Overview
This lecture focused on gravitational potential energy, emphasizing its relative nature and the importance of choosing an appropriate reference level for calculations.
Gravitational Potential Energy Basics
- Potential energy (PE) relates to work and is typically defined as PE = mgh, where m is mass, g is gravity, and h is height.
- The variable h (height) should be measured relative to a chosen reference, not always ground level.
- Potential energy is a relative measurement and must be specified with respect to a particular reference point.
Choosing a Reference Level
- The choice of reference level (where h = 0) is flexible and should depend on the problem context.
- Objects never moving below a certain point make that spot a good candidate for h = 0.
- The numerical value of potential energy changes with different reference levels, but physical outcomes remain unaffected.
Mathematical Representation
- The equation mgh actually expresses a change in potential energy: ΔPE = mgΔh = mg(h_final − h_initial).
- Delta notation (Δ) highlights that it's always the difference in height that matters.
- This flexibility allows for easier calculations by picking the most convenient reference point.
Reference Level Examples (Roller Coaster)
- Setting h = 0 at the bottom of the loop: potential energy is zero at the bottom; higher at upper positions.
- Setting h = 0 at the midpoint: points below have negative potential energy; points above have positive PE.
- Setting h = 0 at the top: all positions below have negative potential energy, larger-magnitude negative values the lower you go.
Direction of Displacement and Force
- Gravitational force always acts downward.
- The displacement vector (change in position) is drawn from object’s location to the reference line.
- Force and displacement in the same direction give positive work (and potential energy), opposite directions give negative values.
Interpreting Potential Energy Values
- Points above the reference level have positive PE; points below have negative PE.
- The magnitude of PE depends on how far the point is from the reference line (larger h, larger |PE|).
Key Terms & Definitions
- Potential Energy (PE) — stored energy due to an object's position relative to a reference point, calculated as mgh.
- Reference Level — the chosen height where potential energy is defined as zero for a specific problem.
- Delta (Δ) — mathematical notation indicating change (e.g., Δh = h_final − h_initial).
- Gravitational Force (mg) — force exerted by gravity, always directed downward.
Action Items / Next Steps
- Review section 3.2 on potential energy, focusing on reference level selection.
- Complete the pop quiz comparing reference levels for potential energy calculations.
- Prepare for discussion of kinetic energy in the next lecture.