Question

Why is work a scalar quantity?
I have heard that the product of 2 vector quantities is a scalar quantity but can you please explain in a bit more detail about why does this happen?
Thanks in advance

Answer 1

For Work , for example, if we do 10 J work when we push object to 10m in east and then when we push 10 m in West with say 15 Joule, the total work would be 25 Joule here we are not bothered here about direction as it doesn't add any extra information.Work here means the lost of energy which doesnot depending on direction. suppose you are lifting a box to a certain height then you are doing work equal to mgh.If h remains same no matter you lift it either straight or zig zag , work remains same.so work is independent of direction or path hence scaler. Work is 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.A vector product of two vectors give a vector. dW=F⃗ ⋅S⃗ =∥F∥∥S∥cosθ dW=F→⋅S→=‖F‖‖S‖cos⁡θ (θθ being the angle between the vectors). No direction, only magnitude.