The plane flies at a speed of 900 kilometers per hour at an altitude of 9 kilometers from the ground.

The plane flies at a speed of 900 kilometers per hour at an altitude of 9 kilometers from the ground. What is the total mechanical energy of an aircraft weighing 20 tons.

Given:

m = 20 tons = 2 * 10 ^ 4 kilograms – the mass of the aircraft;

v = 900 km / h = 250 m / s – aircraft speed;

h = 9 kilometers = 9 * 10 ^ 3 meters – the height at which the plane flies;

g = 10 m / s ^ 2 – acceleration of gravity.

It is required to determine W (Joule) – the total mechanical energy of the aircraft.

Let’s find the potential energy of the aircraft:

E1 = m * g * h = 2 * 10 ^ 4 * 10 * 9 * 10 ^ 3 = 18 * 10 ^ 8 Joules.

Let’s find the kinetic energy of the aircraft:

E2 = m * v ^ 2/2 = 2 * 10 ^ 4 * 250 ^ 2/2 = 10 ^ 4 * 62,500 = 6.3 * 10 ^ 8 Joules.

The total mechanical energy is equal to:

W = E1 + E2 = 18 * 10 ^ 8 + 6.3 * 10 ^ 8 = 24.3 * 10 ^ 8 Joules = 2430 MJ.

Answer: the total mechanical energy of the aircraft is 2430 MJ.