Conservation of mechanical energy

Definition

Conservation of mechanical energy states that in an isolated system with only conservative forces acting, the total mechanical energy (sum of kinetic and potential energy) remains constant. It is a fundamental principle used to solve problems involving conservative forces.

5 Must Know Facts For Your Next Test

1. Mechanical energy is conserved only if no non-conservative forces (like friction) do work on the system.
2. The formula representing conservation of mechanical energy is $KE_1 + PE_1 = KE_2 + PE_2$ where $KE$ is kinetic energy and $PE$ is potential energy.
3. In a pendulum swing, mechanical energy transforms between kinetic and potential forms but remains constant overall.
4. Potential energy depends on position while kinetic energy depends on motion.
5. Gravitational potential energy can be calculated using $PE = mgh$, where $m$ is mass, $g$ is gravitational acceleration, and $h$ is height.

Review Questions

• What conditions must be met for mechanical energy to be conserved?
• How does the conservation of mechanical energy apply to a free-falling object?
• Explain how potential and kinetic energies interchange in a roller coaster ride while conserving total mechanical energy.

Related terms

Kinetic Energy: The energy possessed by an object due to its motion, calculated as $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is velocity.

Potential Energy: The stored energy in an object due to its position or configuration, such as gravitational potential energy given by $PE = mgh$.

Conservative Forces: Forces that do not dissipate mechanical energy; work done by these forces depends only on initial and final positions, not the path taken.