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Work done by kinetic friction on a block modelled as a system

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Let's consider a setup consisting of a table with friction, and a block on top of it. Suppose we drag the block across the table with a constant speed. The applied force F acting through a distance ddoes a work Fd. The frictional force is equal to -F since there is no acceleration. So the total work done on the block by these external forces will be W_{app} + W_{friction} = F_{app}d - f_{Kinetic Friction}d = 0.
 
According to law of conservation of energy, if there is an energy change in the system , it is because the energy is being transferred across the system boundary by a transfer mechanism (work, heat, mechanical waves, matter transfer, electromagnetic radiation etc.)  
So, Delta E_{system} = Sigma T, where Delta E_{system} = Delta K + Delta U + Delta E_{internal} and  Sigma T is an energy transfer mechanism.
 
In our case, we have  W_{app} + W_{friction} = Delta K + Delta E_{internal} , Delta K = 0 as there is no change in speed, then W_{app} + W_{friction} = Delta E_{internal}  , but as W_{app} + W_{friction} = 0 that means delta E_{internal} = 0 So that means there is no increase in the internal energy, but clearly the block heats up. Can anyone explain to me what's happening here? Why is law of conservation of energy being violated? And also I tried to use Latex so the equations would appear as math symbols but apparently it doesn't work here.
asked Sep 19, 2017 in Mechanics by yamin_lone (120 points)

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