What happens to the total energy as the spring bounces? Which types of energy make up the total energy? How do they relate to each other?
Physics · High School · Tue Nov 03 2020
Answered on
When a spring bounces, the total energy of the system undergoes changes, transitioning between potential energy and kinetic energy.
- Potential Energy (PE): At the maximum displacement (compression or elongation) of the spring, the potential energy stored in the spring is at its maximum. This potential energy is elastic potential energy, which depends on the displacement of the spring from its equilibrium position. The formula for elastic potential energy is ��=12��2
- PE=2
- 1
- kx2
- , where �
- k is the spring constant and �
- x is the displacement from equilibrium.
- Kinetic Energy (KE): As the spring is released and the stored potential energy is converted into motion, the potential energy decreases, and kinetic energy increases. At the equilibrium position (when the spring is neither compressed nor elongated), all the potential energy is converted into kinetic energy. The formula for kinetic energy is ��=12��2
- KE=2
- 1
- mv2
- , where �
- m is the mass of the object attached to the spring, and �
- v is its velocity.
As the spring continues to bounce, the process repeats. At the highest points of the bounce, when the object momentarily comes to rest before changing direction, the kinetic energy is momentarily zero, and the potential energy is at its maximum. The total mechanical energy (sum of kinetic and potential energies) is conserved in the absence of external forces like friction or air resistance.
In summary, the total energy of the system is conserved, with the spring's potential energy transforming into kinetic energy and vice versa as the spring undergoes oscillations. This relationship is described by the principle of conservation of mechanical energy, which states that the total mechanical energy in an isolated system remains constant if only conservative forces (like spring forces) are at play.