Suppose I am sliding a block very slowly on a rough surface. If the block has travelled $d$ 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.
Best Answer
This is a common confusion and is due to poor communication, not a failure in your understanding which appears to be correct.
Potential energy is energy that is available by virtue of the configuration of a system. In this case the potential energy is $mgh$. Now, consider what system this potential energy describes. We have $m$, which is a property of the block, but $g$ is a property of the earth, and $h$ is a relationship between the block and the earth. So the system that has potential energy $mgh$ is the system of both the block and the earth.
So, when we say "the potential energy of the block increases", we are actually making a mistake. We should say "the potential energy of the block+earth system increases". Thus, when you say:
If we taught potential energy correctly from the beginning you would have said "Therefore $mgh$ goes from me to block and the block+earth system's potential energy is increased by $mgh$"