Spring Potential Energy
Explore elastic potential energy stored in springs using Hooke's Law (F = -kx) and the energy formula PEspring = ½kx², where k is the spring constant and x is displacement from equilibrium. Visualize how compressing or stretching a spring stores energy that can be converted to kinetic energy. Apply conservation of energy to spring-mass systems, understand the relationship between spring stiffness and stored energy, and solve problems involving springs in toys, shock absorbers, and oscillating systems.
ELASTIC POTENTIAL ENERGY
When a spring is stretched or compressed, work is done against the restoring force. This work is stored as Elastic Potential Energy (). Because the force required to stretch a spring increases linearly with distance (Hooke's Law), the energy stored follows a quadratic relationship with displacement.
CORE FORMULAS
Hooke's Law:\nF_s = kx\n\nElastic Potential Energy:\nU_s = \frac{1}{2}kx^2\n\nWhere is the spring constant (N/m) and is the displacement (m).
HOW TO USE THIS VISUALIZATION
1. **Stretch the Spring**: Drag the mass to change the displacement .\n2. **Adjust Stiffness**: Change the spring constant and observe the force required.\n3. **Watch the Energy Bar**: See how grows rapidly as you increase .\n4. **Release**: Watch the conversion from to Kinetic Energy ().
CORE FORMULAS
AP EXAM CONNECTION
Unit: Unit 3: Work, Energy, and Power (Topic 3.1)
Learning Objective: 3.2.1
COMMON MISCONCEPTIONS
- Thinking energy is linear with displacement (it's quadratic).
- Forgetting that is the change in length, not the total length.
- Confusing the spring constant with the displacement .
KEY TAKEAWAYS
- Energy is stored when springs are deformed.
- Energy depends on .
- Spring constant represents stiffness.
- Area under a Force-Position graph equals work/energy.
PRACTICE QUESTIONS
Q1 (QUANTITATIVE): A spring is stretched from 10 cm to 20 cm. By what factor does the stored energy increase?
Show Answer & Explanation
Answer: 4
Explanation: Energy is proportional to . Doubling the displacement () increases energy by .
