Work, energy, power and system boundaries
Energy methods begin with a system boundary and a list of interactions crossing that boundary. They can avoid tracking every intermediate acceleration, but they do not remove the need to identify forces, displacements and the assumptions of the model. Mechanical energy is not automatically conserved just because the word energy appears in the question.
For a constant force acting through a displacement, work is the scalar product of force and displacement: W = F s cos(theta). The angle belongs to the force and displacement vectors, not an arbitrary incline drawing. A perpendicular force does no work through that displacement. When the relevant force component varies with position, work is the signed area under its force-displacement graph, or the corresponding integral. Negative work means that interaction removes mechanical energy from the chosen moving system.
For a constant-mass particle in the ordinary nonrelativistic model, kinetic energy is one half mass times speed squared. The net work by all forces equals the change in this kinetic energy. If using only the work of an applied force, separately account for gravity, friction or other forces; applied work need not equal the entire kinetic-energy change. Near a planet's surface, a uniform-gravity approximation gives a gravitational potential-energy change m g delta-h. This approximation must not replace the inverse-square potential in a large orbital-distance problem.
For example, a hypothetical 2.0 kg object falls from rest through 3.0 m with g = 9.8 m/s squared, while air resistance is neglected. Its gravitational potential energy decreases by 58.8 J. Its kinetic energy increases by that amount, giving speed sqrt(2 times 58.8 divided by 2.0), approximately 7.67 m/s. The mass cancels from the corresponding ideal speed formula. If resistance dissipates energy, the same height drop produces a smaller speed and a thermal-energy transfer, rather than a failure of overall energy conservation.
An ideal spring stores one half k x squared relative to its relaxed state in the specified linear range. Friction, deformation and electrical resistance can transfer organized mechanical energy into internal energy. For an isolated total system, all relevant forms remain in the accounting even when mechanical energy alone decreases.
Average power is transferred energy or work divided by elapsed time. Instantaneous mechanical power is the scalar product of force and velocity. Efficiency in an ordinary energy-conversion calculation is useful output energy divided by supplied input energy over the same process. State which output is useful and which time interval is used. A heat pump's coefficient of performance uses a different definition and must not be confused with this efficiency ratio.