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Energy from the Moon? Suppose that some time in the future
Chapter 9, Problem 41E(choose chapter or problem)
Problem 41E
Energy from the Moon? Suppose that some time in the future we decide to tap the moon’s rotational energy for use on earth. In additional to the astronomical data in Appendix F, you may need to know that the moon spins on its axis once every 27.3 days. Assume that the moon is uniform throughout. (a) How much total energy could we get from the moon’s rotation? (b) The world presently uses about 4.0 × 1020 J of energy per year. If in the future the world uses five times as much energy yearly, for how many years would the moon’s rotation provide us energy? In light of your answer, does this seem like a cost-effective energy source in which to invest?
Questions & Answers
QUESTION:
Problem 41E
Energy from the Moon? Suppose that some time in the future we decide to tap the moon’s rotational energy for use on earth. In additional to the astronomical data in Appendix F, you may need to know that the moon spins on its axis once every 27.3 days. Assume that the moon is uniform throughout. (a) How much total energy could we get from the moon’s rotation? (b) The world presently uses about 4.0 × 1020 J of energy per year. If in the future the world uses five times as much energy yearly, for how many years would the moon’s rotation provide us energy? In light of your answer, does this seem like a cost-effective energy source in which to invest?
ANSWER:Solution 41E
Step 1 of 5:
Here we shall consider the moon as hard solid sphere with mass m= 7.35 with radius R= 1.74
performing
=1 revolution in dt= 27.3 days, we need to calculate the resultant kinetic energy due to the motion of moon.
In order to calculate the kinetic energy we need to calculate angular speed and moment of inertia.
Given data,
-
Mass of moon, m= 7.35
-
Radius of moon orbit, R= 1.74
-
Angular displacement,
=1 rev
Using 1 rev= rad
=
rad
- Time taken, dt = 27.3 days
Using 1 day= 24 60
60 dt = 27.3
24
60
60 sec
dt= 2358720 sec