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Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550

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BuyFindarrow_forward

Calculus: Early Transcendentals

8th Edition
James Stewart
ISBN: 9781285741550
Textbook Problem

An object moves along the curve C shown in the figure from (1, 2) to (9, 8). The lengths of the vectors in the force field F are measured in newtons by the scales on the axes. Estimate the work done by F on the object.

images

To determine

To Estimate: The work done by the force field F on the object.

Explanation

Given data:

Refer to the Figure at the bottom the question 51 in the textbook.

An object moves along the curve C in the figure from the point (1,2) to (9,8) .

Formula used:

Write the expression to find work done by the object in moving the particle.

CFTds=i=1n[F(xi,yi,zi)T(xi,yi,zi)]Δsi (1)

Here,

T(x,y,z) is the unit tangent vector at the point (x,y,z) on the curve C ,

Δsi is the length between two points of each segment, and

n is the number of segments, where 7 segments from the figure.

From the Figure in the textbook, the length between any two points of each segment is 2.

Δsi=2

As the curve C is composed of straight line segments, FT is the scalar projection of force field vector onto the curve C.

Calculation of work done by the object:

Substitute 2 for Δsi in equation (1) and rewrite the expression as follows.

CFTds=i=17[F(xi,yi,zi)T(xi,yi,zi)]Δsi

CFTds=[F(x1,y1,z1)T(x1,y1,z1)+F(x2,y2,z2)T(x2,y2,z2)+F(x3,y3,z3)T(x3,y3,z3)+F(x4,y4,z4)T(x4,y4,z4)+F(x5,y5,z5)T(x5,y5,z

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Chapter 16 Solutions

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Sect-16.1 P-11ESect-16.1 P-12ESect-16.1 P-13ESect-16.1 P-14ESect-16.1 P-15ESect-16.1 P-16ESect-16.1 P-17ESect-16.1 P-18ESect-16.1 P-21ESect-16.1 P-22ESect-16.1 P-23ESect-16.1 P-24ESect-16.1 P-25ESect-16.1 P-26ESect-16.1 P-29ESect-16.1 P-30ESect-16.1 P-31ESect-16.1 P-32ESect-16.1 P-33ESect-16.1 P-34ESect-16.1 P-35ESect-16.1 P-36ESect-16.2 P-1ESect-16.2 P-2ESect-16.2 P-3ESect-16.2 P-4ESect-16.2 P-5ESect-16.2 P-6ESect-16.2 P-7ESect-16.2 P-8ESect-16.2 P-9ESect-16.2 P-10ESect-16.2 P-11ESect-16.2 P-12ESect-16.2 P-13ESect-16.2 P-14ESect-16.2 P-15ESect-16.2 P-16ESect-16.2 P-17ESect-16.2 P-18ESect-16.2 P-19ESect-16.2 P-20ESect-16.2 P-21ESect-16.2 P-22ESect-16.2 P-23ESect-16.2 P-24ESect-16.2 P-25ESect-16.2 P-26ESect-16.2 P-31ESect-16.2 P-32ESect-16.2 P-33ESect-16.2 P-34ESect-16.2 P-35ESect-16.2 P-36ESect-16.2 P-37ESect-16.2 P-38ESect-16.2 P-39ESect-16.2 P-40ESect-16.2 P-41ESect-16.2 P-42ESect-16.2 P-43ESect-16.2 P-44ESect-16.2 P-45ESect-16.2 P-46ESect-16.2 P-47ESect-16.2 P-48ESect-16.2 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