You know from theoretical considerations that a force field takes the form F(x, y, z) = (x + y, y, Az2), for some constant A. In your lab measure that the work done to move an object from the point (1,0, 0) to the point (0, 2, 1) along a straight line is 70 (in appropriate unit You want to determine the constant A. First, you associate a one-form o to F. You get (your answers should be written in terms of the unknown constant A ): dx+ dy+ dz. Next, you find a parametrization for the line segment. Your parametrization is: a : [0, 1] → R, with a(t) =( You then calculate the pullback of the one-form. You get: a*o = dt. You evaluate the line integral: !! from which you conclude that: A =
You know from theoretical considerations that a force field takes the form F(x, y, z) = (x + y, y, Az2), for some constant A. In your lab measure that the work done to move an object from the point (1,0, 0) to the point (0, 2, 1) along a straight line is 70 (in appropriate unit You want to determine the constant A. First, you associate a one-form o to F. You get (your answers should be written in terms of the unknown constant A ): dx+ dy+ dz. Next, you find a parametrization for the line segment. Your parametrization is: a : [0, 1] → R, with a(t) =( You then calculate the pullback of the one-form. You get: a*o = dt. You evaluate the line integral: !! from which you conclude that: A =
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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![You know from theoretical considerations that a force field takes the form F(x, y, z) = (x + y, y, Az?), for some constant A. In your lab, you
measure that the work done to move an object from the point (1, 0, 0) to the point (0, 2, 1) along a straight line is 70 (in appropriate units).
%3D
You want to determine the constant A
First, you associate a one-form o to F. You get (your answers should be written in terms of the unknown constant A ):
dx+
dy+
dz.
Next, you find a parametrization for the line segment. Your parametrization is:
a : [0, 1] → R³,
with
a(t) =
%3D
You then calculate the pullback of the one-form. You get:
a*@ =
dt.
You evaluate the line integral:
%D
from which you conclude that:
A =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc130140d-aaee-4d36-bbe0-eb62ed01e8c5%2Ff6c609ed-8b08-4b63-97e4-ac391e13f5d1%2F371ztfs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:You know from theoretical considerations that a force field takes the form F(x, y, z) = (x + y, y, Az?), for some constant A. In your lab, you
measure that the work done to move an object from the point (1, 0, 0) to the point (0, 2, 1) along a straight line is 70 (in appropriate units).
%3D
You want to determine the constant A
First, you associate a one-form o to F. You get (your answers should be written in terms of the unknown constant A ):
dx+
dy+
dz.
Next, you find a parametrization for the line segment. Your parametrization is:
a : [0, 1] → R³,
with
a(t) =
%3D
You then calculate the pullback of the one-form. You get:
a*@ =
dt.
You evaluate the line integral:
%D
from which you conclude that:
A =
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