Potential Energy and Potentials

Overview

This lesson shifts from force descriptions to energy descriptions of gravitational fields. You will define gravitational potential, use the point-mass potential equation, and connect potential to gravitational potential energy for two masses.

What You Need to Know

• Use gravitational potential to compare energy changes per unit mass between points in a field.
• Infinity is chosen as the zero of gravitational potential.
• Gravitational potential near a point mass is negative because work is released as a mass moves inward from infinity.
• Potential is energy per unit mass; potential energy depends on the mass placed in the field.
• The gravitational potential energy of two point masses is found from the potential and the second mass.

How to Work Through It

1. Start by recalling work done and energy transfer in a field.
2. Define gravitational potential carefully, including the reference point at infinity.
3. Use the point-mass potential equation and then multiply by mass for potential energy.
4. Interpret negative values and changes in potential or potential energy.

Check Your Understanding

• Why is gravitational potential defined relative to infinity?
• What is the difference between gravitational potential and gravitational potential energy?
• Why is gravitational potential around an isolated mass negative?
• What happens to potential energy as two attracting masses move farther apart?

Common Mistakes

• Dropping the negative sign in gravitational potential or potential energy.
• Confusing potential with potential energy.
• Measuring r from the surface instead of the centre of a spherical mass.
• Treating zero potential as being at Earth’s surface rather than at infinity for this model.

Next Steps

• Practise interpreting changes in potential energy, not just substituting values.
• Use force, field, and energy ideas together in orbital motion.