   Chapter 16.2, Problem 51E

Chapter
Section
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. 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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