Overview
This lecture explains elastic potential energy, how it is stored in stretched springs, and how to calculate it using a given formula.
Elastic Potential Energy
- Elastic potential energy is energy stored in objects when they are stretched or compressed, such as springs.
- Stretching a spring requires applying a force, which scientists call "doing work."
- The stretched spring holds the energy until the force is removed.
Springs and Extension
- Extension refers to how much a spring stretches when a force is applied.
- Extension is represented by the symbol "e."
- If force and extension are plotted on a graph, a straight line through zero indicates direct proportionality.
- If stretched beyond the limit of proportionality, the spring no longer returns to its original shape.
Calculating Elastic Potential Energy
- The formula for elastic potential energy: Elastic potential energy (Joules) = 0.5 × spring constant (k) × extension² (e²).
- Extension must be in meters; convert from centimeters by dividing by 100.
- The spring constant (k) varies depending on the spring.
Example Calculation
- Given: spring extension = 20 cm (0.2 m), spring constant = 100 N/m.
- Elastic potential energy = 0.5 × 100 × (0.2)² = 2 Joules.
Key Terms & Definitions
- Elastic potential energy — Energy stored in stretched or compressed materials like springs.
- Extension (e) — The change in length of a spring when a force is applied.
- Spring constant (k) — A value that measures a spring's stiffness, in Newtons per meter (N/m).
- Limit of proportionality — The maximum point where the extension is directly proportional to the force.
Action Items / Next Steps
- Practice calculating elastic potential energy using the given formula.
- Ensure extensions are always converted to meters before calculations.