Question

A typical loaded commercial jet airplane has an inertia of 2.1 × 105 kg (a) Which do you expect to require more energy: getting the plane up to cruising speed or getting it up to cruising altitude? Will one be a lot more than the other or will they be comparable? (b) How much energy does it take to get the plane to a cruising speed of 270 m/s? (c) How much energy does it take to get the plane to a cruising altitude of 10.4 km? [Ignore dissipation.]

Answer 1

(a) It depends on what cruising speed and cruising altitude

(b)
`7654.5 * 10^6 (J)`

(c)
`21425.04 * 10^6 (J)`

Step-by-step explanation:

Formula for Kinetic energy:
`E_k = (mv^2)/(2)`

Formula for Potential energy
`E_p = mgh`

(a) It actually depends on cruising speed and cruising altitude to tell which one requires more energy. However, cruising speed would have more impact than cruising altitude because it has a power of 2 in the energy formula.

(b) If we plug in v = 270 and m = 210000 to the Kinetic energy formula we should have

`E_k = (210000 * 270^2)/(2) = 7654.5 * 10^6 (J)`

(c) If we plug in h = 10.4 km = 10400 m, m = 210000 and g = 9.81 we should have

`E_p = 210000 * 9.81 * 10400 = 21425.04 * 10^6 (J)`