with helium at a density of 0.179 kg/m3. At this density the balloon has a radius of 0.467 m. The acceleration of gravity is 9.8m/s2. If the filled balloon is fastened to a vertical line, what is the tension in the line? Answer in units of N.

2. Relevant equations
V = (4/3) * pi * r3
Buoyant force B: rhoair * V * g
Weight of helium wh: rhohelium * V * g
Weight of balloon wb: m * g

3. The attempt at a solution
I think I understand all the concepts, but I'm not coming up with the solution in the book. Book's solution is 4.52537 N.

I drew a free body diagram to determine the sum of forces:
B - wh - wb - T = 0

So:
T = B - wh - wb

The density of air isn't given, so I went with what the chart in the book listed: 1.20 kg/m3

V = 0.42662

B = 1.20 * 0.42662 * 9.8 = 5.01703

wh = 0.179 * 0.42662 * 9.8 = 0.74838

wb = 0.0122 * 9.8 = 0.11956

So I end up with: 4.14909 N.

So where am I going wrong? Thanks :)