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# Escape velocity and black holes The work required to ISBN: 9780321570567 2

## Solution for problem 73E Chapter 7.7

Calculus: Early Transcendentals | 1st Edition

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Problem 73E

Escape velocity and black holes The work required to launch an object from the surface of Earth to outer space is given by , where R =6370 km is the approximate radius of Earth, F(x)= GMm/x2 is the gravitational force between Earth and the object, G is the gravitational constant. M is the mass of Earth, m is the mass of the object, and GM = 4 × 1014m3/s2.a. Find the work required to launch an object in terms of m.________________b. What escape velocity ve is required to give the object a kinetic energy equal to W?________________c. The French scientist Laplace anticipated the existence of black holes in the 18th century with the following argument: If a body has an escape velocity that equals or exceeds the speed of light. c =300,000 km/s, then light cannot escape the body and it cannot be seen. Show that such a body has a radius R ? 2GM/c2. For Earth to be a black hole, what would its radius need to be?

Step-by-Step Solution:

Problem 73EEscape velocity and black holes The work required to launch an object from the surface of Earth to outer space is given by , where R =6370 km is the approximate radius of Earth, is the gravitational force between Earth and the object, G is the gravitational constant. M is the mass of Earth, m is the mass of the object, and GM = 4 × 1014 m3/s2.a. Find the work required to launch an object in terms of m.b. What escape velocity is required to give the object a kinetic energyequal to Wc. The French scientist Laplace anticipated the existence of black holes in the 18th century with the following argument: If a body has an escape velocity that equals or exceeds the speed of light. c =300,000 km/s, then light cannot escape the body and it cannot be seen. Show that such a body has a radius R 2GM/c2. For Earth to be a black hole, what would its radius need to beSolution:Step 1To find the work required to launch an object in terms of m.The work required to launch an object from the surface of Earth to outer space is given by , where . Putting in the value of GM and R, we get .So, work done to launch an object of mass m is .

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##### ISBN: 9780321570567

The full step-by-step solution to problem: 73E from chapter: 7.7 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. The answer to “Escape velocity and black holes The work required to launch an object from the surface of Earth to outer space is given by , where R =6370 km is the approximate radius of Earth, F(x)= GMm/x2 is the gravitational force between Earth and the object, G is the gravitational constant. M is the mass of Earth, m is the mass of the object, and GM = 4 × 1014m3/s2.a. Find the work required to launch an object in terms of m.________________b. What escape velocity ve is required to give the object a kinetic energy equal to W?________________c. The French scientist Laplace anticipated the existence of black holes in the 18th century with the following argument: If a body has an escape velocity that equals or exceeds the speed of light. c =300,000 km/s, then light cannot escape the body and it cannot be seen. Show that such a body has a radius R ? 2GM/c2. For Earth to be a black hole, what would its radius need to be?” is broken down into a number of easy to follow steps, and 169 words. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Since the solution to 73E from 7.7 chapter was answered, more than 441 students have viewed the full step-by-step answer. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. This full solution covers the following key subjects: Object, EARTH, escape, required, velocity. This expansive textbook survival guide covers 85 chapters, and 5218 solutions.

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Escape velocity and black holes The work required to