Hello! In my studying of work I've always been told that work done (by what? ) = Force (component along its path) times the distance it moves. Mathematically, W=F.s ... My question here is what is the geometrical presentation of saying Force x Distance ... In other words, when we multiply force vector times the displacement vector, what does it mean. If for example dot product the force vector by the unit vector of say the x axis < 1, 0 ,0 > we will get the x component of the force. What is the case for work?? Thanks a lot for bearing my lengthy piece. And thanks in advance to whoever gives me a kind hand
Take the dot product of the force and the displacement vectors. You are essentially taking the component of the force parallel to the displacement and multiplying it by the displacement.
The idea is that, if an object is moving to the east, and you apply a force on the object directed to the north, the object continues moving to the east at the same speed; so no work is done by the force as far as the movement to the east is concerned. But, the object is accelerating to the north, so the force is doing work on the object in that direction. So the conclusion is that only the component of movement parallel to the direction of the force results in work being done. Chet
That would be the cross product. But work is the dot product. Yes, that is the geometrical presentation of a dot product.