Which equation shows the correct relationship between mechanical energy, kinetic energy, and potential energy?
$ME=KE+PE$
$ME + KE = PE$
$ME=KE-PE$
$ME+PE=KE$
Answer (2)
Mechanical energy (ME) is the sum of kinetic energy (KE) and potential energy (PE).
The correct equation is ME = K E + PE .
Other given equations do not represent the correct relationship.
Therefore, the equation showing the correct relationship is ME = K E + PE .
Explanation
Understanding the Relationship Let's analyze the relationship between mechanical energy (ME), kinetic energy (KE), and potential energy (PE). Mechanical energy is the total energy of a system, which includes both the energy of motion (kinetic energy) and the energy of position (potential energy). Therefore, the mechanical energy is the sum of the kinetic and potential energies.
Formulating the Equation The equation that represents this relationship is: ME = K E + PE This equation states that the mechanical energy (ME) is equal to the sum of the kinetic energy (KE) and the potential energy (PE).
Identifying the Correct Option Now, let's compare this equation with the given options:
ME = K E + PE (This is the correct equation)
ME + K E = PE (Incorrect)
ME = K E − PE (Incorrect)
ME + PE = K E (Incorrect)
The first equation, ME = K E + PE , matches the correct relationship we derived.
Final Answer Therefore, the correct equation showing the relationship between mechanical energy, kinetic energy, and potential energy is: ME = K E + PE
Examples
Understanding the relationship between mechanical energy, kinetic energy, and potential energy is crucial in many real-world scenarios. For example, consider a roller coaster. At the highest point, the roller coaster has maximum potential energy and minimum kinetic energy. As it descends, potential energy converts into kinetic energy, increasing its speed. At the lowest point, it has maximum kinetic energy and minimum potential energy. The total mechanical energy (ignoring friction) remains constant throughout the ride, demonstrating the principle that ME = K E + PE . This principle applies to various systems, from simple pendulums to complex machines, helping engineers design and analyze their performance.
The correct equation that represents the relationship between mechanical energy, kinetic energy, and potential energy is ME = K E + PE . This illustrates that mechanical energy is the sum of kinetic and potential energies. Therefore, the chosen option is ME = K E + PE .
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