Answer to Question #21832 in Mechanics | Relativity for Eugene Wong

Question

I'm 16 and I'm from Malaysia. Here, you only study Physics when you're my age. So, this is my first year studying it and I'm very interested in Physics as I wanted to be an astronomer and becoming one requires you to obtain an excellent grade in Physics.

So, we learned about base quantities and derived quantities, Scalar and Vector quantities today. As most of you know, the formula for 'Work' is 'force x acceleration'. Why is 'Work' is a Scalar quantity when both 'Force' and 'Acceleration' is a Vector quantity ? (Why when both these Vector quantities when multiplied becomes a Scalar quantity ?)

This may seems stupid for me to ask such basic question here on an expert physics website buy I'd appreciate your answers and help very much. Thank you! :)

Answer 1

Work = Force * Displacement.
Both Force and Displacement are indeed vectors, and they have their directions that don't always coincide.

The work naturally has to be a scalar because it measures not only the magnitudes of F and D, but also the correspondence between them (e.g. the angle between two vectors), or, in other words, to which extent this particular displacement was due to this particular force and thus this force can "get credit" for it.

(In general, two vectors multiplied are not necessarily a scalar. Apart from the scalar product of two vectors, there is as well a vector product of two vectors.)