Question

The sign of many physical quantities depends on the choice of coordinates. For example,${\mathbf{a}}_{\mathbf{y}}$ 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.

Short answer

The explanation is not true for work, and the work does not depend on the choice of axis orientations.

Step-by-step solution

Describe the Work-Energy theorem

The work energy theorem tells that the work done on the body results in a change in its kinetic energy.

$$\begin{gathered} {\mathbf{W}}_{\mathbf{total}}\mathbf{=}{\mathbf{K}}_{\mathbf{2}}\mathbf{-}{\mathbf{K}}_{\mathbf{1}}\mathbf{} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{∆}\mathbf{K} \end{gathered}$$

Determine whether the explanation is also true for work also determine whether it is possible to make e positive work negative by a different choice of coordinates

It is known that the kinetic energy of a particle is only dependent on the instantaneous speed of the particle. The sign of the total work done on the particle cannot depend on the orientations of the coordinate axes. It is positive if the particle speeds up and negative if it stows down.

From the definition of work, this is known that if both the force and the displacement change their direction, the overall sign will remain the same.

Therefore, the given explanation is not true for work, and work exerted on the body does not depend on the choice of axis orientations.