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Which equation represents the law of conservation of energy in a closed system?

A. [tex]KE_1 + PE_1 = KE_1 + PE_1[/tex]
B. [tex]PE_1 + PE_1 = KE_1 + KE_1[/tex]
C. [tex]KE_1 - KE_f = PE_i - PE_f[/tex]
D. [tex]KE_1 - PE_1 = PE_1 - KE_1[/tex]



Answer :

GinnyAnswer
In a closed system, the law of conservation of energy means that the total energy remains constant over time. This means that the sum of kinetic energy (KE) and potential energy (PE) at any point in time should be equal to the sum of kinetic energy and potential energy at any other point in time.

Let's analyze the given equations:

1. [tex]\( KE_1 + PE_1 = KE_1 + PE_1 \)[/tex]
2. [tex]\( PE_1 + PE_1 = KE_1 + KE_1 \)[/tex]
3. [tex]\( KE_1 - KE_{\text{f}} = PE_{\text{i}} - PE_{\text{f}} \)[/tex]
4. [tex]\( KE_1 - PE_1 = PE_1 - KE_1 \)[/tex]

The correct representation of the law of conservation of energy in a closed system is Equation 1:
[tex]\[ KE_1 + PE_1 = KE_1 + PE_1 \][/tex]

This equation states that the initial kinetic energy plus the initial potential energy is equal to the final kinetic energy plus the final potential energy, which aligns with the principle that the total energy remains constant.

Thus, the correct equation is:
[tex]\[ KE_1 + PE_1 = KE_1 + PE_1 \][/tex]
Rochirion

Answer:

Option (A)

Explanation:

The law of conservation of energy in a closed system states that the total energy remains constant over time. This means that the sum of the kinetic energy (KE) and potential energy (PE) at the initial state must equal the sum of the kinetic energy and potential energy at the final state.

This would make option (A) correct.

[tex]\boxed{ \begin{array}{ccc} \text{\underline{Energy Conservation:}} \\\\ \text{Total Energy at Start} = \text{Total Energy at End} \\\\ E_{\text{total, initial}} = E_{\text{total, final}} \\\\ \text{Where:} \\ \bullet \ E_{\text{total, initial}} \ \text{is the total initial energy (kinetic + potential + others)} \\ \bullet \ E_{\text{total, final}} \ \text{is the total final energy (kinetic + potential + others)} \end{array} }[/tex]

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