   Chapter 16.3, Problem 22E

Chapter
Section
Textbook Problem

Suppose an experiment determines that the amount of work required for a force field F to move a particle from the point (1, 2) to the point (5, −3) along a curve C1 is 1.2 J and the work done by F in moving the particle along another curve C2 between the same two points is 1.4 J. What can you say about F? Why?

To determine

The behaviour of the force field F along the curves.

Explanation

In case, if the force field F is conservative, then the work done along any curve C CFdr is independent of the path. Hence, the work does not depend upon the curve. The all piecewise-smooth curves that consist of initial and end points possess the same work as the field force is conservative and is not path-dependent on the chosen curve.

It can be observed that the work done on the y field vector F along the two curves C1 and C2 are 1.2 J and 1.4 J respectively

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