How is total mechanical energy calculated in a system?

• A. E = PE + KE
• B. E = Fd
• C. E = mgh + 1/2 mv²
• D. E = Fv

Answer: (A)

Total mechanical energy in a system is calculated by summing the potential energy (PE) and kinetic energy (KE). This relationship is foundational in physics because it illustrates the conservation of mechanical energy in ideal scenarios, where mechanical energy is neither added nor lost.

Potential energy is the stored energy of an object based on its position or configuration, often described as gravitational potential energy when related to height above a reference point. Kinetic energy, on the other hand, is the energy of an object in motion and depends on its mass and velocity. By adding these two forms of energy together—E = PE + KE—we obtain the total mechanical energy, which remains constant in the absence of non-conservative forces like friction.

The other choices focus on different physical concepts. The second option involves work done by a force over a distance but does not account for both potential and kinetic energies. The third option specifically describes the mechanical energy in terms of PE and KE but uses explicit formulas, which is a subset of the more general expression in the first choice. The fourth option relates to power and the rate of doing work, which also does not encompass total mechanical energy.