Hooke's Law Intro and data processing
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Introduction
Natalie Satterfield
February 14, 2012
Hooke's Law Lab
Introduction
In this lab, the spring constant within a specific spring will be calculated using a ruler and force sensor to measure the length of a spring and the force exerted by the spring at that length.
According to Hooke's Law, we know that the extension of a spring (x) is proportional to the force it exerts by the equation:
F = kx
Various forces will be measured according to their corresponding lengths and the data will be graphed on a force vs. extension graph to determine the spring constant for the particular spring used. The slope of the force vs. extension graph is equal to the spring constant, k.
y = mx + b
F = kx
m = k
b = 0 (at 0 extension, force is 0)
DATA COLLECTION AND PROCESSING
Raw Data:
Middle
7.85
1.210
1.259
1.300
3.85
8.85
1.600
1.564
1.533
3.85
9.85
1.769
1.842
1.822
Processed Data:
Extension of the Spring and the Average Force Exerted | ||
Extension x (cm) ∆x = ± 0.1 cm | Average Force F (N) ∆F = ± 0.001 N | Average Force Uncertainties F (N) |
0.0 | 0.000 | 0.001 |
1.0 | 0.480 | 0.02 |
2.0 | 0.709 | 0.02 |
3.0 | 0.989 | 0.004 |
4.0 | 1.256 | 0.05 |
5.0 | 1.566 | 0.03 |
6.0 | 1.811 | 0.04 |
Sample Calculations:
Extension:
= (Length After Extension) - (Length Before Extension)
= 4.85 - 3.85
= 1.0 cm
Extension Uncertainty:
= Length After Extension Uncertainty + Length Before Extension Uncertainty
= 0.05 + 0.05
= 0.1 cm
Average Force:
= (Trial 1 Force + Trial 2 Force + Trial 3 Force) / 3
= (0.490 + 0.458 + 0.491) / 3
= 0.480 N
Conclusion
Improvements:
Ultimately, to improve the weaknesses, limitations, and possible errors listed above a few courses of action would have had to be taken.
First, zeroing the force sensor and ensuring that the force sensor was zeroed before collecting data for all new spring lengths could have gotten rid of the systematic error present within the results and would have allowed the linear regression line to pass through the origin as expected.
Similarly, setting up the equipment so that the spring had to be stretched out on a flat surface, and not while in the air, could have allowed the spring to be held more steadily while taking measurements. Also, clamping the ruler down onto a flat surface instead of, also, holding it up in the air by hand could have, again, lowered the random errors that occurred because of the weaknesses collecting the data for the extension of the spring.
Ultimately, making these improvements could have lowered the random and systematic errors that existed, thus making the data more accurate and precise. This, in turn, could have reduced the anomalous data and created results that more thoroughly portrayed what was expected.
This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.
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