Potential Energy and Energy Conservation

Flashcards about Potential Energy and Energy Conservation, covering gravitational potential energy, conservation of mechanical energy, work done by various forces, elastic potential energy, conservative and nonconservative forces, and the relationship between force and potential energy in one and three dimensions.

Gravitational Potential Energy

The potential energy associated with a particle in a gravitational field.

Work done by weight

Equal to the initial gravitational potential energy minus the final gravitational potential energy: W = U1 - U2

Change in Gravitational Potential Energy

Related to the work done by gravity as: ΔU = -W

Conservation of Mechanical Energy

When only gravity does work on a system, the total mechanical energy of the system is conserved.

Work done by a Spring

Equal to the difference in elastic potential energy: W = U1 - U2

Elastic Potential Energy

The energy stored in an elastic object, such as a spring. An object is elastic if it returns to its original shape after being deformed.

Total Potential Energy (with Gravitational and Elastic Forces)

The sum of the gravitational potential energy and the elastic potential energy: U = Ugrav + Uel

Conservative Force

A force that allows conversion between kinetic and potential energy. Examples include gravity and spring force. The work done is independent of the path and is zero if the starting and ending points are the same.

Nonconservative Force

A force (such as friction) that is not conservative, also known as a dissipative force. The work done depends on the path and is non-reversible.

Conservation of Energy

Energy is never created or destroyed; it only changes form.

Conservative Force in One Dimension

Can be obtained from its potential energy function using: F = -dU/dx

Gradient of U

In three dimensions, when we take the partial derivative of U with respect to each coordinate, multiply by the corresponding unit vector, and then take the vector sum, this is called the gradient of U.