Hooke's Law: Spring Constant

Apply known forces to a vertical spring; measure extension x, linear fit F vs x, read stiffness k.

Beginner· 25 min·Related simulator: Spring-Mass System

Goal

Determine the spring constant k using Hooke’s law F = k·x by recording force and extension pairs and fitting F versus x.

Equipment

  • Coil spring (vertical)
  • Calibrated force scale (slider)
  • Extension sensor (simulated)

Theory

For an ideal coil spring within its elastic region, restoring force scales linearly with displacement from equilibrium: F = k·x. A plot of applied force versus extension passes through the origin with slope equal to k.

Procedure

  1. Read the theory: you will vary the hanging load (applied force F) with the slider.
  2. Choose a force and press “Record measurement”. The simulator reads the extension x (small sensor noise).
  3. Repeat for at least 6 different forces spread across the range — avoid clustering all points at one end.
  4. Inspect the linear fit of F vs x: the slope equals k.
  5. Compare your k with the reference value shown in the result card and write the conclusion.

Experiment

Ideal spring model: extension x = F/k (noise only on sensor reading).

Ideal extension: xideal = F/k ≈ 0.1538 m

Cover a wide span of forces (several distinct values). The fit uses F on the vertical axis versus x.

Measurements

Extension x
m
Force F
N
No measurements yet — take your first reading.

Data processing

Add at least 2 measurements to compute the fit.

Lab report

Opens the system print dialog — choose “Save as PDF” or your printer. Header and footer are hidden when printing.

Hooke's Law: Spring Constant

Generated: 21 Apr 2026, 18:27

Goal

Determine the spring constant k using Hooke’s law F = k·x by recording force and extension pairs and fitting F versus x.

Measurement table

#Extension x (m)Force F (N)
No measurements yet — take your first reading.

Fit and derived value

Add at least 2 measurements to compute the fit.

Conclusion

The fitted spring constant agrees with the reference stiffness within tolerance. Main error sources: finite number of load steps, sensor noise on x, and assuming a perfectly linear spring.

PhysSandbox virtual lab — values come from your session; add your own discussion of error sources.

Conclusion

The fitted spring constant agrees with the reference stiffness within tolerance. Main error sources: finite number of load steps, sensor noise on x, and assuming a perfectly linear spring.