Why Is Work A Scalar Quantity?

Question

when force and displacement are vector quantities, why is work ( the product of the two) a scalar quantity?

Answer 1

Work has only magnitude & no direction. Hence it is  a scalar quantity.

Also it is a dot product of force & displacement.

Force & displacement are vectors because they have both

magnitude & direction.

Answer 2

In work only magnitude is needed, there is no use of direction.

Answer 3

The others seem to have explained it well enough, but just to try and make it simpler let me try:

A vector quantity is one that has a magnitude and direction, so going by that definition, Force, is a vector quantity since it has both (you know how much force is being applied and in what direction).

Similarly, Displacement is also a vector quantity since you know know how far and in what direction. Its an improvement on 'Distance' which only tells you how far, hence scalar.

Now, like ppl have said a dot product of two vectors will give u a scalar. You could simply accept this truth or try and look at the properties of the product which is 'the amount of energy transferred by a force' so it doesn't make sense to give it a direction.

You could also think taking the literal meaning of work, as when work is done, some effort has been made and some change in state has occurred. Again it makes no sense or relevance to know in what direction the work has been done in (work is work :-) )

Hope this helped and didn't just waste ur time having to read my ramblings :-)

Answer 4

There are two ways to multiply vectors:  dot product and cross product.  

The dot product of two vectors results in a scalar quantity, while the cross product results in another vector.  

The formula to find work involves the dot product of the two vectors, and the reasoning can probably be found in a proof online.

Since you are using the dot product, your answer will be scalar.