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My school textbook states if a ball falls due to free fall, its weight will do work, which is transferred to Kinetic Energy when dropped from a certain height.

Hence, work done = energy transferred.

But then it says this is as 'energy is defined as the capacity to do work'.

What does the term 'capacity to do work' mean?

I am very confused! How does this relate to the subject of work done = force x distance moved in direction of the force?

Also, it says that if a 40N force is applied on a box that is moving on a rough surface at constant speed, the work done on the box is "transferred into thermal energy between the box and surface below" - but isn't some of the work done transferred into kinetic energy to keep the box moving?

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    $\begingroup$ "Energy is the capacity to do work " is an extremely bad definition of energy $\endgroup$ – Lapmid Mar 2 '17 at 17:19
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    $\begingroup$ @Sherlock That's not the best phrasing but it is essentially the definition that was used from the time the concept was settled until Emmy Noether provided a better one. And it is still the only definition available at the introductory level. $\endgroup$ – dmckee Mar 2 '17 at 17:57
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    $\begingroup$ "How does this relate to the subject of work done = force x distance moved in direction of the force?" That is the reason the idea is not as trivial as it sounds. There is, however, nothing built into the two statements that tells you that these ideas together form the basis of a self-consistent framework for useful physical analysis: you have to do the math. Start with Newton's laws and kinematics, define kinetic energy, derive the work energy-theorem, think about conservative forces and use that to bootstrap new energies from the work energy theorem, and posit conservation. Then test. $\endgroup$ – dmckee Mar 2 '17 at 18:01
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Also, it says that if a 40N force is applied on a box that is moving on a rough surface at constant speed, the work done on the box is "transferred into thermal energy between the box and surface below" - but isn't some of the work done transferred into kinetic energy to keep the box moving?

The book is wrong. The 40 N force acting on the box is doing work on the box. The friction between the box and the surface below is doing work on the box. The constant speed simply tells you that the total work being done on the box is zero. Something had to get the box moving initially, and once that happens it will moving at constant speed on a straight line (Newton's first law) until something from outside the box acts on the box. In your case, the 40 N does exactly the same work as the friction, but we shouldn't say the work by the 40 N force "is tranferred" to thermal energy. We don't know where the work was transferred. All we know is that the sum of work is zero.

One just as easily (and just as falsely) could argue that the friction is stealing some of the initial kinetic energy, and the 40 N force is adding to the kinetic energy. All we know for sure are the total effects, not the pathways.

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    $\begingroup$ The book is not wrong. The proximal cause of the heating is the work done by friction. But that thermal energy came from somewhere. At one time it was chemical energy in my muscles. It ended up as thermal energy. One of the intermediate steps is that energy transferred from my hand to the box my means of work. We do consider that heat and work are transfers of energy, so I think it's perfectly fine to say that the work done on the box is transfered (by a chain of events) into thermal energy in the surface. $\endgroup$ – garyp Mar 2 '17 at 20:46

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