Students examine a plastic "surface" graph of the gravitational potential energy of a Earth-satellite system to make connections between gravitational force and gravitational potential energy.

In this course, two of the primary examples we will be using are the potential due
to gravity and the potential due to an electric charge. Both of these forces vary
like \(\frac{1}{r}\), so they will have many, many similarities. Most of the
calculations we do for the one case will be true for the other. But there are
some extremely important differences:

Find the value of the electrostatic potential energy of a system consisting of a
hydrogen nucleus and an electron separated by the Bohr radius. Find the value
of the gravitational potential energy of the same two particles at the same
radius. Use the same system of units in both cases. Compare and the contrast
the two answers.

Find the value of the electrostatic potential due to the nucleus of a hydrogen atom
at the Bohr radius. Find the gravitational potential due to the nucleus at
the same radius. Use the same system of units in both cases. Compare and
contrast the two answers.

Briefly discuss at least one other fundamental difference between
electromagnetic and gravitational systems. Hint: Why are we bound to the
earth gravitationally, but not electromagnetically?

Students examine a plastic “surface” graph of the gravitational potential energy of an Earth-satellite system to explore the properties of gravitational potential energy for a spherically symmetric system.

Students use a pre-written Mathematica notebook or a Geogebra applet to explore how the shape of the effective potential function changes as the various parameters (angular momentum, force constant, reduced mass) are varied.

A group of students, tethered together, are floating freely in outer space. Their task is to devise a method to reach a food cache some distance from their group.

Students observe the motion of a puck tethered to the center of the airtable. Then they plot the potential energy for the puck on their small whiteboards. A class discussion follows based on what students have written on their whiteboards.