To do this we will use the law of conservation of energy.
Potential energy = energy due to height = energy lost due to friction+ kinetic energy
So… let’s write the equations… the pint here is to not have to measure the heat loss due to friction so we will not write the equation for it except for a single variable. For example, we won’t include the coefficient of friction.
Potential energy = mass*gravity*height=HeatEnergyLost+0.5*mass*velocity^2
The “^” symbol is the exponent symbol.
So…
HeatEnergyLost=mass*(gravity*height-0.5*velocity^2)
Note that height here should be the change in height and not the absolute height. It doesn’t matter for this scenario if we are talking about a falling object or an object rolling down a track.
Best wishes,
Pharmacoengineering.com