Concept Simulation 7.1 illustrates the physicsprinciples in this problem. An ast

Question

Concept Simulation 7.1 illustrates the physicsprinciples in this problem. An astronaut in his space suit and witha propulsion unit (empty of its gas propellant) strapped to hisback has a mass of 147 kg. During a space-walk, the unit, which hasbeen filled with propellant gas, ejects some gas with a velocity of+31.0 m/s. As a result, the astronaut recoils with a velocity of-0.247 m/s. After the gas is ejected, the mass of the astronaut(now wearing a partially empty propulsion unit) is 163 kg. Whatpercentage of the gas propellant in the completely filledpropulsion unit was depleted?

Explanation / Answer

after the gas is ejected, momentum conservation gives mv = MV where m = mass of gas ejected v = speed of gas = 31 m/s M = mass of astronaut & partially filled propulsio unit =163 V = recoil speed of astronaut = .247 m/s so we can solve for m m = MV/v = 163*.247/31 = 1.3 kg % gas expelled = 1.3/(163+1.3-147) = .075 = 7.5%

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