Question
Wed November 02, 2011 By:
 

Consider a car that move forward and comes back to its initial position. It will have consumed fuel. But by the theoretical formula of work= force* displacement, work done = 0. In that scenario( since fuel was consumed, implying some work should have been done) shouldn't we define work as force* distance? Why don't we define it like that? Why do we consider displacement?

Expert Reply
Thu November 03, 2011
Work is a scalar quantity that can be described as the product of a force times the distance through which it acts, and it is called the work of the force.
But, the component of the force can be described by the scalar quantity called scalar tangential component ( , where  is the angle between the force and the velocity).
Since, velocity is a vector quantity and depends on the direction of movement of body
So, If a force F that is constant with respect to time acts on an object while the object is translationally displaced for a displacement vector d, the work done by the force on the object is the dot product of the vectors F and d where d is the displacment vector.
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