To determine which equation correctly relates mechanical energy (ME), thermal energy (Eth), and total energy (Etot) in a system where friction is present, we need to consider the law of conservation of energy.
In any physical system, energy cannot be created or destroyed but can only be transformed from one form to another. When friction is present, mechanical energy is not entirely conserved because some of it is converted into thermal energy due to the work done against friction.
Here's the step-by-step reasoning:
1. Mechanical Energy (ME): This refers to the sum of kinetic and potential energy in the system. In the absence of non-conservative forces like friction, mechanical energy would be conserved.
2. Thermal Energy (Eth): This represents the energy converted into heat due to friction. Friction generates heat, which is a form of energy that adds to the total energy of the system.
3. Total Energy (Etot): This is the sum of all forms of energy present in the system. When friction is present, the total energy of the system includes both the mechanical energy and the energy lost to thermal energy.
Given that energy is conserved, the total energy in the system will be the sum of the mechanical energy and the thermal energy generated by friction. Thus, the correct relationship should add the mechanical energy and thermal energy to get the total energy.
Let's analyze the provided options:
- Option A: Etot = Eth - ME
This implies that the total energy is the thermal energy minus the mechanical energy, which does not align with the conservation principle because we should be adding not subtracting the two energy forms.
- Option B: Etot = ME × Eth
This implies that the total energy is the product of mechanical energy and thermal energy, which again does not follow from the conservation law because we do not multiply these quantities together.
- Option C: Etot = ME - Eth
This implies that the total energy is the mechanical energy minus the thermal energy. This is incorrect because it suggests that thermal energy reduces the total energy, which is not correct based on energy conservation principles.
- Option D: Etot = ME + Eth
This correctly states that the total energy is the sum of mechanical energy and thermal energy. This follows the law of conservation of energy, where the total energy in a system with friction is the sum of the mechanical energy and the energy converted to heat due to friction.
Therefore, the correct equation that relates mechanical energy, thermal energy, and total energy when there is friction present in a system is:
Option D: [tex]\(E_{\text{total}} = ME + E_{\text{thermal}}\)[/tex]
