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Errors and Uncertainty, Lab Report Example

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Lab Report

Introduction

In experimental science, there is always some amount of uncertainty. Sometimes this uncertainty is resultant of experimental error. In this experiment researchers investigate the impact and sources of such errors. In essence, there are two types of errors. Systematic errors which are the result of the way the experiment is conducted, and random errors which result from natural conditions measurement. These concepts are explored through a simple beam bending experiment.

Theory

Young’s modulus is a method of calculating the load produced on a bending beam. The following figure illustrates the principle.

the principle

The formula to derive Young’s modulus is:

The formula to derive Young’s modulus

Where, F is the load. X is the distance between the support and deflection. L is the distance from the point of application and the support. E is Young’s modulus, and I is the measures of the cross section of the beam as illustrated below.

the cross section of the beam

In other words, the amount of deflection may be expressed as the length of the beam times itself times the load times the difference between 3 times the length from the point of deflection minus the total length over 6 times Young’s modulus times the width times height cubed. Because E is a known constant we can reasonably assume that one measuring device will demonstrate to be more precise than the other.

Methods

The experiment started with s setup of the apparatus. Once the beam was clamp to a frame, it was ready to receive loads. The moment of deflection is measure simultaneously with as potentiometer and point gauge. Then, critical measurements of the beam were made, and an estimate of error conducted. A prediction of the variation of F produces on the result was made. The gauge and potentiometer were zeroed, and 9 loads were added to the end of the beam to produce the deflection. After each load was added readings from the potentiometer and the gauge were recorded. Then, they were unloaded to ready the apparatus fro the next repetition. A total of six repetitions were conducted. From these data points, statistical analysis will reveal which method of measure is more precise based on standard error. Experimenters predict that the dial will be more precise than the potentiometer.

Results

Which data set is most suitable to represent Young’s modulus? The answer may be calculated using the sum of least squares.

Least squares best fit

While the slope and standard error of the slope are found in each set, we may calculate E.

Calculating the mean of means helps calculate the standard error.

Calculating

This allows us to estimate the impact of the average impact of the error.

Finally, graphs of the data sets are illustrated.

Discussion

Are the results expected? If not, why not? I did not expect the errors to be so low. It appears the devices are much more precise than I thought. The theoretical results and the experimental results agree both qualitatively and quantitatively. The only real improvement I can think of is to use devices and materials that are newer. This could resduce the error. Also, collecting more data would help. For example, if the entire classe pooled their observations together.
Conclusion

The aim of this experimental was to explore experimental error in a beam deflection test. It was found that near-similar procedures could produce differing results. What we found was basically a linear relationship between the loads and the measures. The average was +/- 27.25 N/m^2. This error may be explained in a number of ways. Tensile strength could vary as the increase temperature produced by bending occurs. Also, the variation in measuring devises and loads could produce a certain amount of error. Also, a perception of the experimenters observing the data is always possible. Nevertheless, the variation is often manageable with the application of statistical principles.

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