Experimental Uncertainty and Error Analysis

Abstract

The diameter and mass of a steel ball was measured and recorded by the class. These measurements were to determine error in measurements and the derived quantities, volume and density. The diameter was determined using a dial caliper and the mass, a triple beam balance. The results of the error for diameter were not as expected while the results of the volume and density were deviated greatly from expectations; only the weight had a small error.

Experimental

Instruments:

1. Steel ball

2. Dial caliper (Mano Stat Corp.)

3. Triple beam balance (OHAUS)

Procedure:

1. The steel ball was measured for its diameter using the caliper using gloves to not add hand oil to the ball.

2. The ball was placed on the balance with pan to measure mass.

3. The volume was calculated using (4/3)pi(r^3)

4. The density was calculated using mass/density

5. The results were aggregated with the class's.

6. The mean and standard deviation was determined for the four values.

7. A frequency histogram was made for the diameter and mass.

Results and Discussion

The results of the analysis are attached on next page. The relative error of the diameter was 27% while the relative error for mass was .8%. The relative error for volume and density were 54% and 297% respectively. The error for the diameter was quite large and this was due in part by #11 measurement of 0.53. The histogram shows that nearly all of the values lie within one standard deviation of the mean. The mass had a low error but had two competing values in the frequency histogram; the two greatest values had a runner up in between them. This may show that the ball was in fact not completely spherical. The huge variance in the volume and density was probably due to non-uniform calculations done by the students.

Conclusion

The mass was