Question

A 30-seat turboprop airliner whose mass is 14,000 kg takes off from an airport and eventually achieves its cruising speed of 620 km/h at an altitude of 10,000 m. For g = 9.78 m/s^2, determine the change in kinetic energy and the change in gravitational potential energy of the airliner, each in kJ.

Answer 1

Ek=207.569MJ

Ep=136.92MJ

Step-by-step explanation:

kinetic energy is that energy that bodies with mass have when they have movement, while the potential energy is due to the height and mass that bodies have.

taking into account that the plane starts from rest at a height of zero, the following equations are taken to calculate the kinetic energy (Ek) and the potential energy (Ep)

`Ek=0.5mv^(2) \\Ep=mgh`

where

m=mass=14000kg

v=speed=620km/h=172.2m/s

h=altitude=1000m

g=gravity=9.78 m/s^2

solving

Ek=(0.5)(14000)(172.2)^2=207569880J=207.569MJ

Ep=(14000)(9.78)(1000)=136920000=136.92MJ