# Why work is a scalar quantity?

Well of course work is a scalar because that is how it is defined as a scalar product between the force and its displacement. But going a bit further if one wants to answer the question "why is work a scalar" one need to remember that basically work represent in...

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Well of course work is a scalar because that is how it is defined as a scalar product between the force and its displacement. But going a bit further if one wants to answer the question "why is work a scalar" one need to remember that basically work represent in its essence a change in energy, and thus the nature of work is related to the nature of energy itself.

`W =Delta(E)`

Now, why is energy a scalar? Motion of a mass has two quantities associated with it: linear momentum which is a vector and energy which is a scalar. Thus energy is the second physical quantity that shows how much motion a mass has. Since already we have a vector defined to show the quantity of motion (linear momentum) we need also another scalar quantity (energy) to describe the state of motion of a mass. Since linear momentum is always conserved in motion processes (like collision) we need energy (defined as a scalar) to show that some motion processes differ from other processes in some aspects (like for example inelastic collisions that differ from elastic collisions).

This is why work is a scalar: its definition comes from energy considerations, and energy is a scalar.

Observation:

Going a bit further with why energy is a scalar, we need to remember that the total energy is related to mass by the well known relation `E=m*c^2` and since the mass is always a scalar, and the speed is squared, the energy will be also a scalar.

Approved by eNotes Editorial Team