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A rocket on the surface of the earth is roughly 6 million meters from the center of the earth. Suppose this rocket needs to reach an elevation of 1.6 billion meters. (This is roughly the elevation of the Webb space telescope.) A lot of energy for doing this will be "wasted" in the form of heat, light, sound, and other things. But the bare minimum of energy needed to do this is the work required to lift something from 6 million meters up to 1.6 billion meters (as measured from the center of the earth). When we are not constrained to the immediate surface of the earth, acceleration from gravity depends on how far an object is from the earth's center. For this rocket, the force of gravity applied to it while it is at elevation x (from the center of the earth) is 2-1020 Newtons. Find how much work would be needed, at minimum, to put this x2 rocket where it needs to be.

A rocket on the surface of the earth is roughly 6 million meters from the center of the earth. Suppose this rocket needs to reach an elevation of 1.6 billion meters. (This is roughly the elevation of the Webb space telescope.) A lot of energy for doing this will be "wasted" in the form of heat, light, sound, and other things. But the bare minimum of energy needed to do this is the work required to lift something from 6 million meters up to 1.6 billion meters (as measured from the center of the earth). When we are not constrained to the immediate surface of the earth, acceleration from gravity depends on how far an object is from the earth's center. For this rocket, the force of gravity applied to it while it is at elevation x (from the center of the earth) is 2-1020 Newtons. Find how much work would be needed, at minimum, to put this x2 rocket where it needs to be.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A rocket on the surface of the earth is roughly 6 million meters from the center of the earth. Suppose this rocket needs to reach an elevation of 1.6 billion meters. (This is roughly the elevation of the Webb space telescope.) A lot of energy for doing this will be "wasted" in the form of heat, light, sound, and other things. But the bare minimum of energy needed to do this is the work required to lift something from 6 million meters up to 1.6 billion meters (as measured from the center of the earth). When we are not constrained to the immediate surface of the earth, acceleration from gravity depends on how far an object is from the earth's center. For this rocket, the force of gravity applied to it while it is at elevation x (from the center of the earth) is 3. 2-1020 x2 Newtons. Find how much work would be needed, at minimum, to put this rocket where it needs to be.
Transcribed Image Text:A rocket on the surface of the earth is roughly 6 million meters from the center of the earth. Suppose this rocket needs to reach an elevation of 1.6 billion meters. (This is roughly the elevation of the Webb space telescope.) A lot of energy for doing this will be "wasted" in the form of heat, light, sound, and other things. But the bare minimum of energy needed to do this is the work required to lift something from 6 million meters up to 1.6 billion meters (as measured from the center of the earth). When we are not constrained to the immediate surface of the earth, acceleration from gravity depends on how far an object is from the earth's center. For this rocket, the force of gravity applied to it while it is at elevation x (from the center of the earth) is 3. 2-1020 x2 Newtons. Find how much work would be needed, at minimum, to put this rocket where it needs to be.
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