A spring exerts a force when it is stretched or compressed. This force, called the spring force, always acts to restore the spring to its natural length.

Audio Explanation

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

Visual Representation

Compression x (squeeze) Fs (restoring) Rest position Stretching x (stretch) Fs (restoring) Rest position

What is Spring Force?

A spring force is a restoring force exerted by a spring when it is displaced from its equilibrium position.
It always points opposite to the displacement:

  • Stretch → spring pulls back
  • Compression → spring pushes outward

Hooke’s Law

Hooke’s Law relates the force a spring exerts to its displacement:

  • Formula: $F_s = -kx$
    • $F_s$: spring force (N)
    • $k$: spring constant (N/m) – stiffer springs have higher $k$
    • $x$: displacement from equilibrium (m)
    • Negative sign → force opposes displacement

Interactive: Hooke’s Law Simulator

Adjust the spring constant and stretch/compress the spring to see how the force and potential energy change.

Hooke's Law Spring Force Simulator Interactive simulation showing spring force and potential energy as the 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 $F_s$

Adjust the spring constant, then stretch or compress the spring to see the force and energy changes!

Spring Potential Energy

The work done on a spring is stored as elastic potential energy:

  • Formula: $PE_s = \frac{1}{2}kx^2$
    • $PE_s$: elastic potential energy (J)
    • $k$: spring constant (N/m)
    • $x$: displacement from equilibrium (m)

Energy is always positive because it depends on $x^2$.

Why Spring Force Matters

  • Oscillations & Waves: Basis for simple harmonic motion.
  • Engineering Applications: Springs in suspensions, scales, and devices.
  • Energy Conservation: Converts between kinetic and potential energy.

💡 Quick Concept Check:

A spring is compressed by 0.1 meters and exerts a force of 10 N. 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, $F_s = kx$: * First case: $10 \text{ N} = k \times 0.1 \text{ m} \implies k = 100 \text{ N/m}$ * Second case: $F_s = 100 \text{ N/m} \times 0.2 \text{ m} = 20 \text{ N}$ The spring constant is **100 N/m**, and it exerts **20 N** when compressed by 0.2 m.

Practice Problems

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