Wire and rigid support
Provide a straight specimen with a defined 2.000 m gauge length and a secure upper clamp.
Physics / Young’s modulus
FREE TO EXPLOREEXPERIMENT 04 · PHYSICS LABORATORY
Young’s modulus of a wire
Determine the Young modulus of a wire from its extension under a series of increasing tensile forces, and interpret the gradient of an extension–force graph. Explore a virtual apparatus, collect readings and analyse a graph.
CHANGE · OBSERVE · MEASURE
Your virtual workbench.
WIRE 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
This is an ideal, uniform circular wire with constant modulus and small deformation. Added force is measured from a reference state; wire weight, support motion, creep, temperature change, calibration errors and plasticity are not modeled. The extension drawing is exaggerated for visibility. Perfect simulated readings demonstrate the equation and do not establish the uncertainty achievable with physical equipment. Fit scatter alone is not a complete uncertainty budget. The unknown model modulus is 200 GPa. A light initial preload defines the reference length; F and δ are additional increments relative to that reference. All loads stay in the linear elastic regime. The diagram exaggerates extension. Creep, temperature drift, backlash and plastic deformation are omitted.
Know your apparatus.
Load system or calibrated force gauge
Apply additional tensile force from 2 to 20 N in controlled increments.
Micrometer screw gauge
Measure the small diameter at several positions and orientations before calculating cross-sectional area.
Extension indicator and length scale
Record the initial gauge length and changes in length relative to a fixed reference.
FOLLOW THE METHOD
A reason behind every step.
Determine the Young modulus of a wire from its extension under a series of increasing tensile forces, and interpret the gradient of an extension–force graph. Suggested independent settings: 2, 6, 10, 14, 18 N.
Inspect and define the specimen
Check the clamp, identify the fixed gauge endpoints, and record the 2.000 m gauge length. Note that the animation exaggerates extension.
Why this step matters
The length in the calculation must correspond to the length whose extension is measured.
Measure the diameter
Check micrometer zero, measure at several positions in two orientations, and record a representative mean diameter. Use 0.500 mm for the virtual specimen.
Why this step matters
The circular cross-sectional area is calculated from diameter squared.
Set the reference
Straighten the wire with the setup tension and establish the extension reference. Treat displayed force as added force relative to that reference.
Why this step matters
Slack removal and a defined baseline prevent apparent extension from being confused with tensile deformation.
Increase force in steps
Select an added force of 2 N, allow settling, and record extension. Repeat at 4, 6, 8 and 10 N or continue through the allowed 20 N range.
Why this step matters
Several well-separated readings reveal the proportional relation and support a gradient estimate.
Check repeatability
Revisit one load and then remove the added load. In a real lab, record unloading readings and inspect for slip, drift or residual extension.
Why this step matters
Agreement checks whether the chosen linear model remains appropriate and the reference is stable.
Fit and calculate
Plot extension against added force, obtain the gradient, convert it to m/N, calculate A = πd²/4 and then Y = L/(As). Report Y in GPa with the model assumptions.
Why this step matters
A fitted gradient uses the whole set of observations and keeps the connection between the graph and the material property explicit.
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 = mF + b; Y = L₀/(Am)
| # | Incremental tensile force F (N) | Wire extension δ (mm) | Force F (N) | Extension δ (mm) | Remove |
|---|
No readings yet. Take a virtual measurement and record it.
Calculate it yourself.
CHECK YOUR UNDERSTANDING