Quiz01a-s - payload Your Favorite Beer r h The variables...

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Quiz 1a Name: Date: Phys224 Spring 2010 Dr. P. Hanlet Concept (3 points each) 1. Your brakes on your car work due to: (a) Bernouli’s principle (b) Archimede’s principle (c) Pascal’s principle (d) in part by each of the above (e) none of the above 2. A consequence of pressure in a Fuid being a scaler quantity is that: (a) hot air baloons Fy (b) the pressure is the same at each point throughout the volume (c) at a given depth the pressure on an in±nitessimal cube di²ers signi±cantly between sides and top (or bottom) face 1
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Problem (5 pts) Show your work!!! If I can read it, I will give you partial credit!!! Correct answers without work will NOT get full credit. 3. A cylindrical hot air balloon of height h = 15 m and radius r = 3 m. The balloon and basket have a combined mass of 150 kg. If the maximum payload is 250 kg and the density of the cold air is ρ c = 1 . 20 kg/m 3 , what must be the density of the hot air in order to lift the balloon at maximum
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Unformatted text preview: payload? Your Favorite Beer r h The variables are: • h =15 m • r =3 m • m B =150 kg • m P =250 kg • ρ c =1 . 20 kg/m 3 • ρ h =? Archimede’s Principle states that the bouyant force is equal to the weight of the displaced Fuid. Here, the weight of the displaced Fuid must be greater than or equal to the weight of the hot air in the balloon, the balloon, plus its payload: W h + W B + W P = W c where W = mg such that: m h g + m B g + m P g = m c g ρ h V g + m B g + m P g = ρ c V g since ρ = m/V . Solving for ρ h : ρ h V g = ρ c V g-m B g-m P g ρ h = ρ c V g-m B g-m P g V g = ρ c-m B + m P V = ρ c-m B + m P πr 2 h where V = πr 2 h is the volume of air in the balloon. Substituting in values: ρ h = 1 . 20 kg/m 3-150 kg + 250 kg π (3 m ) 2 (15 m ) = 1 . 20 kg/m 3-400 kg 135 π m 3 ±inally: ρ h = 0 . 26 kg/m 3 2...
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Quiz01a-s - payload Your Favorite Beer r h The variables...

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