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 22.0% and the mass of the plane is 200,000 kg. Each gallon of jet fuel produces 1.30 multiplied by 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 55.0 m/s?
(b) How many gallons to get to a cruising speed of 250 m/s and an altitude of 10.0 km?
(c) How much waste heat is produced in each case(in part a and b)? (Both the actual fuel consumption and heat produced will be greater because of air resistance.)
I know how to do the first one.
(0.5*200000*55^2)/[(1.30*10^8)*0.22]
=10.6 gal
And part of (c)
Q waste=1.3*10^8*10.6-0.5*200000*55^2=1.08*10^9 J
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