### Which formula represents the law of conservation of energy?1. \( PE_g = mgh \)2. \( ME = KE + PE \)3. \( ME_{\text{initial}} = ME_{\text{final}} \)4. \( KE = \frac{1}{2}mv^2 \)The law of conservation of energy states that the total mechanical energy (ME) in a closed system remains constant, assuming no energy is lost to friction or other non-conservative forces. The correct formula that represents the law of conservation of energy is:\[ \boxed{ME_{\text{initial}} = ME_{\text{final}}}\]Where:- \(ME_{\text{initial}}\) is the total mechanical energy at the initial state.- \(ME_{\text{final}}\) is the total mechanical energy at the final state.### Explanation of the Other Formulas:1. **\( PE_g = mgh \)**: - This formula represents the gravitational potential energy (\( PE_g \)) of an object at height \( h \) with mass \( m \) in a gravitational field of acceleration \( g \).2. **\( ME = KE + PE \)**: - This formula represents the mechanical energy (\( ME \)), which is the sum of kinetic energy (\( KE \)) and potential energy (\( PE \)) in a system.3. **\( KE = \frac{1}{2}mv^2 \)**: - This formula represents the kinetic energy (\( KE \)) of an object with mass \( m \) and velocity \( v \).### Diagrams and Graphs:As there are no graphs or diagrams provided in the image, this section is not applicable. Generally, in educational websites, diagrams explaining the concepts of mechanical energy, potential energy, and kinetic energy would be provided to help visualize these principles in practical scenarios.

Given There are four options are given We have to choose the correct option for conservation of…

Answered: 12. Which formula represents the law of…

12. Which formula represents the law of conservation of energy? OPE, = mgh ME=KE+ PE MEinitial=MEfinal KE= 1 = nv² 2.21² = O

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Atomic Number

Elements are the building blocks of all the matter that exist in the universe. Every element is made up of atoms that have protons, electrons, and a nucleus. In order to know the difference between the elements, an atomic number is used. Every element has its own individual atomic number. The atomic number is a single most important characteristic of an atom.

Question

### Which formula represents the law of conservation of energy?

1. \( PE_g = mgh \)
2. \( ME = KE + PE \)
3. \( ME_{\text{initial}} = ME_{\text{final}} \)
4. \( KE = \frac{1}{2}mv^2 \)

The law of conservation of energy states that the total mechanical energy (ME) in a closed system remains constant, assuming no energy is lost to friction or other non-conservative forces. The correct formula that represents the law of conservation of energy is:

\[ \boxed{ME_{\text{initial}} = ME_{\text{final}}}\]

Where:
- \(ME_{\text{initial}}\) is the total mechanical energy at the initial state.
- \(ME_{\text{final}}\) is the total mechanical energy at the final state.

### Explanation of the Other Formulas:
1. **\( PE_g = mgh \)**:
- This formula represents the gravitational potential energy (\( PE_g \)) of an object at height \( h \) with mass \( m \) in a gravitational field of acceleration \( g \).

2. **\( ME = KE + PE \)**:
- This formula represents the mechanical energy (\( ME \)), which is the sum of kinetic energy (\( KE \)) and potential energy (\( PE \)) in a system.

3. **\( KE = \frac{1}{2}mv^2 \)**:
- This formula represents the kinetic energy (\( KE \)) of an object with mass \( m \) and velocity \( v \).

### Diagrams and Graphs:

As there are no graphs or diagrams provided in the image, this section is not applicable. Generally, in educational websites, diagrams explaining the concepts of mechanical energy, potential energy, and kinetic energy would be provided to help visualize these principles in practical scenarios.

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