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Unformatted text preview: R The variables are: • R =12 . m • V =? • ρ He =0 . 16 kg/m 3 • ρ air =1 . 25 kg/m 3 • M air =? • M He =? • M b =196 . kg • m =? • W air =? • W He =? • W b =? Archimedes’ Principle states that the bouyant force is equal to the weight of the displaced Fuid, where the weights are the forces. So: W air = W b + W He + W m M air g = M b g + M He g + mg M air = M b + M He + m Solving for m , and invoking the relationships ρ = M/V and V = 4 3 πR 3 : m = M airM bM He = ρ air VM bρ He V = ( ρ airρ He ) · 4 3 πR 3M b Substituting in values: m = 4 3 π ( ρ airρ He ) R 3M b = 4 3 π (1 . 25. 16) kg/m 3 · (12 m ) 3196 . kg = 4 3 · π · 1 . 09 kg/ a a m 3 · 1728 . a a m 3196 . kg = 7889 . 7 kg196 . kg ±inally m = 7693 . 7 kg 2...
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 Spring '10
 Hanlet
 Buoyancy, Force, Mass, Archimedes, cylinder radius r2

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