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Conservative Forces and PotentialsPowerPoint Presentation

Conservative Forces and Potentials

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Forces and potentials

Every conservative force is a spatial derivative of a potential energy function.

Specifically,

F = –(idU/dx + jdU/dy + kdU/dz)

(This is Calculus 3 stuff)

Forces and potentials

Every conservative force is a spatial derivative of a potential energy function.

- Near-surface gravity:

Source: Young and Freedman, Figure 7.22b.

Forces and potentials

Every conservative force is a spatial derivative of a potential energy function.

- Hooke’s law spring:

Source: Young and Freedman, Figure 7.22a.

Equilibrium Potentials

- Stable equilibrium: small excursions damped by a restoring force

- Unstable equilibrium: small excursions amplified by non-restoring force

- Force is zero at an equilibrium point
- Potential is locally unchanging

Whiteboard Work

A particle is in neutral equilibrium if the net force on it is zero and remains zero if the particle is displaced slightly in any direction.

- Sketch a one-dimensional potential energy function near a point of neutral equilibrium.
- Give an example of a neutral equilibrium potential.

K

0

K

r

Energy diagramPlot U as a function of position

Mark total E as a horizontal line

K = E – U

(function of position)

E

U

Diagram shows the partition of energy everywhere.

Poll Question

Which points are stable equilibria?

Add correct answers together.

1. x1.

2. x2.

4. x3.

8. x4.

Source: Young and Freedman, Figure 7.24a.

Poll Question

Which positions are accessible if E = E2?

Add correct answers together.

1. x1.

2. x2.

4. x3.

8. x4.

Source: Young and Freedman, Figure 7.24a.

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