Chapter 8 Physics

Conservative Force

A force where the work done moving an object between two points depends only on the initial and final positions, not on the path taken

What are some conservative forces?

Gravity, elastic/spring force, and electrostatic force.

What are some nonconservative forces?

Friction, air resistance, tension, and applied force.

Closed loop property

The net work done by a conservative force over any closed, round-trip path is exactly 0.

Potential Energy

Stored energy. Associated with the configuration/arrangement of a system of objects interacting via conservative forces.

Does potential energy belong to a system or a single object?

System

Work-Energy Theorem

Wnet = delta K

Work by Conservative force

Wc = - delta U

Work by nonconservative force

Wnc = delta Emech

Gravitational Potential Energy

Ug = mgh

Kinetic Energy

K = ½ m v²

Mechanical Energy

E = K + U

Elastic Potential Energy

U = ½ kx²

Conservation of Energy with only conservative forces doing work

Ki + Ui = Kf + Uf

Conservation of Energy with only nonconservative forces doing work

Ki + Ui + Wnc = Kf + Uf

What is the negative derivative of potential energy?

Conservative force F(x)

How do you measure a change in potential energy? (Calculus)

U = negative integral from xi to xf of F(x) dx

When given a graph of U(x) plotted against x, what happens when the slope is positive?

Force acts in the -x direction

When given a graph of U(x) plotted against x, what happens when the slope is negative?

Force acts in the +x direction

Stable equilibrium

Occurs at a local minimum of U(x)

Unstable equilibrium

Occurs at a local max of U(x)

Neutral Equilibrium

Occurs on a flat plateau where U(x) is constant over a range.

Turning points

Positions where the object’s U = Etotal

What happens to kinetic energy at a turning point

It is zero since K = Etotal - U. The object reverses direction.