Experiment 1: Errors, Uncertainties, and Measurements

Experiment 1: Errors, Uncertainties, and Measurements

Abstract

All the measurements that we make are all subject to error which leads to the uncertainty of the result. Errors in measurements may come from instrument variability, different observers, sample differences, time of day, etc.

In this experiment, the group measured the diameter of a small ball using different kinds of measuring equipments: foot rule, vernier caliper, and micrometer caliper in order to achieve the accuracy of the scientific measurements. After the experiment, the micrometer caliper has the lowest percentage of error.

1. Introduction

Measurement was discovered because of the earliest tools invented by humans and they evolve until the present time. Early men needed to get their jobs done in the most effective way so they created tools that can help them measure since they had to gauge the passing of time, look for ways to divide up pieces of land, develop a system to help keep track of the number of animals they owned and ways to calculate grain so that they could exchange goods with each other. Since then they created tools to measure.

The experimental procedures can only do is to give a value for a specific result that can be considered near to the true value. There can be many sources of errors in getting the right quantity: The observer, because observers are unpredictable, the method of measurement because it can be unreliable, the object to be measured because the size can be non-uniformed, and lastly the equipments used in measuring because it can be faulty or out of adjustment.

In this experiment, the group should be able to achieve the following objectives: (1) to study errors and how they propagate in simple experiments, (2) to determine the average deviation of a set of experimental values, (3) to determine the mean 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, and (6)to determine the density of an object given its mass and dimensions.

2. Theory

Significant figures are very essential in finding the exact measurement. Each recorded measurement values has a certain number of significant digits. Calculations done on these measurements must follow the rules for significant digits. The significance of a digit has to do with whether it represents a true measurement or not. Any digit that is actually measured or estimated will be considered significant. Placeholders, or digits that have not been measured are not considered significant. There are rules in determining the significance of a digit. First, digits from 1-9 are always significant. Second, zeroes between two other significant digits are always significant. Also, one or more additional zeroes to the right of both the decimal place and another significant digit are significant. Lastly, zeroes used solely for spacing the decimal point are not significant.

In every measuring device is different from one another and may be defined as the minimum measurement that it can make, for example, the a ruler’s least count would be the millimeter while in vernier calipers may be solved using this formula:

= [pic 1]

= [pic 2]

= 0.05 mm or 0.005 cm

While the micrometer caliper has a same formula which just differs in the denominator part, it having a circular scale, may be solved using:

= [pic 3]

= [pic 4]

= 0.01 mm or 0.001 cm

In measurement that is usually used in experiments, a lot of trials are taken since, no measurement is exact. A mean is taken which is to be the central value of the measurement. The average deviation was also taken which is a measure of how far apart the measurements are from each other. It is the sum of the deviations of the diameters divided by the number of trials done. The mean is solved using the formula:

=        [pic 5][pic 6]

Wherein  is the average diameter and D is  the diameter of the object measured.[pic 7]

The average deviation of the measurements was computed using the formula:

[pic 8]

Wherein  is the summation of the diameters and n being the number of trials done.[pic 9]

After computing for the mean and the average deviation, the average deviation (A.D.) of the mean diameter was computed using the formula:

[pic 10]

Wherein a.d. is the average deviation and  is the number of trials done.[pic 11]

Percent error is a basis on how accurate a measurement. It shows the difference between the experimental value from the central value. It is computed using the formula:

[pic 12]

Wherein  E is the Experimental value and A is the Accepted Value

After computing for the percent error, it is computed for the volume of the sphere. Volume is the amount of space an object can occupy which is 3-dimensional. The volume was computed using the formula:

V=[pic 13]

Wherein  r is the radius of the sphere.

The density of the ball was taken afterwards. An electronic gram balance was used to measure the weight of the ball. The weight depends on the size of the ball and the material used.

3. Methodology

For Activity 1, there were three measuring devices used in this experiment, foot rule, Vernier caliper and micrometer caliper. A metal ball was measured using these equipments in ten trials each. The least count of each instrument was first determined; least count is defined as the smallest scale division on the instrument. The least count of the foot rule is 1mm, the Vernier caliper is 0.05 mm and the micrometer caliper is 0.01 mm. For the foot rule, measurements were done by determining where the metal ball touched the scale and was noted. For the Vernier caliper, measurements were done by putting the metal ball in the lower jaw and clamping it to determine its measure on the main scale, the value in the main scale is determined by looking at where the zero of the Vernier scale touched, the measure in the Vernier scale is then determined by finding where the Vernier scale perfectly aligned to the main scale, this is the decimal value and it is multiplied to the least count and was noted. For the micrometer caliper, the metal ball was clamped between the anvil and the spindle, and the thimble was spun until the ball was clamped, the ratchet was then clicked. The measure in the sleeve was read and the sleeve scale measurement was also read and it is the decimal place and was multiplied to the least count and was noted. After the ten trials for each of the measuring device, the mean diameter was determined. The deviation for each measurement was then determined by subtracting the mean diameter to the actual measurement itself. The average of the deviations of each measurements of each of the devices was determined. The average deviation of the mean (A.D) was also determined. The percent error of diameter and volume was also computed. The mass was determined by using an electronic scale and was measured in grams. The experimental value of density was then computed and by using the accepted value of destiny that was given (7.874 g/cm3), the percent error for density was determined. For Activity 2, the thumb of each group member was measured using a foot rule and was used to determine if the thumb can be a possible standard to an inch. [pic 14][pic 15]