a.If a roughly spherical asteroid of mean diameter 1 km is approaching Earth at

Question

a.If a roughly spherical asteroid of mean diameter 1 km is approaching Earth at a relative velocity of 20 km s1, show that if it is made of rock with a density of 2,500 kg m3, its kinetic energy (as calculated by an observer standing on Earth) is approximately 2.6 x 1020 J.

(4 marks)

b.Bruce Willis, tethered to the asteroid, sees the Earth closing in on him at the same relative speed. If the mass of the Earth is approximately 6 x 1024 kg, show that his estimate of its kinetic energy is 1.2 x 1033 J.

(4 marks)

c.Explain how, despite the values that you found in parts (a) and (b) being very large but very different, the kinetic energy converted to other forms by the collision can be calculated and has a single value. Assume that the Earth and the asteroid collide inelastically.

Hint: you will need to consider the whole system before and after the impact, and use the principle of the conservation of momentum.

Explanation / Answer

a)KE = 1/2mv^2 = 1/2*density*vol*v^2

KE = 1/2*2500*(4/3*pi*500^3)*20000^2 = 2.6*10^20 J

b) KE = 1/2*6*10^24*20000^2 = 1.2*10^33 J

c) After the collision, the earth-asteroid system will provide the final output of the collision

hence will get a single value output

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