Young's Modulus of a Wire

Aim: To investigate how to obtain a reliable value for the stiffness of the wire from a series of loads.

Load the Wire

Masses on hanger: 0 × 1.0 kg

Each slotted mass is 1.0 kg. The empty hanger just keeps the wire taut — its weight is negligible.

Micrometer — Wire Diameter

Read the sleeve and thimble scales while the jaws are closed on the wire. Release the button to open the jaws again.

Wire Measurements

Diameter, d (mm) Original length, L (m)

Results Table

# Load (kg) Force, F (N) Extension, x (mm) Stress (Pa) Strain Clear row

Aim: To investigate how to obtain a reliable value for the stiffness of the wire from a series of loads.

Part A — Does the wire stretch, and does it recover?

  1. With no masses on the hanger, note where the marker sits on the magnified scale.
  2. Add four masses one at a time, watching the magnified view. Does the marker move by a measurable amount for each 1.0 kg added?
  3. Remove all four masses. Does the marker return exactly to its starting position? What does that suggest about the type of deformation over this range of loads?

Part B — What does the extension depend on?

  1. Load the wire from 1.0 kg to 8.0 kg in 1.0 kg steps. At each step, read the extension to the nearest 0.1 mm and record the load and extension in the results table.
  2. Now unload in 1.0 kg steps, reading the scale again at each load. Do the unloading readings match your loading readings? Why is checking this worth the extra time?
  3. Plot extension against load on graph paper. What shape is your graph, and what does that tell you about how the extension depends on the load?

Part C — Finding the Young modulus (on paper)

  1. Hold the micrometer closed on the wire five separate times, recording the diameter each time. Find the mean and enter it, with the original length from the bench label, in the wire-measurements table.
  2. For each load, calculate the force pulling on the wire (g = 10 N/kg) and enter it in the results table.
  3. Use your mean diameter to find the cross-sectional area of the wire, then calculate the stress and the strain for each load. Watch your unit conversions — the scale reads millimetres.
  4. Plot stress against strain and draw the best-fit straight line through your points. Find its gradient. What physical quantity have you just measured, and what are its units?

Part D — Which measurement limits your result?

  1. Look back at your five diameter readings. Estimate the uncertainty in the diameter and express it as a percentage of the mean.
  2. Estimate the uncertainty in a single extension reading from the magnified scale, and express it as a percentage of your smallest and of your largest extension.
  3. When you calculated the cross-sectional area, how many times did the diameter enter the calculation? What does that do to its percentage uncertainty in the final result?
  4. Which single measurement contributes the largest uncertainty to your value of the Young modulus? What piece of equipment, or change of technique, would reduce it?