Question

"Work is the scalar(dot) product of the force acting on an object and the displacement caused by that force" .What does this expression mean? I want a conceptual answer please.

Answer 1

Hi, work is scalar quantity , it has magnitude only, but no direction, ie you say you have done work of 12 Joules, but you dont need to specify its directions, and it is simply force times displacement, but this is the case when the body is displaced in the direction of force, ie during the process of doing work , the motion of body is in the direction of force, but if the direction of applied force is not in the direction of motion of body, then the work done is equal to the (amount of force in the direction of displacement multiplied by the displacement), you represent this as scalar product of force and displacement.
here you should note that, both force and displacement are vector quantity, they both have magnitude and displacement, so the scalar product of two vectors is the product of magnitude of first vector and magnitude of second vector in the direction of first vector.

Answer 2

dot product is the product of two vector quantities that gives an scalar quantity, now, work is a scalar quantity, you can't specify that you did 5J of work in the particular direction of vector 3i+2j because it makes no sense, because whatever work is done on a body is stored in the form of potential energy in it, which has magnitude but no direction at all. Therefore we need to find a scalar quantity that gives the magnitude and that scalar quantity is dot product of Force and displacement in the direction of force, secondly dot product is give by \[W=F.d \cos \theta\] now lets take an example , if there is a block on which force F is acting at a certain angle we need to resolve force first and then only we can determine how much force is causing the displacement, now displacement due to horizontal component is significant whereas vertical plays no role and horizontal force is given by F cos theta so finally,
\[W= F \cos \theta* d= F.d\] which is a dot product, hope this helps you