In case anyone is wondering, this is not for homework; I finished physics a while ago but this continues to puzzle me. Google turned up nada, so now I turn to the ueber-Google, that is, General Questions :).
So, the work-kinetic energy theorem states that the net work done on an object is equal to it’s change in kinetic energy during a process. Let’s say there’s no change in kinetic energy during a process; for example, you lift a pen from rest on a desk ten centimeters and hold it there. Kinetic energy for final and initial states is zero. Is no net work done on the pen?
My physics friend was trying to argue that work is actually total change in energy, and since the pen gains potential energy, there is work done on the pen. Is that true? If so, why is called the work-kinetic energy theorem? Why not just the work-mechanical energy or work-energy theorem?
Or, are we supposed to look at the kinetic energy not at the ultimate final position, but the penultimate final position, right before you bring it to rest? Kind of like how with kinetic energy problems, you’re often asked to find the KE or velocity the instant before the object stops falling or rolling or whatever.
Technically speaking, this is correct: the amount of work you do on the pen is balanced out by the work done on the pen by gravity. So if you’re looking at the net work done on the pen by all forces, it’s zero.
What I said above, while technically true, is not always the most productive way of looking at things. In particular, if the force on an object depends only on its position, and the vector field described by the force is “curl-free”, then it’s what we call a “conservative force.” This means that rather than having to do a complicated line integral every time we want to figure out the work done by this particular force, we can just write down a function on space called the “potential energy”. The work done by the force is then just the potential energy at the final point minus the potential energy at the initial point, regardless of what weird-ass path it takes between the two points.
Your physics friend, therefore, is then correct in the following sense: when you lift the pen, you do work on it. Gravity, meanwhile, is doing an equal and opposite amount of work on the pen as you lift it; this gravitational work is better known as “gravitational potential energy.” Since we’re often used to taking gravity as a given, and applying forces to overcome it, this is usually a more productive way of looking at things.