Hooke's law describes how many springs respond when they are stretched or compressed. It says that the restoring force from a spring is proportional to the displacement from equilibrium. This idea matters because springs appear in scales, car suspensions, trampolines, clocks, and many measuring devices.
Learning this law helps connect forces, motion, energy, and graph interpretation.
Key Facts
- Hooke's law: F = -kx, where F is restoring force, k is spring constant, and x is displacement from equilibrium.
- The negative sign in F = -kx means the spring force acts opposite to the displacement.
- Spring force magnitude: |F| = k|x|.
- For a hanging mass at rest: mg = kx, so x = mg/k.
- Elastic potential energy stored in a spring: U = 1/2 kx^2.
- On a force versus extension graph, the slope in the linear region is the spring constant: k = ΔF/Δx.
Vocabulary
- Hooke's law
- Hooke's law states that a spring's restoring force is proportional to its displacement from equilibrium within the elastic limit.
- Spring constant
- The spring constant k measures how stiff a spring is and has units of newtons per meter.
- Restoring force
- A restoring force is a force that acts to bring an object back toward its equilibrium position.
- Equilibrium position
- The equilibrium position is the position where the net force on the spring mass system is zero.
- Elastic limit
- The elastic limit is the maximum stretch or compression after which a spring no longer returns to its original shape.
Common Mistakes to Avoid
- Ignoring the negative sign in F = -kx, which is wrong because the sign shows that the spring force points opposite the displacement.
- Confusing mass and weight, which is wrong because a hanging mass pulls with weight mg, not just m.
- Using centimeters instead of meters in calculations, which is wrong because the SI unit for k in F = kx is newtons per meter.
- Applying Hooke's law beyond the elastic limit, which is wrong because the force extension relationship may stop being linear after permanent deformation begins.
Practice Questions
- 1 A spring with k = 200 N/m is stretched by 0.050 m. What is the magnitude of the restoring force?
- 2 A 0.50 kg mass hangs at rest from a vertical spring and stretches it by 0.10 m. Using g = 9.8 m/s^2, find the spring constant.
- 3 A force extension graph is linear at first and then begins to curve upward after a large extension. Explain what the straight part and curved part tell you about the spring's behavior.