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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
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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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.
Transcribed Image Text: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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why does F(r(t))=-r/(1+(a-1)t)^3/2 instead of r^3? does |r| just equals to 1+(a-1)t?

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