Answered: calculate the energy required to send a…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter11: Gravity, Planetary Orbits, And The Hydrogen Atom

Section: Chapter Questions

Problem 30P

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calculate the energy required to send a 1 kg object from the surface of Earth to the satellite located 42.16*10^6m from the center of the Earth. Assume the location from which the object is being launched is 6.37*10^6m from the center.

a. Use the object's weight at the surface of the earth (g=9.8) to find Newton's proportional constant k for this object.

b. Write a definite integral that calculates the energy required to send the object to orbit, then use the Fundamental theorem of calculus to calculate the energy.

c. Write t he formula for a Reimann sum that is guaranteed to estimate the energy required to send the object to orbit, accurate with 10^5 J.

d. calculate the fraction of the object's total distance traveled at which half of the total required energy is expended.

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