Final answer:
When tossing a ball without air resistance, potential energy and kinetic energy vary throughout its flight but are not the same except at one point. Energy conservation dictates that the sum of both energies remains constant in the absence of external forces like air resistance.
Step-by-step explanation:
If you toss a ball straight up without air resistance, the potential energy and kinetic energy are not necessarily the same at all points during its flight. Potential energy is at its maximum when the ball reaches its highest point and kinetic energy is zero. Conversely, when the ball is released, it has maximum kinetic energy and zero potential energy. As the ball rises, kinetic energy is converted to potential energy, and this process reverses as the ball falls back down, assuming no energy is lost.
When considering the example of a ball being tossed with air resistance, the final velocity and final kinetic energy of the ball would both decrease. This occurs because energy is transferred to the surrounding air as heat due to the effects of resistance.
Conservation of Energy
The proposition of kinetic energy equalling potential energy only holds in a frictionless environment at the instantaneous moment when the ball changes direction. This is due to the conservation of energy, where the change in kinetic energy (ΔΚΑΒ) is equal to the negative of the change in gravitational potential energy (ΔUAB).