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Question Video: Identifying Work Done in Terms of Changes in Potential and Kinetic Energy Mathematics

True or False: The change in kinetic energy + the change in potential energy = the work done by non-conservative forces.

02:18

Video Transcript

True or False: The change in kinetic energy plus the change in potential energy is equal to the work done by nonconservative forces.

We begin by recalling the conservation of energy principle. This states that if no resistance or nonconservative forces are acting on the system, then the initial kinetic energy plus the initial potential energy is equal to the final kinetic energy plus the final potential energy. In other words, the sum of the kinetic and potential energies remains constant during the motion. However, if we have a situation where the initial energies are greater than the final energies, then the change in energy or the energy that is dissipated from the system must be attributed to work done by nonconservative forces.

In this case, we have the following equation. The initial kinetic energy plus the initial potential energy plus the work done by nonconservative forces is equal to the final kinetic energy plus the final potential energy. Rearranging this equation, we have the work done is equal to the final kinetic energy minus the initial kinetic energy plus the final potential energy minus the initial potential energy. On the right-hand side of our equation, we have the change in kinetic energy, denoted Δ𝐾𝐸 or Δ𝐾. This is the difference between the final kinetic energy and the initial kinetic energy. Likewise, we have the change in potential energy, the difference between the final potential energy and the initial potential energy.

The work done by nonconservative forces is therefore equal to the change in kinetic energy plus the change in potential energy. And we can therefore conclude that the statement in the question is true.

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