Defining Work & Work Done (College Board AP® Physics 1: Algebra-Based)

What is work?

• Work is the amount of energy transferred into or out of a system when an applied force displaces an object

• The units for work are newton-meters,

  • Where

• Work is a scalar quantity with a magnitude only

  • However, work can be positive, negative, or zero

• Work has a positive value when the force is applied in the same direction as the object's motion

  • The speed of the object will increase

• Work has a negative value when the force is applied in the opposite direction to the object's motion

  • The speed of the object will decrease

Work done by a conservative force

• Conservative forces are forces that conserve mechanical energy within a system

  • For example, when an object is dropped from a height, the gravitational potential energy is transformed into kinetic energy

  • No energy is dissipated to the surroundings in this energy transfer (ignoring air resistance)

• The work done by a conservative force exerted on a system is path-independent

  • It depends only on the initial and final configurations (positions) of the system

  • It does not depend on the path taken to move an object between its initial and final position

  • For example, an object dropped from a height will transfer the same amount of gravitational potential energy to kinetic energy whether it is dropped vertically or at an angle

• The work done by a conservative force on a system will be zero if the system returns to its initial configuration

• Hence, the change in potential energy of the system will be zero if the system returns to its original position

  • For example, if an object dropped from a height is returned to its original height, it will have the same amount of gravitational potential energy in its final position as it did in its starting position

• Potential energies are associated only with conservative forces

• For example:

  • Gravitational potential energy

  • Electrostatic potential energy

  • Spring potential energy

Work done by a nonconservative force

• Nonconservative forces are forces that do not conserve mechanical energy within a system

  • For example, when an object is rolled across the ground, the frictional force will cause the object to slow to a stop

  • The force of friction causes energy to be dissipated to the surroundings, so the system will have less energy in its final position than it did in its initial position

• The work done by a nonconservative force is path-dependent

  • It does depend on the path taken to move an object between its initial and final position

  • For example, an object that follows a longer curved path will dissipate more energy due to friction than an object that follows a shorter straight path

• Examples of nonconservative forces are:

  • friction

  • air resistance

• Applied forces that push or pull an object are also nonconservative forces, such as:

  • tension

  • physically pushing or pulling an object