Question

which equation correctly relates mechanical energy, thermal energy, and total energy when there is friction present in the system?

a. ( e_{\text{thermal}} = \text{me} - e_{\text{total}} )

b. ( e_{\text{thermal}} = e_{\text{total}} + \text{me} )

c. ( e_{\text{thermal}} = e_{\text{total}} - \text{me} )

d. ( e_{\text{thermal}} = \frac{e_{\text{thermal}}}{\text{me}} )

Explanation:

When friction is present, total energy ($E_{\text{total}}$) is the sum of mechanical energy (ME) and thermal energy ($E_{\text{thermal}}$) due to energy conservation (some mechanical energy is converted to thermal energy). So, rearranging $E_{\text{total}} = \text{ME} + E_{\text{thermal}}$ gives $E_{\text{thermal}} = E_{\text{total}} - \text{ME}$. Option A has the wrong sign, B adds instead of subtracting, and D is an incorrect ratio.

Answer:

C. $E_{\text{thermal}} = E_{\text{total}} - \text{ME}$