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oldhw 14 - alexander(jra2623 oldhomework 14 Turner(92510 1...

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alexander (jra2623) – oldhomework 14 – Turner – (92510) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points A car of weight 2060 N operating at a rate of 172 kW develops a maximum speed of 25 m / s on a level, horizontal road. Assuming that the resistive force (due to friction and air resistance) remains constant, what is the car’s maximum speed on an incline of 1 in 20; i.e. , if θ is the angle of the incline with the horizontal, sin θ = 1 / 20 ? Correct answer: 24 . 6312 m / s. Explanation: If f is the resisting force on a horizontal road, then the power P is P = f v horizontal . so that f = P v h = 1 . 72 × 10 5 W 25 m / s = 6880 N . On the incline, the resisting force is F = f + m g sin θ = f + W 20 = P v h + W 20 . And, F v = P , so v = P F = P P v h + W 20 = 1 . 72 × 10 5 W 1 . 72 × 10 5 W 25 m / s + 2060 N 20 = 24 . 6312 m / s . 002 (part 2 of 2) 10.0 points What is its power output on a 1-in-10 incline if the car is traveling at 14 m / s? Correct answer: 99204 W. Explanation: On the reduced incline, we again have, P = F v = ( f + m g sin θ ) v The only change from the previous problem is sin θ = 1 10 , so P = parenleftbigg f + W 10 parenrightbigg v = parenleftbigg p v h + W 10 parenrightbigg v = parenleftbigg 1 . 72 × 10 5 W 25 m / s + 2060 N 10 parenrightbigg (14 m / s) = 99204 W . 003 10.0 points A certain waterfall is 118 . 7 m high and has water flow rate of 30 . 2 m 3 / s. The acceleration of gravity is 9 . 8 m / s 2 . Find the maximum electric power that can be generated by these falls assuming 100% conversion of mechanical energy to electric energy. (Take the density of water to be 1 . 00 × 10 3 kg / m 3 ) Correct answer: 3 . 51305 × 10 7 W. Explanation: Basic Concepts: Potential Energy and Power Solution: When water falls from a high place, its potential energy decreases; for the waterfall, the variation of potential energy per second is Δ U = ( ρr ) g h = (1000 kg / m 3 ) (30 . 2 m 3 / s) × (9 . 8 m / s 2 ) (118 . 7 m) = 3 . 51305 × 10 7 J / s .

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alexander (jra2623) – oldhomework 14 – Turner – (92510) 2 When converted into electric energy, the power is P = Δ U = 3 . 51305 × 10 7 W . 004 10.0 points A 103 kg physics professor has fallen into the Grand Canyon. Luckily, he managed to grab a branch and is now hanging 98 m below the rim. A student (majoring in lin- guistics and physics) decides to perform a rescue/experiment using a nearby horse. Af- ter lowering a rope to her fallen hero and attaching the other end to the horse, the stu- dent measures how long it takes for the horse to pull the fallen physicist to the rim of the Grand Canyon.
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