Potential energy and conservation of energy

Learning objectives

Explain that potential energy belongs to a system of interacting objects rather than to a single object, and that the position of zero potential energy may be chosen freely

Calculate gravitational potential energy near a planet's surface as ΔU = mgΔy, and use the general form U = −Gm₁m₂/r where the field cannot be treated as uniform

Calculate the elastic potential energy stored in an ideal spring as ½kx² and relate it to the area under a force–extension graph

Apply conservation of total energy to analyze motion, including situations in which friction or drag transfers energy out of the mechanical system, and state clearly which system is being analyzed

Interpret a potential energy against position graph to find the force on an object, locate stable and unstable equilibrium positions, and identify the region of motion allowed by a given total energy

Design an experiment to test conservation of mechanical energy and evaluate whether the observed discrepancy is consistent with energy transferred by friction