Hooke's Law: Spring Constant

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

School· 25 min·Related simulator: Classical MechanicsSpring-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 (horizontal schematic)
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

Read the theory: you will vary the applied force F on the horizontal spring with the slider.
Choose a force and press “Record measurement”. The simulator reads the extension x (small sensor noise).
Repeat for at least 6 different forces spread across the range — avoid clustering all points at one end.
Inspect the linear fit of F vs x: the slope equals k.
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).

Applied force F (load)F = 8.00 N

Ideal extension: x_ideal = 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.

Uncertainty

Instrument uncertainty (simple propagation)

Estimate Δx (extension sensor)

±0.00050 m

Estimate ΔF (force reading)

±0.08 N

For each row, treat k ≈ F/x. Independent first-order errors give δk/k ≈ √((ΔF/F)² + (Δx/x)²). Values below use your sliders.

Take measurements to estimate propagated uncertainty.

Pointwise k = F/x is for intuition; your linear fit of F vs x uses all points (see regression σ on the result card).

Lab report

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

One click opens the print dialog — choose “Save as PDF”.

Hooke's Law: Spring Constant

Generated: 28 May 2026, 02:01

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.