(a)
The kinetic energy of an asteroid having radius
(a)
Answer to Problem 12Q
Solution:
The kinetic energy of the asteroid is found out to be
Explanation of Solution
Given data:
The velocity of the asteroid hitting the Earth is
The radius of the asteroid is
The density of the asteroid is
Formula used:
The mass of the asteroid can be calculated by the following expression:
Here,
The expression for the volume of a sphere is:
Here,
Conversion formula from kilometer to meter is:
1 km = 1000 m
The kinetic energy is calculated by the below expression:
Here,
Explanation:
Recall the expression for calculating the volume.
Substitute 1 km for
Recall the expression of mass.
Substitute
The mass of asteroid is
Recall the expression for the kinetic energy.
Substitute
Conclusion:
Thus, the kinetic energy of the asteroid is found out to be
(b)
The comparison between the energy released by the impact of asteroid mentioned in sub-part (a) to the energy released by a 20-kiloton nuclear weapon, which was similar to the nuclear weapon dropped on Hiroshima.
(b)
Answer to Problem 12Q
Solution:
The energy released during nuclear destruction is 40 times smaller than the energy released during the asteroid strike.
Explanation of Solution
Given data:
The energy released by the nuclear weapon is 20-kilotons.
Formula used:
1 kiloton of TNT emits
The expression of energy released in joules is:
Explanation:
From sub-part (a), the value of kinetic energy of the asteroid is
Recall the expression of energy released in joules.
Substitute
Refer to the value of energy released by the impact of an asteroid that is
The energy released in nuclear attack is
Taking the ratio of both the above energies,
Conclusion:
Therefore, the kinetic energy of the asteroid striking the Earth’s surface is
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