I am currently studying the relationships between energy work and force. I am trying to conceptualize them into one concept of causality. When a force is applied work is done, and energy is transferred but does this not mean that energy is essentially just stored work being transferred? Also, this explanation doesn't seem like a line of causality. When I try to make sense of the relationships I think of the force being the causation of work and so the energy being the stored force, because energy is defined as the ability to do work which is caused by force and so stored in the force until it can be transferred into work. In other words, I am lost, please help!
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$\begingroup$ Causation or causality are superfluous here and thus probably causes your confusion. Work is not "caused" by force, work of a force is defined as component of this force in direction of displacement of the body, times displacement. Thus non-zero work needs two factors: force and displacement. There can be force without displacement, or displacement without force, and in these cases, work is zero. $\endgroup$– Ján LalinskýJan 25 at 11:38
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$\begingroup$ $W=\int\vec F\cdot d\vec s$ If you are saying that $W$ is stored $\vec F$, then equally one can say that $W$ is also stored $d\vec s$. Just because we can treat potential energy as a kind of stored force does not mean that we can generalize the notion, for example in the case of friction there is nothing being stored (perhaps except heat, but it isn't stored for long either). $\endgroup$– GedankenExperimentalistJan 25 at 11:39
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$\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$– Community BotJan 25 at 12:19
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$\begingroup$ Energy is not a stored force as you said in the title. Both Energy and force have completely different meanings. Energy is an ability to do work, whereas force is rate of change of momentum with time. Work here means it's just a way of transfer of energy $\endgroup$– Tejas DahakeJan 25 at 13:17
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$\begingroup$ "When a force is applied work is done". Not necessarily. Only when a net force is applied to something is work done. $\endgroup$– Bob DJan 25 at 13:49
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2 Answers
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Energy is defined as the capacity to do work, as it is rightly pointed out by you. When a force acts on a body in the direction of the displacement of the body, we say that the force has done some work on the body.
Work done(W) = F. ds = F.ds.cosθ ; where θ is the angle between the force applied and the direction of displacement (since both are vector quantities so direction plays an important role).
Very basic of physics - Energy can neither be created nor destroyed, it can only be transformed from one form to another. Work done on a body= energy gained/lost by it.
When you do some work on a body, what you're essentially doing is that you're providing it with energy. When you push a ball(by applying force), you do some work on it. The work done by you on the ball has now become its energy. That energy would be used by the ball to travel some distance. The energy of the ball would be spent in travelling some distance and the ball will eventually come to rest as the floor on which the ball was moving applies the force of friction which opposes the motion of ball.
I hope this helps.
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1$\begingroup$ Energy is not capacity to do work, it does not mean anything. If something has energy that means it has an 'ability' to do work. $\endgroup$ Jan 25 at 13:11
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$\begingroup$ @TejasDahake Energy is typically defined as the capacity (as in potential) for doing work. See hyperphysics.phy-astr.gsu.edu/hbase/egex2.html $\endgroup$– Bob DJan 25 at 13:45
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$\begingroup$ @BobD so what is more correct is it capacity or ability? By the way you can check this out. And majority of scientists treat energy as an ability to do work as I said in my previous comment. $\endgroup$ Jan 25 at 15:26
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$\begingroup$ @BobD capacity sounds kind of a boundary limit for something which is true till some extent that if a body possesses a certain amount of energy then it only has an ability to do that much amount of work. $\endgroup$ Jan 25 at 15:34
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2$\begingroup$ @TejasDahake FYI, Googling "definition of energy" I found, simply taking the hits in order without regard to authoritativeness, that after 14 hits, the score was 5 for ability, 6 for capacity, 1 saying "capacity or ability" and 2 using neither term. Seems like seeking agreement on a definition may be a "fools errand". Good luck! $\endgroup$– Bob DJan 25 at 21:17
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Work is energy transfer due to force times displacement in the direction of the force.
Force alone is a necessary but not sufficient condition for work to be done. I can apply a force to a wall but if it does not move I do no physics work (though I may expend energy internally in my attempt).
Likewise, displacement is a necessary but not sufficient condition for work to be done. An object can move (be displaced) at constant speed in a straight line with no force, thus no work is done. An object can move perpendicular to the line of action of the force and no work is done.
Force plus displacement in the direction of the force are the necessary and sufficient conditions for work (energy transfer) to be done.
Hope this helps.
