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Astronomers estimate that a $2.0-\mathrm{km}$ -wide asteroid collides with the Earth once every million years. The collision could pose a threat to life on Earth. (a) Assume a spherical asteroid has a mass of 3200 $\mathrm{kg}$ for each cubic meter of volume and moves toward the Earth at 15 $\mathrm{km} / \mathrm{s} .$ How much destructive energy could be released when it embeds itself in the Earth? (b) For comparison, a nuclear bomb could release about $4.0 \times 10^{16} \mathrm{J} .$ How many such bombs would have to explode simultaneously to release the destructive energy of the asteroid collision with the Earth?

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Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

Cornell University

Hope College

University of Sheffield

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eso. First of all, we want to find the mass of the asteroid. Um and this is just density times folly on DSO assuming spherical spherical asteroid, this is density times 4/3 pi times radius cubed s 02 kilometer asteroid has, ah volume of houses of two kilometer wide Estrada's radius off one kilometer of their 1000 meters. So therefore, the energy that was released by the asteroid it's just it's Connecticut and even that's 1/2 em being out square. It's national bossy. That's 1/2 road times 4/3 pi r Cubed times you're not squared and so this is 1/2 times rose 3200 kilograms per meter cube. That's the density times 4/3 pi times are as we mentioned as I mentioned is 1000 uh, meters cubed one Cormier's 1000 meters times velocity initial velocity squared, which is 1.5 times 10 to the four meters per second quality squint. And so this will give you one point. Fought something very close to 1.51 times 10 to the 21 Jules. An extraordinary amount of energy on. And to show you how extraordinary you divide that you divide 1.51 times 10 of the 21 Jules over the energy of a single nuclear bomb off four times 10 to the 16 Jules. And so this comes out to be, um, Jule per bomb. So this comes out to do 38,000 nuclear bombs. That's how much energy is released by one asteroid impact of this kind.

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