When analyzing the relationship between mechanical energy, thermal energy, and total energy in a system where friction is present, it is crucial to understand the implications of energy transformation.
1. Mechanical Energy (ME) might consist of both kinetic and potential energies. It is the energy associated with the motion (kinetic) and position (potential) of objects in a system.
2. Thermal Energy (TE) represents the energy lost due to frictional forces. Typically, when friction is present, mechanical energy is partially converted into thermal energy.
3. Total Energy (E_total) is the sum of all forms of energy in the system, both conserved and dissipated. In a closed system with friction, the total energy is the sum of the mechanical energy and the thermal energy generated due to friction.
Now, let's analyze each option:
A. [tex]\( E_{\text{total}} = E_{\text{thermal}} - ME \)[/tex]
- This states that the total energy is the thermal energy minus the mechanical energy. This doesn't make physical sense because it incorrectly suggests that adding thermal energy to mechanical energy would reduce the total energy.
B. [tex]\( E_{\text{total}} = ME \times E_{\text{thermal}} \)[/tex]
- This implies that the total energy is the product of mechanical energy and thermal energy. This is not accurate since energy forms add together rather than multiply.
C. [tex]\( E_{\text{total}} = ME + E_{\text{thermal}} \)[/tex]
- This equation correctly states that the total energy in the system is the sum of mechanical energy and thermal energy. When friction is present, mechanical energy is converted into thermal energy, and this thermal energy adds to the system's total energy.
D. [tex]\( E_{\text{total}} = ME - E_{\text{thermal}} \)[/tex]
- This suggests that total energy is the mechanical energy minus the thermal energy, which again doesn't reflect the actual process because it would imply that the presence of thermal energy reduces the total energy, which is not true.
Given these explanations, it is clear that the correct equation relating mechanical energy, thermal energy, and total energy when there is friction is:
[tex]\[ \boxed{C. \quad E_{\text{total}} = ME + E_{\text{thermal}}} \][/tex]
