A fully loaded Boeing 747-400 takes 40 seconds to reach its takeoff speed at 80

Question

A fully loaded Boeing 747-400 takes 40 seconds to reach its takeoff speed at 80 m/s. The mass of the plane is 400,00kg. Include the force of rolling friction from the wheels, Ur=.02. 1.) What is the magnitude of the force of rolling friction as the plane accelerates down the runway? 2.) If the cross-sectional area of the 747 is 35 m^2, how large is the force of drag at the takeoff speed? Assume the coefficient of drag Cd=0.5 3.) If we ignore drag, how much thrust would the engines have to provide to get the 747 up to takeoff speed?

Explanation / Answer

a)

f = u mg = 0.02 * 40000 * 9.8 = 7840 N

b)

F = 0.5 rho v^2 Cd A = 0.5*1.29*80*80*0.5*35 = 72240 N

c)

d = 40 * 80 = 3200 m

0.5 m v^2 = (F-f) d

0.5 * 40000*80*80 = (F - 7840) * 3200

F = 47840 N

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