POTENTIAL ENERGY

"It may be so, there is no arguing against facts and experiments"
Isaac Newton

• Potential Energy is energy "by virtue of position" and is defined with respect to conservative forces.
• A system with Potential Energy has the "potential" to perform work.  It can be shown that, for conservative forces, when there is no change in velocity

so that

which means that knowing F(x) and the locations of A and B we can evaluate the integral but cannot determine the absolute value of U_B. Thus PE is a relative quantity, only differences in PE are absolutely defined. In order to define a PE scale we arbitrarily define the PE at some point to be zero.

• Gravitational Potential Energy

By setting the gravitational force F(x) = -mg above, we find that the work done against the force of gravity to raise an object a height "h" is given by  mgh.  The object stores this work in the form of Gravitational Potential Energy (where we define the earth’s surface as the zero of gravitational potential energy).

PE = mgh

• Elastic Potential Energy

For a stretched spring, F(x) = -kx, which leads to the expression for PE stored in a stretched spring

setting the PE at x = 0 to zero.

• Other forms of PE: Electrical, Magnetic, Chemical.
• Although we often talk about the potential energy of an object, the potential energy is a property of the "system", in the gravitational case the object and the earth.

• The relationship between PE and force in one dimension can also be written

which allows us to easily obtain the force if the form of the PE is known.

In three dimensions the force/PE relationships can be written

"In the English Channel today, a ship carrying red paint collided with a ship carrying purple paint.  The crew are believed to have been marooned."

Ronnie Barker

Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu