3.3.A—Describe the potential energy of a system

Describe the potential energy of a system.

• A system composed of two or more objects has potential energy if the objects within that system only interact with each other through conservative forces.
• Potential energy is a scalar quantity associated with the position of objects within a system.
• The definition of zero potential energy for a given system is a decision made by the observer considering the situation to simplify or otherwise assist in analysis.
• The relationship between conservative forces exerted on a system and the system’s potential energy is
• The conservative forces exerted on a system in a single dimension can be determined using the slope of the system’s potential energy with respect to position in that dimension; these forces point in the direction of decreasing potential energy. Relevant equation: F dU x dx () x =−
• Graphs of a system’s potential energy as a function of its position can be useful in determining physical properties of that system. TOPIC 3.3 Potential Energy
  • i. Stable equilibrium is a location at which a small displacement in an object’s position results in a force exerted on the object opposite to the direction of the small displacement, accelerating the object back toward the equilibrium position.
  • ii. Unstable equilibrium is a location at which a small displacement in an object’s position results in a force exerted on the object in the same direction as the small displacement, accelerating the object away from the equilibrium position.
  • iii. In a given dimension, stable equilibrium positions exist at locations where the potential energy as a function of position in that dimension has a local minimum.
  • iv. In a given dimension, unstable equilibrium positions occur at locations where the potential energy as a function of position in that dimension has a local maximum.
• The potential energy of common physical systems can be described using the physical properties of that system.
  • i. The elastic potential energy of an ideal spring is given by the following equation, where Δx is the distance the spring has been stretched or compressed from its equilibrium length. Relevant equation:
  • ii. The general form for the gravitational potential energy of a system consisting of two approximately spherical distributions of mass (e.g., moons, planets, or stars) is given by the equation UG mm r g 12=− .
  • iii. Because the gravitational field near the surface of a planet is nearly constant, the change in gravitational potential energy in a system consisting of an object with mass m and a planet with gravitational field of magnitude g when the object is near the surface of the planet may be approximated by the equation
• The total potential energy of a system containing more than two objects is the sum of the potential energy of each pair of objects within the system.