Question

An airplane (mass 80000kg) has a thrust of 160000N.
a) Estimate the work needed to reach the take-off speed of 60m/s from rest? Neglect air drag and rolling resistance, assuming that the acceleration is constant. You can calculate this in 2 ways: calculate the distance and determine the energy, or use the kinetic energy difference. Do it both ways!
b) How long is the minimum runway, assuming a safety factor of 2. Compare this value to the shorter runway at Tallahassee Airport (TLH).

Answer 1

a)

using conservation of energy

W = 0.5 m v^2 = 0.5* 80000* 60^2

W = 1.44* 10^8 J

considering the 2nd approach

we need to find the acceleration fiest

a = F/m = 160000 / 80000 = 2 m/s^2

using 3rd equation of motion

d = v^2/ ( 2 a) = 60^2 / ( 2* 2) = 900 m

then workdone stored as kE

kE = Fd = 160000* 900 = 1.44* 10^8 J

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b) length of runway

W = Fd

1.44* 10^8 = 160000* d

d = 900 m

for factor of safety of 2,

runway = 900* 2 = 1800 m = 1.8 km

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