Young's Modulus
Author: Jacob Hoffner
Lab Partners: Zach Christoff and Alyssa Jordan
Date: April 2016
Lab Partners: Zach Christoff and Alyssa Jordan
Date: April 2016
Purpose
To investigate the tensile strength and elasticity in a metal (brass) wire.
Theory
We are to find Young's Modulus, E. In order to do so, we must discover the stress and strain of the material being used. The stress and strain will be used in a stress vs. strain graph, and the slope of this line will be E, Young's Modulus. In order to determine the Tensile Strength of the brass material being measured, we must find what maximum mass the brass wire can bear before fracture. The graph to the right indicates a sample of a stress vs. strain graph and how a material being measured for Young's Modulus would act upon such conditions.
In this lab, we will be using an optical lever to discover out measurements. A laser reflecting off of a chuck bearing the brass wire will indicate the change in length, delta l, by augmenting the minuscule changes in the wire. Two similar triangles will be used. The length from the cylindrical chuck to the ruler where the laser beam is in one triangle related to the change in position of the laser beam is one triangle. The second triangle will be the radius of the chuck in relation to the length created at the edge of the chuck by the change in position, which will be twice the change in l. Stress and StrainStress and Strain must be found in order to find Young's Modulus.
Stress is the overall crosssectional area found on the wire. Stress is Force over Area, while Area is based on the wire's cylindrical shape. The Force will be applied by a hanging mass. Strain is the change in length of the wire in relation to the initial length in the wire. The change in length will be determined using the proportional equation found using the FBD. This quantity will be substituted into this strain equation:

Tensile Strength and Young's ModulusTensile Strength (Ultimate Strength) will also be determined by the Force over the Area, however the Force is determined by the maximum amount of Force used on the system, or the maximum mass multiplied by gravity.
Tensile Strength
Young's Modulus is then defined by the slope of the line of a graph comparing stress to strain, as E equals stress over strain (rise over run).

Experimental Technique
In order to measure Young's modulus, we must first do initial testing on the wire material of choice to find how much weight the material can bear. I used brass wire. The setup of this lab consisted of a stand holding a wire hanger at the top and a mass holder hanging from the wire at the bottom. This setup was used to find out how much weight the wire can hold before fracture by placing masses on the mass holder in increments.
Then, the wire was wrapped around the chuck bearing the mirror used to reflect the laser for the optical lever. A laser was positioned at the far end of the table away from the apparatus. The laser stand has a ruler facing the wire stand. The laser was pointed at the chuck's mirror, and the laser was reflected back onto the ruler next to the laser. The subtle changes in the wire will move the cylindrical chuck, therefore moving the mirror and laser beam. The optical lever created allow us to see the laser move on the ruler with every increment of weight added to the mass holder, and ultimately the wire.
The information collected, along with the measurements of distances everything is from each other, will be used to create a strain vs. stress graph to determine Young's Modulus. Using the information in the theory section, we will construct a chart showing the values found in the brass wire tested. The chart will be converted to a graph, where the information found and the slope of the graph's line will find our ultimate answer.
Then, the wire was wrapped around the chuck bearing the mirror used to reflect the laser for the optical lever. A laser was positioned at the far end of the table away from the apparatus. The laser stand has a ruler facing the wire stand. The laser was pointed at the chuck's mirror, and the laser was reflected back onto the ruler next to the laser. The subtle changes in the wire will move the cylindrical chuck, therefore moving the mirror and laser beam. The optical lever created allow us to see the laser move on the ruler with every increment of weight added to the mass holder, and ultimately the wire.
The information collected, along with the measurements of distances everything is from each other, will be used to create a strain vs. stress graph to determine Young's Modulus. Using the information in the theory section, we will construct a chart showing the values found in the brass wire tested. The chart will be converted to a graph, where the information found and the slope of the graph's line will find our ultimate answer.
Micrometer used to find width of brass wire.
Data
Below are the data for finding the measurements of the lab:
Analysis
Below are the sample calculations of stress, strain, tensile strength, and the percent error:
Based on the graph, we can compare our Young's Modulus, E, to the accepted value, and then find Percent Error.
Conclusion
In this lab, we were to investigate the elasticity and tensile strength of a brass wire. This lab included much percent error, as some measurements were arduous to keep consistent and accurate. Parallax error could be an issue to due our line of sight of the laser beam. The constant stretching and unstretching of the wire could have made the wire more brittle and altered the position of the optical lever. Each measurement made could have been at different intervals from the last due to how much the wire has stretched in that amount of time. After finding Young's Modulus, I have discovered a 80% error from the accepted value. It was hard to find the exact breaking point of the brass wire, as shown by the percent error in the Tensile Strength value found of 324%. Although we achieved breaking the brass wire, we have much percent error to consider. Overall, the lab was successful in discovering the stress and strain relationship in the brass wire, which led to our overall completion of the lab.
References
Giancoli, Douglas C. "Static Equilibrium; Elasticity and Fracture." Physics for Scientists & Engineers with Modern Physics. 4th ed. Upper Saddle River, NJ: Prentice Hall, 2000. Print.
Bowman, D. (n.d.). Lahs Physics. Retrieved October 1, 2015, from http://lahsphysics.weebly.com/
Bowman, D. (2015, October 1). Chapter 12: Static Equilibrium; Elasticity and Fracture. Lecture presented at Physics, Lehighton.
Bowman, D. (n.d.). Lahs Physics. Retrieved October 1, 2015, from http://lahsphysics.weebly.com/
Bowman, D. (2015, October 1). Chapter 12: Static Equilibrium; Elasticity and Fracture. Lecture presented at Physics, Lehighton.