1. What is Hooke's Law?

Hooke's Law is a principle of physics that states that the force needed to extend or compress a spring by some distance is proportional to that distance. The formula is expressed as F = -k × x, where F is the restoring force, k is the spring constant, and x is the displacement from the equilibrium position.

2. How Does the Calculator Work?

The calculator uses Hooke's Law formula:

Where:

• \( F \) — Restoring force (N)
• \( k \) — Spring constant (N/m)
• \( x \) — Displacement from equilibrium (m)

Explanation: The negative sign indicates that the restoring force acts in the opposite direction to the displacement, which is why it's called a "restoring" force - it tries to restore the spring to its equilibrium position.

3. Importance of Restoring Force Calculation

Details: Calculating restoring force is essential in mechanical engineering, physics experiments, and designing spring-based systems. It helps determine how springs will behave under different loads and displacements.

4. Using the Calculator

Tips: Enter spring constant in N/m and displacement in meters. The spring constant must be a positive value, while displacement can be positive or negative (indicating direction).

5. Frequently Asked Questions (FAQ)

Q1: What does the negative sign in the formula mean?
A: The negative sign indicates that the restoring force acts in the opposite direction to the displacement. If you stretch a spring (positive x), it pulls back (negative F). If you compress it (negative x), it pushes back (positive F).

Q2: What is the spring constant?
A: The spring constant (k) is a measure of the stiffness of a spring. A higher k value means a stiffer spring that requires more force to stretch or compress it.

Q3: Does Hooke's Law apply to all springs?
A: Hooke's Law applies only within the elastic limit of the spring. If stretched or compressed beyond this limit, the spring may not return to its original shape and the law no longer applies.

Q4: Can displacement be negative?
A: Yes, displacement can be negative, representing compression of the spring (when the displacement is opposite to the defined positive direction).

Q5: What are typical units for these measurements?
A: Spring constant is typically measured in newtons per meter (N/m), displacement in meters (m), and force in newtons (N).