How to Find Young's Modulus for Copper Wire

Set-up and Data Collection

• 1

  Measure the thickness of the copper wire using the micrometer. Record the diameter of the wire in your lab notebook. Measure the diameter at least five points along the length of wire to obtain a representative average diameter.

• 2

  Mount a pulley on the side of a table near the end.

• 3

  Cut a piece of wire 2-meters long and clamp one end on the table 1.5 meters back from the pulley using the G-clamp. Run the wire over the pulley and allow it to hang toward the floor.

• 4

  Place some newspaper on the floor below the pulley.

• 5

  Attach a weight hanger to the end of the wire. Affix a white label at the end of the piece of wire.

• 6

  Place a meter stick next to the end of the wire. Use the label on the wire to find the length of the wire. The elongation of the wire during the experiment can be found by measurements of the movement of the end of the label.

• 7

  Place a 100g weight onto the weight hanger and record the weight and distance of movement.

• 8

  Remove the weights each time you complete recording the weight, to see if the wire returns to its original length.

• 9

  Continue adding weights and recording the data for each newly added weight until the wire breaks. Each time you add weights, place them gently on the hanger.

Calculations

• 10

  Calculate the average thickness of the copper wire based on the five measurements you took. For example, assume you collected the following thickness measurements for the copper wire at five different points along the length of the wire: 2.13, 1.96, 2.07, 2.20 and 2.17 microns. Sum the five measurements and divide by five to yield the average diameter of the copper wire. The average diameter is 2.106 micrometers. Convert micrometers to meters by using 1 micrometer equals 1 x 10^-6 meters. The average diameter of the copper wire is 2.106 x 10^-6 meters.

• 11

  Calculate the cross-sectional area of the copper wire using the geometric formula, area = pi * radius^2. Use radius equals 1/2 of the diameter. r = d / 2 = 2.106 x 10^-6 / 2 = 1.053 x 10^-6 meter. Calculate the area of the end of the copper wire, A = pi * r^2 = pi * (1.053 x 10^-6)^2 = pi * 1.109 x 10^-12 = 3.48 x 10^-12 meter^2. The area of the end of the wire is the cross-sectional area.

• 12

  Find the stress on the copper wire using stress = F * area. The F = 100g * number of weights * gravity. For example, the force associated with the fifth weight hanging from the wire is equal to, F = 5 * 100g * 9.8 m sec^2. Force uses units of Newton, which are kg/m^2. Convert the weight to kg and solve for the force. 100g = 0.1 kg. F = 5 * 0.1 * 9.8 = 4.9 N/m^2.

• 13

  Find the strain on the wire using strain = x / L, where x is the stretching of the wire and L is the original length of the wire. For example, assume that after placing five 100g weights on the hanger, the wire length measured 1.16 m with an original length of 1.15 m. Strain = .01 / 1.15 = 8.7 x 10^-3.

• 14

  Calculate Young's Modulus by dividing the stress by the strain. For example, at the point where added weight is 0.5 kg the stress is 4.9 and the strain is 8.7 x 10^-3. Young's Modulus = stress / strain = 4.9 / 8.7 x 10^-3 = 563.21 N/m^2. The best value for Young's Modulus is found by plotting stress versus strain for all the data points and calculating the slope of the resulting best-fit line.