To determine the correct relationship between mechanical energy (ME), kinetic energy (KE), and potential energy (PE), let's analyze the definitions and relationships of these types of energy.
1. Mechanical Energy (ME) is the total energy of a system that is the sum of its kinetic and potential energy.
2. Kinetic Energy (KE) is the energy an object possesses due to its motion.
3. Potential Energy (PE) is the energy stored in an object due to its position or configuration.
The correct relationship is:
[tex]\[ ME = KE + PE \][/tex]
This equation states that the total mechanical energy of a system is the sum of its kinetic energy and potential energy. Let’s compare this with the given options:
1. \( ME = KE + PE \)
2. \( ME + KE = PE \)
3. \( ME = KE - PE \)
4. \( ME + PE = KE \)
Option 1: \( ME = KE + PE \)
This matches our definition perfectly, where the mechanical energy is the sum of kinetic and potential energy.
Option 2: \( ME + KE = PE \)
This suggests that the total energy plus kinetic energy equals potential energy, which does not align with the established definition.
Option 3: \( ME = KE - PE \)
This suggests that mechanical energy is the kinetic energy minus the potential energy, which is incorrect based on the defined relationship.
Option 4: \( ME + PE = KE \)
This suggests that mechanical energy plus potential energy equals kinetic energy, which is also incorrect.
Based on the analysis, the correct equation is:
[tex]\[ ME = KE + PE \][/tex]
Thus, the right choice is:
[tex]\[ \boxed{1} \][/tex]
