Work and energy: conceptual doubt

[Lalit Tolani]

Suppose I am sliding a block very slowly on a rough surface. If the block has traveled ##d## distance then work done by me is ##W_1=\mu mg d## and that by friction is ##W_2=-\mu mg d##.

Now the energy transferred from me to block is ##\mu mgd## and that taken by friction from block is ##\mu mgd ##, The net energy of block remains same but the energy taken by friction evolves as heat and that is equal to my chemical energy consumed, so total energy of ##block + me## system remains constant.

Now If I pull a block of mass ##m## slowly towards up to a height ##h##, then work done by me is ##W_1=mgh## (assuming ##h## is much less than radius of earth) and that by gravity is ##W_2=-mgh##. Therefore ##mgh## goes from me to block and ##mgh## from block to earth, So here also energy of block doesn't change, then why do we say that potential energy of block increases.

I know I am lacking something here, as the total energy of the system would not be conserved if the block's energy doesn't change and my energy decreases.

Please help me in understanding where I am wrong.

 

[Doc Al]

So here also energy of block doesn't change, then why do we say that potential energy of block increases.

The kinetic energy of the block doesn't change, since the net work done on it is zero. Note that there are two ways to talk about the work done by gravity in these sorts of situations: You can explicitly treat gravity as a force, calculating the work it does on the object. Or you can treat it by using gravitational potential energy. But what you cannot do is use both -- that would be counting gravity twice, in effect.

 

[Nugatory]

So here also energy of block doesn't change, then why do we say that potential energy of block increases.

When you get a chance, try reading https://www.feynmanlectures.caltech.edu/I_04.html

Some of the problem here is that the English language is being used imprecisely; strictly speaking we don't have "potential eergy of the block", we have the potential energy of the entire system consisting of the Earth and the block.

Imagine that we've enclosed the whole shebang (earth, block, you, lifting mechanism) in a huge box. Now the total amount of energy inside the box will be conserved as long as we count an increase in potential energy as the block and the Earth are pulled apart.