The work-energy theorem states that the net work done by all forces on a particle is equal to the change in kinetic energy of the particle. I have a few queries on this theorem:

  1. Do the timing of the forces matter here? Suppose, force $A$ was acting from the beginning, then came in $B$, then $C$ and so on. In other words,not all forces started acting together, some were applied before and some after some time,then at any instant will the work done by all those forces be equal to the change in kinetic energy, since some forces were acting when the others hadn't been introduced yet?

  2. What do we mean by initial and final here? Does initial mean the time from when at least a force has been introduced?(I am saying thr word at least because as i clarified in my first point that multiple forces could act on the particle,not all of them at the same time. First a single force will act,then after some time others will start being applied) And what about the word Final? Does this final mean when no other force is acting on the object,in other words moving with constant velocity? Or does this final mean whenever we want to measure the energy,in other words at any instant of time?

Please clear my misconception.


1 Answer 1

  1. Understand that the net work done on a particle equals the net force acting on the particle over the distance it acts. There is no such thing as "instantaneous" work, because for a net force to act over a distance requires time. See here.

So if there are various forces acting on a particle over different times, in order to apply the work energy theorem you need to specify a time or distance over which the force(s) acts. That, in turn, means you may or may not have a change in KE over a specific time/distance. Bottom line, you need to specify the time or distance over which all the forces act in order to apply the work energy theorem. So, yes, the timing of the forces do matter.

  1. I think my answer to 1 covers 2 as well.

Hope this helps.

  • $\begingroup$ Thank you very much for replying. Could you please kindly check my new post? I have added a problem there which will help me get the gist of your answer and will be very effective for me. Thank you again. $\endgroup$
    – madness
    Aug 26, 2022 at 23:30
  • $\begingroup$ @madness By "my new post" do you mean this: physics.stackexchange.com/questions/724975/… $\endgroup$
    – hft
    Aug 26, 2022 at 23:54

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