Helical spring and rigid stand
Provide a linear elastic restoring force with uniform coil pitch and known proportional limit.
Physics / Hooke’s law
FREE TO EXPLOREEXPERIMENT 12 · PHYSICS LABORATORY
Calibration of a helical spring and determination of the spring constant
Determine the spring stiffness constant and verify Hooke’s law of linear elasticity by measuring extension as a function of applied tensile load. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
SPRING EXTENSION Δ—
MEASUREMENT STATUS
Ready for a virtual observation.
Adjust the apparatus, then take a reading.
Readings are generated by an ideal model. The diagram is schematic and is not to scale.
Simulation assumptions and limits
The virtual apparatus simulates an ideal helical spring obeying linear Hookean elasticity with uniform wire properties. In physical laboratory experiments, spring self-mass (which contributes an effective dynamic mass), initial coil winding tension, temperature dependence of the steel’s shear modulus, and minor support flexure contribute to real-world deviations. Instrument reading quantization is modeled at 0.1 mm, matching a millimeter mirror scale. The ideal teaching model obeys Hooke’s law δ = F/k across the tested loading range. Real laboratory springs often possess initial coil tension, requiring a small threshold force before extension commences, which manifests as a non-zero horizontal intercept. Fitting extension against force yields slope m = 1/k in SI units (m N⁻¹); the spring stiffness constant is recovered from the inverse gradient k = 1/m in N m⁻¹.
Know your apparatus.
Mass hanger and calibrated slotted weights
Apply reproducible downward gravitational tensile forces in calibrated increments.
Vertical millimeter mirror scale
Measure pointer displacement accurately while eliminating optical parallax by line-of-sight reflection alignment.
Lightweight index pointer
Indicate spring elongation directly on the scale without adding significant parasitic tare mass.
FOLLOW THE METHOD
A reason behind every step.
Determine the spring stiffness constant and verify Hooke’s law of linear elasticity by measuring extension as a function of applied tensile load. Suggested independent settings: 0.5, 1.0, 1.5, 2.0, 2.5 N.
Level the apparatus and zero the pointer
Ensure the support stand is vertically upright and stable. Suspend the spring and empty mass hanger freely. Note the initial position of the index pointer against the millimeter scale as the zero reference reading.
Why this step matters
A rigid, vertical mounting prevents lateral rubbing of the spring coils against the scale and establishes an accurate baseline for all subsequent elongation measurements.
Apply the first calibrated tensile load
Carefully add a 0.50 N load (approx. 51.0 g mass) to the mass hanger. Allow any vertical bouncing or swinging motion to subside completely.
Why this step matters
Static equilibrium must be fully established so that the downward gravitational pull mg is exactly balanced by the upward elastic restoring force kδ.
Eliminate parallax and record pointer position
Position your eye so that the tip of the pointer exactly covers its reflected image in the mirror scale. Read the pointer position to the nearest 0.1 mm.
Why this step matters
A mirror scale eliminates line-of-sight perspective distortion, ensuring the recorded scale reading corresponds to the true physical horizontal position of the pointer.
Measure extension across the incremental series
Systematically increase the stretching force in steps of 0.50 N up to 2.50 N (or 3.00 N maximum). At each step, record the total applied force and the corresponding pointer position.
Why this step matters
Collecting multiple observations over an evenly spaced force range provides the data needed for a robust least-squares linear regression and residual analysis.
Perform a decremental unloading verification
Gradually remove the weights in reverse order (2.50 N down to 0.50 N, and finally zero load). Check that the pointer returns to its initial unloaded position.
Why this step matters
Verifying that the pointer returns to its initial zero reading confirms that all measurements remained safely inside the elastic limit and checks for plastic deformation.
Fit extension against force and determine stiffness
Plot extension δ on the vertical axis against force F on the horizontal axis. Compute the best-fit line δ = mF + b using ordinary least squares. The spring constant is k = 1/m.
Why this step matters
Linear regression over all data points provides a more reliable estimate than single-point ratios and allows calculation of the slope standard error.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into a result.
Points are your observations. The fit uses SI x and y values before display scaling.
LINEAR FIT · y = mx + b
δ = (1/k)F + b; k = 1/m
| # | Stretching load F (N) | Spring extension δ (mm) | Applied stretching force F (N) | Spring extension δ (mm) | Remove |
|---|
No readings yet. Take a virtual measurement and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING