Errors, Uncertainties, and Measurements Essay Example for Free

Errors, Uncertainties, and Measurements Essay Measurements are all subject to error which leads to the uncertainty of the result. Errors may come from systematic errors (deterministic error) or random error (not deterministic error). In this experiment, the group measured the diameter of sphere using different kinds of measuring devices (foot rule, vernier caliper, and micrometer caliper) in order to achieve accuracy in the scientific measurements. After experimenting, it was revealed that the micrometer caliper has the lowest percentage of error. 1. Introduction In the early days, people used mostly human body parts for measuring. And because the measurement depended on the body size and length of the person measuring, it often leads to varying measurements which leads to inaccuracy and errors in the measurements. In the following years, a better system of units of measurement was developed – the metric system. The metric system is an international decimalized system of measurement, first adopted in France in 1791. Numerous measuring instruments have this system of measurement. Aside from meter sticks and ruler, the vernier caliper and micrometer caliper also use this system. The vernier caliper is a measuring device which takes advantage of a vernier scale, a scale used to provide very precise measurements. The vernier adds an extra digit of accuracy to any measurement, allowing it to be highly accurate. Like other calipers, a vernier caliper has an L-shaped design with a movable arm which can be adjusted to allow the object being measured to fit between the arms, and a measurement to be taken. It has two scales – main scale and vernier scale. The main scale is fixed while the vernier scale can slide along the main scale as the movable arm is shifted. Measurements are taken by looking for the mark on the main scale which is just to the left of the zero on the vernier caliper for the first measurement, and then looking to see which mark on the vernier caliper comes most closely into alignment with a mark in the main scale. Micrometer caliper is a calibrated screw device for finding exact measurements in which an object to be measured is to be enclosed between two jaws, one fixed while the other movable by means of a fine screw. When the jaws are just touching the object, the distance between the jaws can be read on an associated scale, ofteh to an accuracy of 10 -4. It uses the principle of a screw to amplify small distances that are too small to measure directly into large rotations of the screw that are big enough to read from a scale. Most micrometers have their readout right on the handle of the instrument. This experiment aims to achieve the following objectives: (1) to study errors and how they propagate in simple experiment, (2) to determine the averge deviation of a set of experimental values, (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 detemine the density of an object given its mass and dimensions. 2. Theory Significant figures are very essential in science. Each recorded measurement 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. Least count of any precision instrument is defined as the least distance travelled by it. For a micrometer it is measured in the following manner. Least count (L.C) of a screw gauge = Pitch/ Number of circular scale division. Pitch and Number of circular scale divisions are the two factors determining the least count of Micrometer. 3. Methodology In measuring the diameter of the sphere provided, the group was given three measuring devices. To determine the average deviation and mean of a set of experimental values as well as the diameter of the sphere, the group was given the three measuring tools to study the measurement and its errors. First, the group determined the least count of the vernier caliper, micrometer caliper and the foot rule then we made ten measurements for the diameter of the sphere using the foot rule. After completing the ten measurements, the group then calculated the mean diameter of the sphere by adding all the independent measurements and divided it to 10. Next, the group calculated the deviation (d) of each measurement of diameter from the mean diameter. After getting the deviation of each measurement, the group calculated for the average deviation (a.d). The average deviation is the sum of the deviations (d) divided by the number (n) of observations.