Chapter 16.2, Problem 32E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

(a) Find the work done by the force field **F**(*x*, *y*) *= x*^{2} **i** + *xy* **j** on a particle that moves once around the circle *x*^{2} + *y*^{2} = 4 oriented in the counterclockwise direction.

(b) Use a computer algebra system to graph the force field and circle on the same screen. Use the graph to explain your answer to part (a).

**(a)**

To determine

**To find:** The work done by the force field

Explanation

**Given data:**

The force field is

The particle moves once around the circle

**Formula used:**

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

Here,

Parameterize the circle

Consider the position vector as follows.

Substitute

Write the point

Write the force field as follows.

**Calculation of**
**:**

Substitute

**Calculation of**
**:**

To find the derivative of the vector function, differentiate each component of the vector function.

Differentiate each component of the vector function

Rewrite the expression as follows

**(b)**

To determine

**To find:** The work done by the force field

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