Astronomers estimate that a 2.0- km -wide asteroid collides with the Earth once

Question

Astronomers estimate that a 2.0- km -wide asteroid collides with the Earth once every million years. The collision could pose a threat to life on Earth.

Assume a spherical asteroid has a mass of 3200 kg for each cubic meter of volume and moves toward the Earth at 16 km/s . How much destructive energy could be released when it embeds itself in the Earth?

For comparison, a nuclear bomb could release about 4.0×1016 J . How many such bombs would have to explode simultaneously to release the destructive energy of the asteroid collision with the Earth? n =

Explanation / Answer

a. volume of asteroid
V = d³/6 = *(2000m)³ / 6 = 4.2e9 m³
so its mass is
M = 3200kg/m³ * 4.2e9m³ = 1.344e13 kg
and so its KE at 16 km/s = 16000 m/s is
KE = ½ * 1.344e13kg * (16000m/s)² = 1.7203e21 J

b. # of bombs N = 1.7203e21J / 4.0e16J/bomb = 43007.5 bombs

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.