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Quiz01b-s

Quiz01b-s - R The variables are • R =12 m • V = • ρ...

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Quiz 1b Name: Date: Phys224 Spring 2010 Dr. P. Hanlet Show your work!!! If I can read it, I will give you partial credit!!! Correct answers without work will NOT get full credit. Concept (3 points each) 1. A barge floats due to: (a) Bernouli’s principle (b) Archimede’s principle (c) Pascal’s principle (d) all of the above (e) none of the above 2. If you apply a force | vector F 1 | to your brake pedal, and the master cylindar has radius r 1 , then the force applied to your brakes with slave cylinder radius r 2 is increased from | vector F 1 | by a factor: (a) r 1 r 2 (b) r 2 r 1 (c) r 2 1 r 2 2 (d) r 2 2 r 2 1 (e) none of the above 1

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Problem (5 pts) 3. A spherical, helium-filled balloon has a radius, R =12 . 0 m. The balloon, support cables, and basket have a mass of M b =196 . 0 kg. What maximum mass m can the balloon support while it floats at an altitude at which the helium density is ρ He =0 . 16 kg/m 3 and the density of air is ρ air =1 . 25 kg/m 3 ? Assume that only the balloon displaces the air.
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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 air-M b-M He = ρ air V-M b-ρ He V = ( ρ air-ρ He ) · 4 3 πR 3-M b Substituting in values: m = 4 3 π ( ρ air-ρ He ) R 3-M b = 4 3 π (1 . 25-. 16) kg/m 3 · (12 m ) 3-196 . kg = 4 3 · π · 1 . 09 kg/ a a m 3 · 1728 . a a m 3-196 . kg = 7889 . 7 kg-196 . kg ±inally m = 7693 . 7 kg 2...
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Quiz01b-s - R The variables are • R =12 m • V = • ρ...

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