- #1

gmorrill

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## Homework Statement

An empty rubber balloon has a mass of 0.0122 kg. The balloon is filled with helium at a density of 0.179 kg/m

^{3}. At this density the balloon has a radius of 0.467 m. The acceleration of gravity is 9.8m/s

^{2}. If the filled balloon is fastened to a vertical line, what is the tension in the line? Answer in units of N.

## Homework Equations

V = (4/3) * pi * r

^{3}

Buoyant force B: rho

_{air}* V * g

Weight of helium w

_{h}: rho

_{helium}* V * g

Weight of balloon w

_{b}: m * g

## 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 - w

_{h}- w

_{b}- T = 0

So:

T = B - w

_{h}- w

_{b}

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

^{3}

V = 0.42662

B = 1.20 * 0.42662 * 9.8 = 5.01703

w

_{h}= 0.179 * 0.42662 * 9.8 = 0.74838

w

_{b}= 0.0122 * 9.8 = 0.11956

So I end up with: 4.14909 N.

So where am I going wrong? Thanks :)