# Where does the work done by friction get converted into?

Lets consider my hand (say parallely) moved a block in a rough surface with constant velocity. What is work done by the friction and my hand? Assuming body is displaced for 1m distance by 10N force. Then according to my understanding, 1st Case : work done by my hand is 10J and work done by friction is -10J, as it acts opposite to displacement. So by conservation of energy, 10J is converted into heat and sound, but where does that -10J go? Or am I missing something here? 2nd Case : Both work done cancels each other and net work done is zero. In this case, how heat is produced between them? Please explain conceptually and mathematically if possible !

10 J of work is done by you so your body loses 10 J of internal energy (mainly chemical potential energy; and in reality it loses more due to the imperfect machinery of the body).

-10 J of work is done by friction so the surface gain 10 J of energy in the form of heat.

As for the block, net work done on it is zero so its energy doesn't change.

Or put another way, you use 10 J of your chemical potential energy in your body to do work on the block, and the block transfer this 10 J of energy to the rough surface by doing work on it. So the net result is your chemical energy becomes heat energy of the surface (assuming your body machinery is perfect, as I mentioned, otherwise heat is also produced in your body).

Work is an entity that depends on the frame of reference.

As reckoned from the frame of reference of the block, its displacement is zero, so no work is done on the block. But, your hand is experiencing a displacement and is being acted upon by the frictional force. So, for this frame of reference, there is work done by the block on your hand. This work is converted to heat at the (massless) interface, and the heat then flows partially into your hand and partly into the block. The split between the block and your hand is determined by the thermal properties of both.

As reckoned from the rest frame of you hand, its displacement is zero, so no work is done on your hand. But the block is experiencing a displacement (relative to your hand) and is being acted upon by the frictional force. So, for this frame of reference, there work done by your hand on the block. This work is converted to heat at the (massless) interface and the heat then flows partially into your hand and party into the block.

So the thermal effect is the same in both frames of reference.