Potential Energy of a Spring Calculator with Two Points

Elastic Potential Energy Formula:

\[ PE = \frac{1}{2} \times k \times (x_2 - x_1)^2 \]

Elastic Potential Energy (PE): J

1. What is Potential Energy of a Spring?

Definition: Elastic potential energy is the energy stored in elastic materials as a result of their stretching or compressing.

Purpose: This calculator helps determine the energy stored in a spring when it's displaced from its equilibrium position.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ PE = \frac{1}{2} \times k \times (x_2 - x_1)^2 \]

Where:

\( PE \) — Elastic potential energy (Joules)
\( k \) — Spring constant (N/m)
\( x_1 \) — Initial position (meters)
\( x_2 \) — Final position (meters)

Explanation: The potential energy depends on the spring constant and the square of the displacement from equilibrium.

3. Importance of Spring Potential Energy Calculation

Details: Understanding spring energy is crucial in designing mechanical systems, shock absorbers, and various engineering applications.

4. Using the Calculator

Tips: Enter the spring constant (must be positive), initial position, and final position. The difference between positions determines the displacement.

5. Frequently Asked Questions (FAQ)

Q1: What does the spring constant represent?
A: The spring constant (k) measures the stiffness of a spring - how much force is needed to stretch or compress it by a certain distance.

Q2: Can x₁ be greater than x₂?
A: Yes, the calculator works for both compression (x₂ < x₁) and extension (x₂ > x₁) scenarios.

Q3: Why is potential energy always positive?
A: The energy depends on the square of displacement, making it always positive regardless of direction.

Q4: What if the spring returns to equilibrium?
A: When x₂ = x₁, the potential energy is zero as there's no displacement from equilibrium.

Q5: How does this relate to Hooke's Law?
A: Hooke's Law (F = -kx) gives the force, while this formula gives the energy stored from doing work against that force.