Youngs Modulus of the material - searles apparatus method

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Elastica Lab

Young's Modulus · Searle's Method

Laboratory Instruments Graphs Data

Undergraduate Physics · Elasticity

Stretch a wire.
Watch stiffness reveal itself.

A full digital re-creation of the Searle's apparatus experiment — load a wire, measure its diameter under a micrometer, read its extension through a travelling microscope, and watch Young's modulus emerge from real measurement, not a lookup table.

SVG apparatus Live Hooke's-law physics Stress–strain plotting Atomic-scale model

The governing formula

Y = F · LA · ΔL

F — applied force (N)

L — original length (m)

A — cross-section area (m²)

ΔL — extension (m)

Before you begin

Aim & theory

To determine the Young's modulus of the material of a given wire by Searle's method, and to study how stress relates to strain across the elastic and plastic regimes.

01

Learning objectives

Operate a micrometer screw gauge and travelling microscope with correct zero-error correction; apply Hooke's law to a real loaded wire; distinguish elastic from plastic deformation; quantify measurement uncertainty.

02

Theory summary

Within the elastic limit, stress is proportional to strain. The constant of proportionality — Young's modulus, Y — characterises a material's stiffness. Beyond the yield point, deformation becomes permanent; beyond the ultimate tensile strength, the wire necks and fractures.

03

Apparatus

Rigid support frame, experimental and reference wires, weight hanger with slotted weights, vernier pointer, travelling microscope, micrometer screw gauge, and a metre scale for measuring original wire length.

Step 1

Choose a wire material

Each material carries its own engineering properties — Young's modulus, density, and elastic limit — pulled from realistic reference values. Switching materials live-updates every downstream simulation.

Step 2

The virtual laboratory

Drag slotted weights onto the hanger. The wire elongates according to Hooke's law for the selected material — there are no scripted values, every extension is computed live.

Slotted weights — drag to hanger

Live readout

Total load0.000 kg

Force, F0.000 N

Extension, ΔL0.000 mm

Stress, σ0.00 MPa

Strain, ε0.000000

StateElastic

Step 3

Take your measurements

Before the experiment can proceed, measure the unloaded wire's diameter with the micrometer screw gauge, then confirm your reading. The actual diameter is randomised each session.

Micrometer screw gauge

Pitch = 0.5 mm, 50 divisions on the circular scale → least count = 0.5/50 = 0.01 mm. Rotate the thimble to close the jaws on the wire.

Thimble

Zero error

Main scale: 0.00 mm  +  Circular: 0.00 mm
Observed reading: 0.000 mm  |  Zero error: 0.00 mm
Corrected diameter: 0.000 mm

Travelling microscope

Vernier: 20 divisions = 0.95 cm of main scale → least count = 0.005 cm = 0.05 mm. Used to track the pointer's vertical position as the wire stretches.

Coarse

Fine

Parallax err.

Cross-wire position: 0.000 mm
True pointer position: 0.000 mm
Measurement error: 0.000 mm

Step 4

Live calculation, expanded

Every figure below is recomputed the instant a weight is added or removed, or a slider is moved.

Cross-sectional area, A —

A = πr², where r is half the corrected micrometer diameter.

A = π × (d/2)² = —

Force, F —

F = mg, the weight of the total suspended load.

F = m × 9.81 = —

Stress, σ —

σ = F / A — force per unit cross-sectional area.

σ = F ÷ A = —

Strain, ε —

ε = ΔL / L — fractional change in length.

ε = ΔL ÷ L = —

Young's modulus, Y —

Y = σ / ε = FL / (AΔL), valid while the wire remains within its elastic limit.

Y = σ ÷ ε = —

% error vs reference Y = —

Percentage elongation —

% elongation = (ΔL / L) × 100 = —

Reference

Formula explorer

Click any variable to see what it means, its SI unit, and how it's physically measured in this apparatus.

Y = F L / AΔL

Click a variable above to learn about it.

Microscopic view

Atomic-scale deformation

Synchronised with the applied load: as stress rises, atomic bonds stretch elastically, then yield permanently, neck, and finally fracture.

Step 5

Stress–strain curve

Built live from your loading history. Scroll to zoom, drag to pan, hover for tooltips.

Reference data

Material comparison

Switch the active material above to see every simulation update; this table lets you compare all five at a glance.

Material	Young's modulus (GPa)	Density (kg/m³)	Elastic limit (MPa)	Tensile strength (MPa)	Typical use

Extension

Temperature effects

Heating the wire causes thermal expansion, lengthening it before any load is even applied — this shifts the apparent stress and strain readings.

Wire temperature

25 °C

Linear thermal expansion coefficient applied per material.

Recalculated values

Thermal ΔL0.000 mm

New wire length—

Adjusted stress—

Adjusted strain—

Uncertainty

Error simulation

Dial in realistic sources of experimental uncertainty and see how they propagate into your final result.

Sources

Least count

Parallax

Random

Zero error

Human reading

Propagated uncertainty

Combined ΔY/Y0.0 %

Corrected Y—

Uncertainty range—

Step 6

Observation table

Every load application is logged here automatically. Cells are editable for manual correction; export or print when finished.

#	Load (kg)	F (N)	d (mm)	A (mm²)	L₀ (mm)	L (mm)	ΔL (mm)	σ (MPa)	ε	Y (GPa)

Step 7

Graphing module

Choose a relationship to plot from the logged observation data, complete with a best-fit regression line.

Best fit: —

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