2.00E+08 2.50E+08 3.00E+08 3.50E+08 4.00E+08 f(x) = 287527461001.53x - 36951537.42 Stress vs Strain Graph 2 Strain Stress (N/m) F = mg = (1 kg)*(9.8m/s 2 ) = 9.80 N ΔL = L 2 – L 1 = 7.61 mm – 7.42 mm = .19 mm
Strain = ΔL / L = .19 mm / 680 mm = 2.79 x 10 -4 Stress = F / A = 9.80 N / 2.12 x 10 -7 m 2 = 4.62 x 10 7 Discussion: 1. When the elastic limit is not exceeded, the deformation is recoverable so comparing both cases of increasing and decreasing the hanging weights, the strain should be the same for the same stress. That is the Young’s Modulus should be the same for both cases. Do you observe this? a. Yes, when you increase and decrease the weights, Young’s Modulus remains the same for both cases. When you look at the graphs, you can see that they are inverses of each other. 2. In your plot, how well the data point falls in a straight line? What would be the factors that cause the deviation from the straight line? a. The points did not fall in a perfectly straight line. This error could have been caused because of human error and/ or because of equipment not being accurate or calibrated. 3. If the wire in your apparatus is replaced with one twice as thick, which of the following would change when you add the first kilogram, and how: ΔL, F, stress, strain, and value of Young’s Modulus? a. If the wire is replaced with one that is two times as thick, stress would be half as much as it is originally. The new value of Young’s Modulus would also be half its original value because stress and area are inversely proportional. Also, because you would be dividing double the amount you were before. In total: stress, strain, and Young’s Modulus would all change. 4. Does is make any significant difference whether you measure the diameter and the length of the wire at the beginning (with only 1 kg), or when there are 7 kg total loaded on the hook? a. Yes, it does matter because the added weight on the wire could cause it to stretch. The wire could also decrease in diameter if enough weight is added due the wire being stretched and pulled. Conclusion: In conclusion, we learned how to find Young’s Modulus. We were able to get it by graphing stress vs strain and finding the slope. We also learned that stress and strain are proportional to each other during this experiment.
- Spring '17