Impulse Physics Academy
IMPULSE VIRTUAL LABS · IGCSE

Extension of a spring

Investigate force, extension and elastic behaviour

What are we investigating?

How does the extension of a spring change when the applied force increases?

e = R − R₀

Extension is the change in length: subtract the original pointer reading R₀ from the new pointer reading R. A ruler reading by itself is not an extension.

F = mg   ·   F = ke

Convert mass from grams to kilograms before using F = mg. This simulation uses g = 10 N/kg, so 100 g produces 1 N.

k is the spring constant. Use N/cm when extension is in cm, or N/m when extension is in m. Multiply k in N/cm by 100 to obtain N/m.

Two different limits

Limit of proportionality: the end of the straight-line region. Below this, force and extension are directly proportional: Hooke’s law applies.

Elastic limit: beyond this, the spring does not return to its original length after all the load is removed.

A curved loading graph alone does not prove permanent deformation. Unload the spring and compare its final reading with R₀.

The virtual springs have an illustrative nonlinear region and permanent deformation. These thresholds are model choices, not recommended loads for real springs.

Success criteria

I can read a ruler at eye level, calculate extension and force, plot force against extension, and use a gradient to find the spring constant.

Method

  1. Use a clamp stand, spring, pointer, vertical ruler and masses. In a supervised practical, follow the teacher’s load limit and keep a suitable tray beneath the masses.
  2. Record the pointer reading with no applied load: R₀. Keep the ruler fixed throughout.
  3. Add a small known mass. Wait for the spring to settle; read at pointer level to avoid parallax.
  4. Calculate F = mg and e = R − R₀. Record both with units.
  5. Repeat for several different loads within the permitted range. Repeat readings to assess consistency.
  6. Remove masses in steps and record unloading readings. Compare the final no-load reading with the original.
  7. Plot F on the vertical axis and e on the horizontal axis. Use a large triangle on the best-fit straight line to calculate k = ΔF / Δe.

Mass accounting: the virtual connector has negligible mass; the displayed mass is the total applied mass. In a real experiment include the hanger’s mass, or clearly use the hanger-only position as a reference and measure added force and added extension consistently.

Fair test: keep the same spring, ruler position and reading method. Changing the virtual spring starts a new data set.

Add a mass to begin. Optional practice never blocks the controls.

Optional reading practice

Read the enlarged ruler. Enter the pointer reading, extension from the original reference, and applied force. You can record directly at any time after the spring settles.

Results

Each row records the same rounded ruler reading used by the calculation checker. Repeated clicks record the same observation; unload and reload for a new trial.

#Mass / gF / NR₀ / cmR / cme / cmDirectionCondition

Force against extension

Cyan: eligible linear readings. Amber: nonlinear or permanently changed spring. Circles: loading/reference; squares: unloading. Best-fit line uses eligible readings only.

Hover over the graph or tap a point to read its coordinates.

Find the spring constant

Choose two widely separated points on the fitted line. Read their coordinates from the graph, then calculate:

k = (F₂ − F₁) / (e₂ − e₁)

Use the straight section, not a line joining every point. A line close to the origin supports direct proportionality within the measured range.

Explain your findings