How long would it take a 1.50 Times 10^5 kg airplane with engines that produce a
ID: 1471788 • Letter: H
Question
How long would it take a 1.50 Times 10^5 kg airplane with engines that produce a maximum of 100 MW of power to reach a speed of 200 m/s and an altitude of 12.0 km if air resistance were negligible? If it actually takes 850 s, what is the power applied, in megawatts? Given this power, what is the average force of air resistance if the airplane takes 1200 s? Assume that a mountain climber uses oxygen and does work at 1.5 times the rate for climbing 116 stairs/min (1.96 L/min, 685 W), because of low air temperature and winds. Calculate how many liters of oxygen a climber would need for 11.0 h of climbing. (Note that only 40% of the inhaled oxygen is utilized and the rest is exhaled. Also note that your answer is in liters at sea level.) How much useful work does the climber do if he and his equipment have a mass of 82.0 kg and he gains 1100 m of altitude? What is his efficiency for the 11.0 h climb?Explanation / Answer
Total energy = To lift the plane to a height of 12 km + To make it fly with a velocity of 200 m/s
E = Mgh + 1/2 MV2 = M [gh + 1/2V2]
M = 1.5 x 105, h = 12000 m, V = 200 m/s
E = 1.5 x 105 x [9.8 x 12000 + 0.5 x 2002]
= 206.4 x 108 J
Power = Energy / Time = 100 x 106 W
Time = Energy/Power
= 206.4 x 108 J / 100 x 106 W = 206 s
(b)
Power = Energy / Time
Time = 850 s
Power = 206.4 x 108 J / 850 s = 24.3 MW
(c)
Total energy spent by a 24.3 MW engine in 1200 s = 291.6 x 108 J [with air resistance]
Total energy spent by 24 W engine in 850 s = 206.4 x 108 J [with out air resistance]
Difference in energy = 85.2 x 108 J
This differece came because of air resistance
Energy = Force x distance
Distance = velocity x time = 200 x 1200 = 2.4 x 105 m
Force = Energy/distance = 85.2 x 108 J / 2.4 x 105 m = 35.5 x 103 N = 35.5 kN.
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