Young's Modulus Experiment Notes

Young's Modulus Determination

Introduction to Young's Modulus

• Definition: Young's modulus is a measure of the stiffness of a solid material and is defined as the ratio of tensile stress to tensile strain within the limits of proportionality.

Apparatus Required

• Measurement Tools:
  • Tape measure/metre rule
  • Micrometer screw gauge
• Wires:
  • Test wire (wire Q) and comparison wire (wire P) made from the same material.

Procedure for Determining Young's Modulus

1. Measure Length and Diameter:

   • Using a tape measure/metre rule, measure the length, $l$, of wire Q (test wire).
   • Measure the diameter, $d$, of wire Q using a micrometer screw gauge.

2. Setup:

   • Suspend both wires P and Q from a common support as illustrated in Fig 1.

3. Loading:

   • Attach a fixed mass on wire P (comparison wire).
   • Vary the load, denoted by $F$, on wire Q (test wire).
   • Measure the resulting extensions, denoted by $e$, produced in wire Q using a vernier arrangement between wires P and Q.

Data Analysis

• Graphing:

  • Plot a graph of load $F$ against extension $e$.
  • If the limit of proportionality is not exceeded, the graph will show a straight line demonstrating Hooke's Law.

• Calculating the Gradient:

  • Determine the gradient of the graph.
  • Young's modulus $E$ can be calculated using the relationship:
    $E = \frac{F}{e}$
    (Exact formula dependent on both stress and strain definitions should be specified as required)

• For Increased Accuracy:

  • Gradually unload wire Q and make new measurements of corresponding extensions.
  • Calculate mean extensions and use these values to refine the graph plot.

Notes on Error Minimization

• Comparison Wire Usage:

  • Serving as a reference standard, the calibration eliminates systematic errors due to:
    i. Expansion from temperature changes.
    ii. Sagging of the support structure.

• Diameter Measurement Considerations:

  • Measure the diameter of wire Q at three different points in different orientations to minimize errors due to:
    i. Ovality of the wire.
    ii. Unevenness in the wire’s cross section.

• Wire Characteristics:

  • Long Wire:
    • Allows for measurable extension to be produced.
  • Thin Wire:
    • Enables a large tensile strain from a small load.