— ## What is Spring Force? A spring force is a restoring force exerted by a spring when it is stretched or compressed from its equilibrium (natural) position. It’s called a “restoring” force because it always tries to bring the spring back to its original, relaxed length. — ## Hooke’s Law Hooke’s Law states that the force required to extend or compress a spring is directly proportional to the distance of that extension or compression. * Formula: $F_s = -kx$ * $F_s$: The spring force (in Newtons, N). * $k$: The spring constant (in N/m). This is a measure of the stiffness of the spring. A larger $k$ means a stiffer spring. * $x$: The displacement (stretch or compression) from the spring’s equilibrium position (in meters, m). * The negative sign indicates that the spring force is always in the opposite direction to the displacement. If you stretch the spring (positive $x$), the force pulls it back (negative $F_s$). If you compress it (negative $x$), the force pushes it out (positive $F_s$). — ## Interactive: Hooke’s Law Stretch and compress a spring to see how the spring force and potential energy change! <div class="animator-container"> <div class="input-controls"> </div> <div style="margin-bottom: 0.8rem;"> </div> Hooke's Law Spring Force Simulator An interactive simulation demonstrating Hooke's Law, showing spring force and potential energy as a spring is stretched or compressed. Wall Mass Equilibrium (x=0) Displacement (x): 0.00 m Spring Force (Fs): 0.0 N Potential Energy (PEs): 0.0 J $F_s$ <div id="animationExplanation" class="animation-explanation" aria-live="polite"> <p>Adjust the spring constant, then stretch or compress the spring to see the force and energy changes!

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Spring Potential Energy

When you stretch or compress a spring, you are doing work on it, and this work is stored as elastic potential energy (often called spring potential energy, $PE_s$). This energy can then be released to do work (e.g., launch a projectile).

  • Formula: $PE_s = \frac{1}{2}kx^2$
    • $PE_s$: Elastic potential energy (in Joules, J).
    • $k$: Spring constant (in N/m).
    • $x$: Displacement from equilibrium (in meters, m).

Notice that potential energy depends on $x^2$, so it’s always positive, whether the spring is stretched or compressed.

Why Spring Force Matters

  • Oscillations and Waves: Spring force is the basis for understanding simple harmonic motion, which describes oscillations (like a mass on a spring) and wave phenomena.
  • Engineering: Springs are used in countless applications, from car suspensions and shock absorbers to scales, trampolines, and retractable pens.
  • Energy Conservation: Spring potential energy is a key form of energy studied in the context of conservation of energy.

Audio Explanation

Prefer to listen? Here's a quick audio summary of spring force and Hooke's Law.

💡 Quick Concept Check:

A spring is compressed by 0.1 meters and exerts a force of 10 Newtons. What is its spring constant ($k$)? If it is compressed by 0.2 meters, what force will it exert?

Click to Reveal Answer
Using Hooke's Law, $F_s = kx$: For the first case: $10 \text{ N} = k \times 0.1 \text{ m} \implies k = 100 \text{ N/m}$. For the second case: $F_s = 100 \text{ N/m} \times 0.2 \text{ m} = 20 \text{ N}$. So, the spring constant is **100 N/m**, and it will exert **20 N** of force when compressed by 0.2 meters.

Ready to put your understanding of spring force into practice? Check out these related skills:

Practice Problems

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