Which equation correctly relates mechanical energy, thermal energy, and total energy when there is friction present in a system?
A. [tex]$ME =E_{\text {thermal }}-E_{\text {total }}$[/tex]
B. [tex]$ME =E_{\text {total }}-E_{\text {thermal }}$[/tex]
C. [tex]$ME =E_{\text {total }}+E_{\text {thermal }}$[/tex]
D. [tex]$ME =\frac{E_{\text {total }}}{E_{\text {thermal }}}$[/tex]

Mechanical energy is converted into thermal energy due to friction.
Total energy remains constant and equals the sum of mechanical and thermal energy: E total ​ = ME + E thermal ​ .
Rearrange the equation to isolate mechanical energy: ME = E total ​ − E thermal ​ .
The correct equation is: ME = E total ​ − E thermal ​ ​ .

Explanation

Understanding the Energy Relationship In a system where friction is present, mechanical energy is converted into thermal energy. The total energy of the system remains constant. Therefore, the total energy is the sum of the mechanical energy and the thermal energy.

Expressing the Relationship We can express this relationship as: E total ​ = ME + E thermal ​ where:



E total ​ is the total energy of the system,
ME is the mechanical energy of the system, and
E thermal ​ is the thermal energy of the system.


Isolating Mechanical Energy To find the equation that correctly expresses mechanical energy (ME) in terms of total energy ( E total ​ ) and thermal energy ( E thermal ​ ), we need to rearrange the equation: ME = E total ​ − E thermal ​

Identifying the Correct Option Comparing this derived equation with the given options, we find that option B matches our result: B. ME = E total ​ − E thermal ​


Examples
Consider a sled sliding down a snowy hill. Initially, the sled has potential energy (a form of mechanical energy). As it slides down, friction between the sled and the snow converts some of this mechanical energy into thermal energy, which heats up the sled and the snow. The total energy of the system (sled + snow) remains constant, but the mechanical energy decreases as thermal energy increases. Understanding this energy conversion is crucial in designing efficient machines and understanding various physical phenomena.

Answered by GinnyAnswer | 2025-07-08

In a system with friction, the correct relationship between mechanical energy, thermal energy, and total energy is given by the equation ME = E total ​ − E thermal ​ . This means that mechanical energy decreases as it is converted to thermal energy, keeping the total energy constant. Therefore, the correct answer is option B.
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Answered by Anonymous | 2025-07-26