Work in a gravitational field For large distances from the surface GMm of Earth, the gravitational force is given by F1x2 1x + R22 where G = 6.7 * 10-1"N m²>kg² is the gravitational constant, M = 6 * 1024 kg is the mass of Earth, mis the mass of the object in the gravitational field, R = 6.378 * 10° m is the radius of Earth, and x U O is the distance above the surface of Earth (in meters). a. How much work is required to launch a rocket with a mass of 500 kg in a vertical flight path to a height of 2500 km (from Earth's surface)? b. Find the work required to launch the rocket to a height of x kilometers, for x 7 0. c. How much work is required to reach outer space 1xS »2? d. Equate the work in part (c) to the initial kinetic energy of the rocket, mv, to compute the escape velocity of the rocket.
Work in a gravitational field For large distances from the surface GMm of Earth, the gravitational force is given by F1x2 1x + R22 where G = 6.7 * 10-1"N m²>kg² is the gravitational constant, M = 6 * 1024 kg is the mass of Earth, mis the mass of the object in the gravitational field, R = 6.378 * 10° m is the radius of Earth, and x U O is the distance above the surface of Earth (in meters). a. How much work is required to launch a rocket with a mass of 500 kg in a vertical flight path to a height of 2500 km (from Earth's surface)? b. Find the work required to launch the rocket to a height of x kilometers, for x 7 0. c. How much work is required to reach outer space 1xS »2? d. Equate the work in part (c) to the initial kinetic energy of the rocket, mv, to compute the escape velocity of the rocket.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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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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Transcribed Image Text:Work in a gravitational field For large distances from the surface
GMm
of Earth, the gravitational force is given by F1x2
1x + R22
where G = 6.7 * 10-1"N m²>kg² is the gravitational constant,
M = 6 * 1024 kg is the mass of Earth, mis the mass of the object
in the gravitational field, R = 6.378 * 10° m is the radius of Earth,
and x U O is the distance above the surface of Earth (in meters).
a. How much work is required to launch a rocket with a mass of
500 kg in a vertical flight path to a height of 2500 km (from
Earth's surface)?
b. Find the work required to launch the rocket to a height of x
kilometers, for x 7 0.
c. How much work is required to reach outer space 1xS »2?
d. Equate the work in part (c) to the initial kinetic energy of the
rocket, mv, to compute the escape velocity of the rocket.
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