Energy Skate Park (II)

Today, we continued yesterday's investigation and discovered several new things by adding the thermal energy (friction) into the energy system. These new discoveries include:

1) Thermal energy appears when the object is in motion. It increases when kinetic energy or potential energy increase.

2) Thermal energy increases the most when it approaches the bottom of the skating track. It increases less when potential energy is greater than kinetic energy.

3) Total energy is the sum of kinetic energy, gravitational potential energy, and thermal energy. The object travels slower and slower as thermal energy increases, and it finally comes a stop when thermal energy equals to total energy, when potential and kinetic energy equal to zero.

Something intrigued me is that thermal energy increases as the total energy increases. For instance, thermal energy is greater if I drop the person from above the track comparing to put him right on the track. I assume this is because more kinetic energy turn into thermal energy under higher speed.

After today's learning, I still have the following questions: how can we calculate thermal energy mathematically by knowing the kinetic energy, potential energy or total energy? Also, how big must the kinetic energy be in order to over come thermal energy so the object can successfully travel through the point in the following picture? Why would potential energy equal to zero when the person stops due to thermal energy?