Hooke’s law states that, within the elastic range, the force exerted by a spring is proportional to its extension or compression: F = k × x. This fundamental law is part of the high school physics curriculum.
Discover FizziQ
How to measure it in class
With the FizziQ app, it is possible to verify Hooke’s law and study oscillations.
Steps:
- Hang the smartphone from a vertical spring
- Measure the extension x for different added masses
- Use the accelerometer to measure the maximum acceleration during oscillations
- Calculate the restoring force F = m × a_max
- Plot F versus x and verify the proportionality
- Determine the spring constant k
Scientific activities on this topic
- Spring oscillations
- Mass-spring oscillator: period (possible extension with FizziQ)
- Damping: three regimes
Learn more
Statement of the law:
For a spring with spring constant k, the restoring force is: F = -k × x
The minus sign indicates that the force opposes the displacement (restoring force).
Range of validity:
Hooke’s law is only valid within the elastic range, that is, for deformations small enough for the spring to return to its original shape. Beyond the elastic limit, the spring deforms permanently.
Spring constant:
The constant k (in N/m) characterizes the stiffness of the spring:
- High k → stiff spring (hard to stretch)
- Low k → soft spring
Elastic energy:
The elastic potential energy stored in a spring is: E_p = ½ × k × x²
Formula
Restoring force: F = -k × x
Oscillation period (mass-spring system): T = 2π × √(m/k)
Elastic potential energy: E_p = ½ × k × x²
where:
- F: restoring force (N)
- k: spring constant (N/m)
- x: extension/compression (m)
- T: oscillation period (s)
- m: mass (kg)
Application examples
- A spring with stiffness k = 100 N/m extends by 5 cm under a force of 5 N
- Car suspensions follow (approximately) Hooke’s law
- Trampolines, spring mattresses and click pens use springs
- The smartphone’s accelerometer uses silicon micro-springs
FAQ
Q: How to measure k with FizziQ? A: Hang different masses and measure the extension. k = F/x = mg/x. Or measure the oscillation period: k = 4π²m/T².
Q: Why does the spring eventually break if pulled too much? A: Beyond the elastic limit, the atomic bonds in the metal are permanently broken. Hooke’s law is no longer valid.
Q: Does the law apply to compression? A: Yes, for a helical spring. The formula is the same with negative x (compression).
Q: What happens when springs are combined? A: In series: 1/k_eq = 1/k₁ + 1/k₂ (softer). In parallel: k_eq = k₁ + k₂ (stiffer).
Related concepts
Harmonic Oscillator - Elastic Energy - Period