Why is work a scalar quantity although force and displacement are vector quantities? (Answers apart from work has magnitude but no direction). I want to know why work has no direction.
A quantity which has only magnitude but no direction is known as a scalar quantity.
Work is done only when a force produces motion.And it is the product of the force exerted on the the body and the distance moved by the body in the direction of force.
i.e. W =F.s
Work is actually the scalar product of force and displacement and hence is a scalar quantity.
i.e. W = Fs cos θ
where F is the force, s the displacement and θ the angle between force and displacement. According to the angle θ, work can be positive, negative, or zero.
Work is the outcome of the force and displacement caused by the body.
Force and displacement are vector quantities (they have both magnitude and direction) and the dot product of two vector quantites always gives a scalar quantity. So work has only magnitude but not direction.