Conservation of Mechanical Energy

Definition

Conservation of mechanical energy states that in a closed system, the total mechanical energy (the sum of kinetic and potential energy) remains constant if only conservative forces are acting. This principle highlights the interchangeability between kinetic energy, which is the energy of motion, and potential energy, such as gravitational potential energy, under the influence of gravity or other conservative forces, while ensuring no energy is lost to friction or air resistance.

5 Must Know Facts For Your Next Test

1. In a system where only conservative forces act, such as gravity, the mechanical energy remains constant throughout the motion.
2. When an object falls under the influence of gravity, its gravitational potential energy decreases while its kinetic energy increases, keeping the total mechanical energy unchanged.
3. Energy transformations occur in simple harmonic motion where potential and kinetic energies convert back and forth while maintaining total mechanical energy.
4. Non-conservative forces like friction or air resistance can result in a loss of mechanical energy from the system, leading to a decrease in total mechanical energy.
5. The conservation of mechanical energy allows for the prediction of an object's speed or height at various points in its path based on initial conditions.

Review Questions

• How does the conservation of mechanical energy apply to objects in free fall and their transformation between potential and kinetic energy?
  • In free fall, as an object descends, its gravitational potential energy decreases while its kinetic energy increases due to acceleration from gravity. This exchange occurs in such a way that the total mechanical energy remains constant. At its highest point, all energy is potential; as it falls, that potential energy converts into kinetic energy until it reaches maximum speed just before impact.
• Discuss how conservation of mechanical energy is illustrated in systems exhibiting simple harmonic motion.
  • In simple harmonic motion, such as a mass on a spring or a pendulum, conservation of mechanical energy demonstrates how potential and kinetic energies swap throughout the motion cycle. At maximum displacement, all the mechanical energy is stored as potential energy. As the object moves towards equilibrium, potential energy transforms into kinetic energy until it reaches maximum speed at the center point, where all the mechanical energy is kinetic again.
• Evaluate how external forces impact the conservation of mechanical energy in a system and provide examples.
  • External forces like friction or air resistance disrupt the conservation of mechanical energy by converting some mechanical energy into thermal energy or sound. For example, when a ball rolls down a hill on grass rather than a smooth surface, it experiences friction that dissipates some of its initial potential energy as heat instead of converting it entirely into kinetic energy. This means that even though potential and kinetic energies may still fluctuate within the system, overall mechanical energy will decline due to these non-conservative forces.

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 of an object due to its position or configuration, commonly associated with gravitational force, calculated as $$PE = mgh$$, where 'm' is mass, 'g' is acceleration due to gravity, and 'h' is height.

Work-Energy Theorem: A principle that states the work done on an object is equal to the change in its kinetic energy, highlighting the relationship between work and energy in mechanical systems.