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

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 3000 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? Express your answer using two significant figures. Part B For comparison, a nuclear bomb could release about 4.0times10^16 J. How many such bombs would have to explode simultaneously to release the destructive energy of the asteroid collision with the Earth? Express your answer using two significant figures.

Explanation / Answer

part a )

maximum destructive energy that can be released is the case when all the kinetic energy of the asteroid is consumed.

therefore E = 1/2 m v^2

m= density * volume

= 3000* (4/3* pi * 1000^3 ) = 1.2567*10^13 kg

given v = 16000m/s

therefore

E= 1/2 * 1.2567*10^13  * 1600 * 1600

= 1.6084 x 10^19 Joules!

part B)

each bomb is capable of 4 x 10^16 joules

therefore no of bombs that are needed to produce the required energy are

1.6 x 10^19 / 4 x 10^16 = 402.123

that is 402 such nuclear bombs are required!

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