Question

work is a scalar quantity but force and displacement are vector quantity..
so, why is work a scalar quantity where as the equation f×s are vector quantity?

Answer 1

12down voteaccepted

It's defined as a dot-product (or scalar product) of force and displacement, both of which are vectors.

A scalar product of two vectors gives a scalar result (aptly named!).

dW=F⃗ ⋅S⃗ =∥F∥∥S∥cosθdW=F→⋅S→=‖F‖‖S‖cos⁡θ(θθ being the angle between the vectors).

No direction, only magnitude.

Thinking logically, what would be the direction of work, anyway? You may say, "In the direction of displacement!", but then why not in the direction of force? And if you say the direction of both, well then, it isn't always the same! A force can do work on a body even displacing at an angle to the direction of force (θθ!).

=>Note that when θθ is 90∘90∘, the result will be zero (cos90∘=0cos⁡90∘=0). When force and displacement are perpendicular, the force does no work on the body!

don't worry this is not copied from other website i have app in my pc

Answer 2

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Above answer is absolutely correct

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Scalar Quantity

• Scalar quantity is the Physical quantity that is derived on the basis of magnitude.

Example :-

• Distance, speed, mass, etc.

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Vector Quantity

• Vector quantity is the physical quantity that requires both magnitude and direction.

Example :-

• Acceleration, momentum, displacement, etc.

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