Physics of Weight-Lifting I have a question regarding the concept of "work done" in Classical Mechanics, inspired by my time in real life situation of me the gym.
"Work done" depends on the direction of the force and the displacement.  If the force is aligned with the displacement, then the work done is positive.  If the force is anti-aligned with the displacement, then the work dine is negative.
This means that, if the force I applied is anti-aligned with the displacement, then energy is transferred to me.  However, in weight lifting, I still need to put force and (therefore) effort when I lower my dumbbell: in essence, I was still using up chemical energy when lowering my dumbbell.  This means that chemical energy is used up, even when the dumbbell transfers energy to me: isn't this a violation of conservation of energy?
 A: What you are referring is not a violation of conservation of energy, but is just an inefficiency.  For human muscles, applying force requires energy, and whether or not that force does work is not highly significant in the equation (it's not entirely relevant here, but even in ideal settings efficiency is only about 30%).
The force produced by muscles can be used for many things, for example, to decrease the energy of a thing (eg, to slow something down that's moving, like catching a ball, or hold something up like when slowly lowering a weight), or to increase the energy of a thing (like to throw a ball or lift a weight). The important point is that, from the perspective of the muscle, these force are both produced the same way in the muscle.  (That is, theoretically, it's plausible in the former case that the energy could be recaptured by the muscles, but without such a mechanism, from the perspective of the muscles, the forces used when adding energy are produced in the same way as the forces used when reducing energy.)
In general, animals just live with these inefficiencies, but there are a few ways to get around them that are occasionally used.
The most common inefficiency is that using muscles to produce a force to hold something stationary takes energy.  The mechanism to reduce these inefficiencies is through skeletal structures that reduce the muscular forces, so that in common tasks like standing, your muscles aren't holding you up all the time, but instead your bones are stacked to reduce the force the muscles need to supply.  This, for example, is the purpose of "locking" one's knees.
When lowering a weight slowly, it's this force of holding a weight stationary and associated energy expend that you feel (since acceleration is so low).  When doing a bench press you can start with your bones well aligned and the force from the muscles increases as your arm bones become increasingly unaligned, so it might feel like slow motion is the cause of the energy expenditure, but it's mostly just the static problem since you're very far from free-fall.
A less common and more interesting biological attempt to reduce these inefficiencies are biological springs.  (A spring would be the usual mechanism for efficiently capturing the energy of lowering the weight.)  I've heard that the human achilles tendon acts as a spring as we run.  When we land it stretches out, and the stretch recoil helps propel us in the next step.  I've also heard that the wishbone of birds is designed to act as a spring.  I'm sure there are others.  A search returned this paper: "Flexible mechanisms: the diverse roles of biological springs in vertebrate movement" which looks very promising.
I assume the reason that springs aren't more common is that their stretching requires force, and which therefore reduces the applied force that can be produced by the opposing muscle.  So a spring makes sense in the achilles tendon, but wouldn't be a good strategy for a bicep.
It also seems theoretically plausible to recapture the energy through a chemical mechanism (say, converting ADP to ATP), rather than a mechanical mechanisms (like a spring), but I'm not aware of any systems like this and doubt it exists in vertebrates.  Even in human designed systems, engines that convert chemical energy into mechanical energy rarely recapture that energy (eg, cars don't reconvert CO2 into gasoline when they break).
A: If you try to bring down the weights without effort, your hands will gain speed. So energy is definitely transferred to our hands. The question is how our hands dissipate the kinetic energy gained. I guess the exact answer lies in the biological functioning of muscles.
