Chapter 16.2, Problem 47E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

(a) Show that a constant force field does zero work on a particle that moves once uniformly around the circle *x*^{2} + *y*^{2} = 1.

(b) Is this also true for a force field **F**(x) = *k***x***,* where *k* is a constant and **x** = `⟨`

*x*, *y*`⟩`

?

**(a)**

To determine

**To show:** The constant force field does zero work on a particle.

Explanation

**Given data:**

The particle moves once uniform around the circle

**Formula used:**

Write the expression to find the work done on the object by the force field

Here,

Write the expression to find

Here,

Consider the constant force vector as follows.

Here,

As the particle moves around the circle

Write the position vector from the parametric equations as follows.

**Calculation of**
**:**

Substitute

**(b)**

To determine

**To verify:** The work done by a force field

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