A meteor weighing 2 kilograms falls into the atmosphere at a speed of 2 km / s at an altitude of 300

A meteor weighing 2 kilograms falls into the atmosphere at a speed of 2 km / s at an altitude of 300 kilometers. At an altitude of 100 meters, it burns up, but has a speed of 72 kilometers per hour. Why did it burn down.

Given:

m = 2 kilograms is the mass of the meteorite;

H1 = 300 kilometers = 3 * 10 ^ 5 meters – the initial height of the meteorite;

v1 = 2 km / s = 2 * 10 ^ 3 m / s – the initial speed of the meteorite;

v2 = 72 km / h = 20 m / s – the final speed of the meteorite;

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

H2 = 100 meters – the final height of the meteorite.

It is required to determine A – the work of the air resistance forces, as a result of which the meteorite heated up and burned out.

According to the law of conservation of energy:

m * g * H1 + m * v1 ^ 2/2 = m * g * H2 + m * v2 ^ 2/2 + A, hence

A = m * g * H1 + m * v1 ^ 2/2 – m * g * H2 – m * v2 ^ 2/2;

A = m * g * (H1 – H2) + m / 2 * (v1 ^ 2 – v2 ^ 2) = 2 * 10 * (3 * 10 ^ 5 – 100) + 2/2 * (2000 ^ 2 – 20 ^ 2) = 20 * 299900 + (4000000 – 400) = 5998000 + 3999600 = 9997600 Joules.

As you can see, almost 99 percent of the mechanical energy that the meteorite possessed during its entry into the Earth’s atmosphere went to work the air resistance force, as a result of which it heated up and burned out.

Answer: the force of air resistance is 9997600 Joules.