The change in potential energy does indeed equal the change in kinetic energy, but this equality holds true under specific conditions, primarily when considering a closed system with no external work done or energy losses, such as friction. This principle is a reflection of the conservation of mechanical energy.
For instance, when an object falls freely under the influence of gravity, its potential energy decreases as it descends, while its kinetic energy increases as it speeds up. The total mechanical energy of the object remains constant if we ignore air resistance and other forms of energy dissipation.
Mathematically, this can be expressed as:
ΔPE + ΔKE = 0
Where ΔPE is the change in potential energy and ΔKE is the change in kinetic energy. Rearranging gives us:
ΔPE = -ΔKE
This means that the loss in potential energy (as the object falls) will equal the gain in kinetic energy (as the object speeds up). In essence, energy is transformed from one form to another, preserving the total energy within the system.
It’s important to note that this principle is essential in various real-world applications, from roller coasters to physics problems involving projectile motion, making it a foundational concept in physics.