16 (6) - hernandez(ejh742 oldhomework 16 Turner(58120 1...

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hernandez (ejh742) – oldhomework 16 – Turner – (58120) 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 1260 N operating at a rate of 140 kW develops a maximum speed of 37 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: 36 . 394 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 . 4 × 10 5 W 37 m / s = 3783 . 78 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 . 4 × 10 5 W 1 . 4 × 10 5 W 37 m / s + 1260 N 20 = 36 . 394 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 11 m / s? Correct answer: 43007 . 6 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 . 4 × 10 5 W 37 m / s + 1260 N 10 parenrightbigg (11 m / s) = 43007 . 6 W . 003 10.0 points A certain waterfall is 137 . 6 m high and has water flow rate of 28 . 8 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 . 88362 × 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 ) (28 . 8 m 3 / s) × (9 . 8 m / s 2 ) (137 . 6 m) = 3 . 88362 × 10 7 J / s .
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hernandez (ejh742) – oldhomework 16 – Turner – (58120) 2 When converted into electric energy, the power is P = Δ U = 3 . 88362 × 10 7 W . 004 10.0 points A 131 kg physics professor has fallen into the Grand Canyon. Luckily, he managed to grab a branch and is now hanging 76 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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