Potential Energy and Work-Energy Theorem Summary

  • Potential Energy

  • External forces do work and change system energy.

  • When enlarging the system, external forces become internal and may influence energy calculations.

  • Internal conservative forces contribute to potential energy changes.

  • External to Internal Forces

  • Example: Two objects exerting forces on each other.

  • The system's choice affects the application of Newton's 2nd law and energy considerations.

  • Changes in Potential Energy

  • Conservative internal forces lead to changes in potential energy.

  • Formulas involve integrating force over distance.

  • Gravitational Potential Energy

  • Defined with respect to Earth's center; includes changes during free fall.

  • Near Earth's surface:

    • ( ( \Delta Ug = mg (yf - y_i) ) ) where (y) is height.

  • Spring Potential Energy

  • Energy associated with spring compression/stretching:

    • ( ( \Delta U{sp} = \frac{1}{2} k(xf^2 - x_i^2) ) ).

  • Work-Energy Theorem and Internal Forces

  • Internal forces cannot change total energy; they redistribute energy within the system.

  • Example: Ball falling where kinetic energy increases as gravitational potential energy decreases.

  • System Choices

  • Applicability of work-energy theorem changes based on whether you include an object as part of the system.

  • Examples

  • Two identical objects falling under gravity interacting through a conservative force.

  • An inclined block attached to a spring and a pulley, illustrating work done by forces and energy changes.

  • Analysis begins with defining the system and identifying all energy contributions (kinetic, potential, thermal) in various scenarios.