Physics Experiment 1 131p27

Experiment 1: Errors, Uncertainties, and Measurements Laboratory Report Daud Abraham jr, Dela Cruz Mariel, Dioso Clarenz Clare, Dionisio Karl Anthony Department of Biology College of Sciences, University of Santo Tomas España Street, Manila Philippines that remains constant or depends in a Abstract All measurements of quantities that can assume a continuous range of values consist of two parts: the reported value itself and the uncertainty of the measurement. Measurements are subject to error which leads to the uncertainty of the result. Error does not only mean just outright mistakes. Gross errors sometimes happen and usually yield results that are sufficiently unexpected. Accuracy is the goal we aim for in scientific measurements.  1. Introduction The purpose of measurement is to provide information about a quantity. No measurement is exact. When a quantity is measured, the result depends on the measuring system, the measurement procedure, the skill of the person, and the environment. Measurement uncertainty is a non-negative parameter characterizing the dispersion of the values attributed to a measured quantity (Webster). The uncertainty shows the incomplete knowledge of the quantity. All measurements are subjected to uncertainty, and a measured value is only complete if it is associated by a statement of the uncertainty given. The measuring system may provide measured values that are not far from the true value. There are two types of measurement error, systematic and random. A systematic error is a component of error

specific manner on some other quantity. Readings will consistently be either too high or too low, thus, repeated trials will not reduce systematic error. On the other hand, a random error is associated with the fact that when a measurement is repeated, it will provide a different value. It is random since the next measured value cannot be predicted from the previous values. The effect of random error can be reduced through repeated experimental trials, since there is an equal probability of them being high or low each time a reading is taken. Accuracy refers to how closely the measured value of a quantity corresponds tits true value. Precision expresses the degree of reproducibility, or arrangement between repeated measurements. In this experiment, the group should be able to achieve the following objectives: (1) to study errors and how they propagatein simple experiment, (2) to determine the average deviation of a set of experimentalvalues, (3) to determine the mean of a set of experimental values as well as set of average deviation of the mean, (4) to familiarize the students with the vernier caliper, micrometer caliper, and foot rule, (5) to compare the accuracy of these measuring devices, (6) and to determine the density of an object given its mass and dimensions.

2.Theory     Where a.d. is the average deviation  which is the sum of the deviations (d),  and divided by number of  observations(n)    Where A.D. is the average deviation  of the mean diameter which is a.d.  divided by the square root of (n)    Where Percent error is equivalent to  average deviation divided by mean  diameter 3.Methodology In the experiment, the materials used were a metal ball with a mass of 18.85g and a density of 7.86g, foot rule, vernier caliper, micrometer caliper and electronic gram balance. Firstly, the measuring devices were checked from errors. Least counts of every device were obtained. 5 independent measurements of the diameter of the metal ball for each measuring device were taken. After which, the mean diameter for each measuring device and the deviation of each measurement from the mean were obtained. Next, the average deviation, a.d., was obtained. With the recently computed average deviation, the average deviation, A.D., of the mean diameter was computed. Then, the percentage error was obtained. The volume of the metal ball was computed using the obtained diameter and with the volume and the mass of the metal ball, the density was computed. The computed density was compared with the given accepted density and the percentage error was calculated. Measurements of the width of the thumb of each member were obtained by measuring with a foot rule 4. Data and Analysis of Data it is noticed from the data that the micrometer caliper has the least

percentage error. This is because the least count of the micrometer caliper is less than the other two making the micrometer caliper’s measurement to be more accurate. Errors of measurement may be due to the measuring devices because like for the foot rule, the calibrations had larger spaces. For the calipers the errors were from variations of the independent measurements of the diameter of the ball. To avoid errors, it is needed to check the measuring devices for errors and fixing the measuring devices. As for the thumb, it may not be a standard for measurement since it varies in length for every person. Trial 1 2 3 4 5. Mean diameter a.d. A.D. Volume Mass Experimental value of density Accepted value of density %error of denity

Group member Width of thumb

Diameter of Sphere(cm) Foot Vernier Micrometer rule caliper caliper 1.50c 1.670cm 1.663cm m 1.60c 1.665cm 1.663cm m 1.50c 1.665cm 1.663cm m 1.60c 1.665cm 1.663cm m 1.60c 1.665cm 1.663cm m 1.60c 1.666cm 1.663cm m 0.04c 0.02cm 0.000cm m 0.02c 0.0009cm 0.000cm m 2.1 2.421 2.408 18.85g 18.85g 18.85gm 8.98g 7.786g 7.828g 7.86g

7.86g

7.86g

14.24 %

.94%

.41%

1 1.3

2 1.3

3 1.1

4 1.2

5.Conclusion An error is the difference between a computed or measured value and a true or theoretically correct value. Random error is always present in measurement and it refers to the statistical

fluctuations in the measured data due to the precision limitations of the measurement device while systematic errors are caused by the imperfect calibration of measurement, Instruments or imperfect methods of observation, or interference of the environment with the measurement process, and always affect the results of an experiment in a predictable direction. 6. Applications 1. Among the three measuring devices, the vernier caliper gave the least percent error. Yes, the accuracy of a measurement is affected by the least count and the least count also indicates the degree of accuracy of measurement that can be achieved by the measuring instrument. 2. An error is a deviation from accuracy or correctness. Errors are classified into two categories. First is the systematic error, which results due to faulty measurement practices. Second is the random error, which are caused by unknown and unpredictable changes in the experiment. We encountered systematic error due to personal biases. 3. There are different parts of the body that can be used for measuring, such as the hands, feet, breast, waist and almost all parts of it. Many of the systems of measurement, which had been in use, were to some extent based on the dimensions of the human body according to the proportions and as an effect units of measure could vary not only from location to location, but from person to person.

7. References [1] Dealing with error and uncertainty in measured values .Retrieved on November 25, 2010 from http://www.chem1.com/acad/webtext /pre/mm2.html [2] Melissinos and Napolitano. 2003. Experiments in modern physics. Academic Press, USA: Elsevier Science. [3] Tsokos. Physics for the Cambridge: University Press.