Suppose we apply a force of 1N on an object in space,due to Newton's 1st law of motion it should go on forever,therefore it's displacement goes on increasing.Does that mean that work done is infinite,as work is product of force and displacement.I can't wrap my head around it??please clear my doubt
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2 Answers
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You are missunderstanding Newton's first law, I would say. The law is usually stated as "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force".
So if a net force of 1N keeps acting unchecked by any other force and always in the same direction, the object will accelerate in the direction of this force. Obviously, if you run the system for infinite time the amount of work is infinite. At any finite time, the displacement is finite and so is the work done.
In the case of no forces but $\vec{v} \neq \vec 0$, the work is zero since there is displacement but there is no force so the product vanishes.
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If you apply the force for a limited time the object will initially accelerate according to Newtons second law, but once the the force is remove it will continue on at constant velocity in accordance with Newton's first law. From then on if there is no net force on the object to change its velocity, it will continue at that velocity per Newton's first law, and no more work is done in connected with its subsequent displacement.
Only as long as there is a net force on the object will work be done equal to the force times the displacement.
Hope this helps.
