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There are two approaces. One is empirical the other is indepth theoretical microscopic consideration. Empirical - Fa = Applied force , mu = coeff. of friction as per the case i.e. static at the time of starting of motion , dynamic / rolling while in motion. Let alpha = factor deciding conversion of frictional energy into heat energy . h = heat energy solely generated due to friction then h = alpha*mu*F*d where d is distance travelled by keeping F same . Also one fine point is alpha depends on instantaneous temperature and mu on surface roughness. All these values for practical purpose must be determined by experiment.

Detailed microscopic considerations are beyond the scope of this forum !

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