Chapter 6, Problem 6.1DQ

The sign of many physical quantities depends on the choice of coordinates. For example, a_y for free-fall motion can be negative or positive, depending on whether we choose upward or downward as positive. Is the same true of work? In other words, can we make positive work negative by a different choice of coordinates? Explain.

To determine

Validate the effect of direction on physical quantities like work.

Answer to Problem 6.1DQ

No, work is positive or negative does not depend on coordinates that has been chosen.

Explanation of Solution

Work is the displacement of any object due to the application of load. It is a non vector quantity because its value does not vary with the change in direction.

The magnitude of work can be either positive or negative that depends upon the direction of applied force and displacement.

If the directions of the applied force and displacement caused by it are same, work done will be positive $\left(+\text{ve}\right)$.

If the directions of the applied force and displacement caused by it are opposite, work done will be negative $\left(-\text{ve}\right)$.

Conclusion: No, work is positive or negative does not depend on coordinates that has been chosen.