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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

When a particle is located a distance x meters from the origin, a force of cos ( π x / 3 ) newtons acts on it. How much work is done in moving the particle from x = 1 to x = 2 ? Interpret your answer by considering the work done from x = 1 to x = 1.5 and from x = 1.5 to x = 2

To determine

To find:

The work done in moving the particle from x=1 to x=2 and interpret the answer by considering the work done from x=1 to x=1.5 and from x=1.5 to x=2

Explanation

1) Concept:

Use the formula to calculate the work done.

2) Formula:

The work done in moving the object from a to b is given by

W=abf(x)dx

3) Given:

fx=cos(πx3)

4) Calculation:

The work done in moving the particle from x=1 to x=2 is given by using the formula

W=12cos(πx3)dx

Simplify,

=sinπx3π312

=3πsinπx312

=3πsinπ(2)3-sinπ(1)3

=3π32-32

=0 N.m

=0 J

Interpretation:

The work done in moving the particle from x=1 to x=1.5 is given by using the formula

W=11.5cos(πx3)dx

Simplify,

=sinπx3π311.5

=3πsinπx311.5

=3πsinπ(1.5)3-sinπ(1)3

=3πsinπ2-sinπ(1)3

=3π1-32

=32π2-3 N·m

=32π2-3  J

Work done is positive which means that kinetic energy is increasing

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