Chapter 16, Problem 10RE

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

Find the work done by the force field **F**(*x*, *y*, *z*)* = z* **i** *+ x* **j***+y* **k** in moving a particle from the point (3, 0, 0) to the point (0, π/2, 3) along

(a) a straight line

(b) the helix *x* = 3 cos *t, y = t*, *z =* 3 sin *t*

(a)

To determine

The work done by the force field

Explanation

**Given data:**

The moving particle points are as follows.

**Formula used:**

Write the expression vector representation of line segment.

Here,

Write the expression to find the work done.

Write the required differential and integration formulae to evaluate the given integral.

Find parametric representation of line segment for *x*-coordinate using equation (1).

Substitute

Differentiate

Find parametric representation of line segment for *y*-coordinate using equation (1).

Substitute

Differentiate

Find parametric representation of line segment for *z*-coordinate using equation (1).

Substitute

Differentiate

Write the expression for

Differentiate equation (3) with respect to

**(b)**

To determine

The work done by the force field

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