To properly understand the relationship between mechanical energy, thermal energy, and total energy when there is friction present in the system, let's review the concepts involved:
1. Mechanical Energy (ME): This is the sum of kinetic and potential energy in a system.
2. Thermal Energy (E_thermal): This is the energy dissipated due to friction or other non-conservative forces, often leading to an increase in temperature.
3. Total Energy (E_total): This is the sum of all the energies in the system, including mechanical and thermal energy.
In a system with friction, some of the mechanical energy is converted into thermal energy. This means that the total energy of the system (E_total) is the sum of the remaining mechanical energy (ME) and the thermal energy generated due to friction (E_thermal).
Given these definitions, we can form a relationship:
[tex]\[ E_{\text{total}} = ME + E_{\text{thermal}} \][/tex]
From the above equation, if you solve for thermal energy (E_thermal), you get:
[tex]\[ E_{\text{thermal}} = E_{\text{total}} - ME \][/tex]
This equation correctly shows that the thermal energy is the difference between the total energy and the mechanical energy. Thus, the correct option is:
[tex]\[ \boxed{D. \ E_{\text{thermal}} = E_{\text{total}} - ME} \][/tex]
