2. Let F be the 3D vector field defined by F = -r/r³, where as always r = (x, y, z). This vector field models the gravitational force experienced by an object towards a mass at the origin. Let C be the oriented curve which points in a straight line from (1, 0, 0) to (a, 0, 0). Compute fF.T ds, by finding a parametrization r(t) for C, and turning the line integral into an ordinary integral. This number represents the work done by gravity on an object as it moves along the path C.

2. Let F be the 3D vector field defined by F = -r/r³, where as always r = (x, y, z). This vector field models the gravitational force experienced by an object towards a mass at the origin. Let C be the oriented curve which points in a straight line from (1, 0, 0) to (a, 0, 0). Compute fF.T ds, by finding a parametrization r(t) for C, and turning the line integral into an ordinary integral. This number represents the work done by gravity on an object as it moves along the path C.

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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Question

2. Let F be the 3D vector field defined by F = -r/r³, where as always r =
(x, y, z). This vector field models the gravitational force experienced by
an object towards a mass at the origin. Let C be the oriented curve which
points in a straight line from (1, 0, 0) to (a, 0, 0). Compute fF.T ds, by
finding a parametrization r(t) for C, and turning the line integral into an
ordinary integral. This number represents the work done by gravity on an
object as it moves along the path C.

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