3.2 Work

Describe the work done on an object or system by a given force or collection of forces.

• Work is the amount of energy transferred into or out of a system by a force exerted on that system over a distance.
  • i. The work done by a conservative force exerted on a system is path-independent and only depends on the initial and final configurations of that system.
  • ii. The work done by a conservative force on a system—or the change in the potential energy of the system—will be zero if the system returns to its initial configuration.
  • iii. Potential energies are associated only with conservative forces.
  • iv. The work done by a nonconservative force is path-dependent.
  • v. The most common nonconservative forces are friction and air resistance.
• Work is a scalar quantity that may be positive, negative, or zero.
• The work done on an object by a variable force is calculated using where the integral is taken over the path from point a to point b.
  • i. The dot product between two vectors, A  and B  , results in a scalar quantity of magnitude
  • ii. Only the component of the force exerted on a system that is parallel to the displacement of the point of application of the force will change the system’s total energy.
  • iii. If the component of the force exerted on a system that is parallel to the displacement is constant, the work done on the system by the force is given by the derived equation
  • iv. The component of the force exerted on a system perpendicular to the direction of the displacement of the system’s center of mass can change the direction of the system’s motion without changing the system’s kinetic energy.
• The work–energy theorem states that the change in an object’s kinetic energy is equal to the sum of the work (net work) being done by all forces exerted on the object. Relevant equation:
  • i. An external force may change the configuration of a system. The component of the external force parallel to the displacement times the displacement of the point of application of the force gives the change in kinetic energy of the system.
  • ii. If the system’s center of mass and the point of application of the force move the same distance when a force is exerted on a system, then the system may be modeled as an object, and only the system’s kinetic energy can change.
  • iii. The energy dissipated by friction is typically equated to the force of friction times the length of the path over which the force is exerted.
• Work is equal to the area under the curve of a graph of F|| as a function of displacement. BOUNDARY STATEMENT AP Physics C: Mechanics only expects students to analyze the transfer of mechanical energy, although students should be aware that mechanical energy may be dissipated in the form of thermal energy or sound.