Calculations, Graphs and Error Analysis
Any error in the calculations would be mostly from human error. Since both the springs and the rubber bands total stretch distance was guestimated, the values are likely to be obscured. Also, the readings may have been read incorrectly, or typed wrong into the computer. This also may have contributed error to the lab. The graphs showed that stretch increased with force, as to be expected. All of the graphs were fairly linear, with not too much curve to them. The graph of spring 1, showed quite a bit of waver, most likely indicating error. Error over all probably contributed quite a bit to this lab. Human error is largely expected from the measurements and guestimations of the springs and rubber band. Also, some confusion came up from the directions in calculating the potential energy. The used k values are listed in the data tables, however, since the k was supposed to be found in the steps after this section, it was questionable which value was to truly be used.
y
=
25.282x
-‐
0.4492
R²
=
0.98803
0
0.5
1
1.5
2
0
0.02
0.04
0.06
0.08
0.1
Force
(N)
Stretch
(m)
Stretch
vs.
Force
93
The rubber band did not seem to follow expectations of the lab. The rubber band had a graph nearly as linear as the others. It only has a slight curve. The rubber band used was old, very stretchy, and very small. This may have altered data, but it was the only appropriate rubber band in the household. All others were far too large.
Discussion, Results, and Conclusion
- A. How does the relative stiffness of a spring relate to its spring constant?
- The stiffer the spring the greater the spring constant is.
B. How does PE change relative to the stretch of the spring?
o PE increases as the stretch increases.
C. Indicate on your graph for the rubber band where the linear behavior stops. What does this mean?
o This should be where the rubber band has maxed out on the distance it can be stretched, but since it has more flexibility than a spring, it can still ever so slightly increase, so the graph should round out.
D. Which is stronger in the region where Hooke’s law is obeyed, the spring or the rubber band?
Explain.
o The spring should follow Hooke’s law the best. The rubber band is a hyper-elastic material and is expected to only experimentally follow Hooke’s law for a limited range.
E. Explain what happens to the “spring constant” of the rubber band for the nonlinear part of your curve.
o The spring constant stops increasing proportionally to the stretch distance. The rubber band stops obeying Hooke’s law.
Results
The spring constants were as follows for spring one 46.53 N/m, for spring two 43.69 N/m, and for the rubber band 25.28 N/m.
Conclusion
Overall the objective of the lab, to investigate Hooke’s law and to determine the spring constant for two springs and a rubber band, was met. In the lab, spring one had a calculated constant of 46.53 N/m, spring two had a calculated constant of 43.60 N/m, and the rubber band had a calculated constant of 25.28 N/m. Hooke’s law was seen to be obeyed most directly by the springs, but not as much by the rubber band. During the lab, it was also found that potential energy increases as the string stretch 94 distance was increased. Human error was probably the largest factor of error in this lab. Different estimations introduced large likely hood of error into both the measurements and calculations from those measurements. However, the lab was still completed smoothly.
