11. While taking a plane flight to a meeting, a physicist decides to do a mental

Question

11.

While taking a plane flight to a meeting, a physicist decides to do a mental calculation of how much fuel the plane would consume in the absence of friction, assuming its engines have an efficiency of 21.0% and the mass of the plane is 200,000 kg. Each gallon of jet fuel produces 1.30 ? 108 J of heat when burned.

(a) How many gallons of fuel are used to get the plane from rest to the takeoff speed of 50.0 m/s?
1          gal

(b) How many gallons to get to a cruising speed of 250 m/s and an altitude of 8.0 km?
2           gal

(c) How much waste heat is produced in each case? (Both the actual fuel consumption and heat produced will be greater because of air resistance.)
3          

J (in part a)
4          

J (in part b)

Explanation / Answer

useful heat from 1 gallon = 0.21*1.3*10^8 = 27.3e+6 J



a) Q = W = 0.5*M*V^2 = 0.5*200000*50^2 = 250e+6 J

fuel required = 250e+6/27.3e+6 = 9.157 gallons

b) Q = M*g*h+0.5*M*V^2 = (200000*9.8*8000) + (0.5*200000*250^2)= 21.93e+9 J

fuel required = 21.93e+9/27.3e+6 = 803.2967 gallons

c) 0.79*9.157*1.3*10^8 = 940.4239e+6 J

d) 0.79*803.2967*1.3*10^8 = 82.498571e+9 J

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