Final answer:
The change in gravitational potential energy of an object falling under gravity equals the work done by gravity, even when an opposing force is applied. The opposing force affects the net work done, but not the energy conservation relationship between work and potential energy. Other forms of energy lost in the process are not considered in this ideal scenario.
Step-by-step explanation:
When an object falls under the influence of gravity, there's a decrease in its gravitational potential energy (UG), which is due to its position or height relative to Earth. This decrease in potential energy is translated to work done by gravity, denoted as Wdonebygravity. According to the conservation of energy principle, the work done by gravity on an object is equal and opposite to the change in the object’s gravitational potential energy, or -ΔUG = Wdonebygravity, where the negative sign indicates a decrease in potential energy.
If an upward force is applied to the object that is less than the gravitational force, the object will still accelerate downward. While our applied force does work against gravity, it does not change the fact that the total change in potential energy of the object is equal to the work done by gravity, assuming no other forms of energy like heat or sound are being generated. However, if we consider the resulting force (gravity minus our applied force), the work done by the resulting force will indeed be slightly less than the work done by gravity alone due to the upward force applied.
In an ideal scenario with no external losses (like heat or sound), the total mechanical energy is conserved. This means that the loss in potential energy due to an elevation change equals the increase in kinetic energy, disregarding the unbalanced forces. However, if any energy is lost to other forms, such as heat due to air resistance or sound, then the gain in kinetic energy will be less than the loss of potential energy.