Work in physics is mathematically defined as force $F$ applied on an object multiplied by the displacement $d$ it covers in the direction of the force. In a system where, a restrictive force exists like friction due to contact between objects or in a field where work done changes into potential energy, displacement is finite.But according to Newtons second law of motion when a force is applied on an object, it produces acceleration in that object which causes a change in velocity in a "certain" time. Moreover when the force has been applied, according to Newtons 1st law of motion it should displace "infinitely" with a constant velocity which is changed due to the force applied. My question here is that what is the real definition of 'displacement' in work formula?
$$ W = F d \cosθ$$
Is the displacement infinite making work infinitely increasing or it is the displacement covered by that object while the force is being applied or when there is acceleration being produced?
Best Answer
The work occurs while the force is applied.
So the
din the formula is the distance the object moves while the work occurs.Independent of that, the object, which was accelerated by the work, wil displace further afterwards.
There are two uses of the term "displacement" for different things in your question I think. Sorting that out may help clear up your confusion about it.
The "certain" time is the time during which work is done, because force is applied. After that, the object will move with it's new velocity, caused by the acceleration by the work. It will keep that velocity until a new force is applied, changing it's velocity again.
That new force could be friction, stopping a piece of wood pushed by the force, or gravitational attraction of a planet nearby an asteroid.