Question

2. A meteoroid is a small fragment of rock that orbits a planet or the sun. When a meteoroid enters a planet's atmosphere, it most likely will burn up entirely, glowing brilliantly as it does so. It is then referred to as a meteor. Consider a meteoroid that has an initial speed of 15,000km/s when it enters the thin upper region of Earth's atmosphere. Suppose this meteoroid encounters a force of resistance with a magnitude of 9.00x102 N, so that after it travels 500.9 km parallel to Earth's surface the meteoroid's speed is 14.97 km/s. Assume that the meteoroid does not lose any mass as its temperature increases, and that the change in the gravitational potential energy is negligible. What is the mass?

Answer 1

The mass of the meteoroid is approximately 1.07 x 10⁶ kg.

How can you find the mass?

To find the mass, we can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy. In this case, the work done on the meteoroid by the force of resistance is equal to its change in kinetic energy.

Work done by resistance:

W = Fr * d = (9.00 x 10² N) * (500,900 m) = 4.51 x 10⁸ J

Change in kinetic energy:

ΔKE = (1/2) * m * (vf² - vi²)

where m is the mass of the meteoroid.

Combining these equations,

4.51 x 10⁸ J = (1/2) * m * ((14,970 m/s)² - (15,000 m/s)²)

Solving for m:

m ≈ 1.07 x 10⁶ kg

Therefore, the mass of the meteoroid is approximately 1.07 x 10⁶ kg.