Physics 215 Experiment 1: Measuring Lengths and Analyzing Errors, Lab Reports of Physics

Download Physics 215 Experiment 1: Measuring Lengths and Analyzing Errors and more Lab Reports Physics in PDF only on Docsity! Physics 215 - Experiment 1 Measurement, Random Error & Error analysis Advanced reading- from Physics by Giancoli, 6th Edition (Sections 1-4, 1-5 & 1-6) Part A-Measurement of Length and Error Analysis Equipment: 1 Ruler 1 Vernier Caliper 1 Micrometer Caliper Several Coins. Objective: The object of this experiment is twofold: 1. To learn to measure lengths using a ruler, vernier caliper, and micrometer caliper. 2. To become acquainted with types of error and statistical methods for analyzing one's data and for estimating its ac- curacy. 3. To determine the density of a block of metal. Theory: In using a ruler three things must be remembered: (1) the reading should be estimated to one half of the smallest division; (2) the ends of the ruler should not be used since the ends may have become damaged and no longer be square; (3) errors of parallax should be avoided by placing the scale against the ob- ject to be measured. In using a vernier caliper tenths of a division are not esti- mated; they are read off the vernier scale. Notice that 10 divi- sions on the vernier scale corre- sponds to 9 divisions on the main scale. Therefore, the mark on the vernier scale which best lines up with a mark on the main scale gives the reading of a tenth of the smallest division on the main scale (see fig. 1. 1). Figure 1-1 In using a micrometer caliper, centimeters and tenths of a cen- timeter are read from the scale on the barrel. Then thousandths of a centimeter are read from the scale on the thimble. Since this scale only goes from 0 to 50 thou- sandths the thimble must be turned twice to move one-tenth of Physics 215 - Experiment 1 Measurement, Random Error & Error analysis a centimeter. If the scale is over halfway between the marks on the barrel, then 50 thousandths must be added to the reading. Ten-thousandths of a centimeter should be estimated. (See fig. 1.2.) A zero correction for the mi- crometer caliper should be deter- mined and recorded. For exam- ple, if the micrometer caliper reads 0.002 cm when closed, then every reading will be too large by this amount and the zero correc- tion must be subtracted from each reading. When closing the micrometer caliper the small knurled knob must be used so that the caliper will not be dam- aged by overtightening. Figure 1-2 Statistical Analysis Of Data and Errors Mean If one makes a series of n measurements with results xl,x2, ...xn, the mean, or average value, x , of the measurements is defined as x = 1 n xi i=1 n ! = 1 n (x1 +x2 + ...+xn ) x will be the most probable value for the quantity being measured. By itself, however x gives no in- dication of the reliability of the results, that is, of what statistical error there may be in the results. To analyze this facet of the prob- lem one needs the standard de- viation or root mean square of the data. Standard Deviation Or Root Mean Square The standard deviation (or root mean square) of the above n measurements is defined as ! = x 1 "x( ) 2 # n "1( ) $ % & & ' ( ) ) 1 2 Physics 215 - Experiment 1 Measurement, Random Error & Error analysis Part B- Random Error Analysis Objective The purpose of this experiment is to make a series of measure- ments involving a sufficient number of trials to permit the use of a statistical theory of errors to evaluate the results. Part 1: Equipment: Steel Ball Carbon Paper Sheets of Ruled Paper ruler Procedure: Place a sheet of paper over a layer of carbon paper approxi- mately 30 cm from the table on the laboratory floor. Mark a line on the paper which is parallel to the edge of the table. Using a plumb bob, locate the position of the edge of the table on the floor and accurately measure x, the distance from the table and at- tempt to hit the line on the paper as the ball strikes the floor. Measure the horizontal distance from the position of the edge of the table to the actual impact point, call it x1 (measure to the nearest cm). Repeat these in a vertical column. We will now ob- tain two numbers which will give a measure of the variability of your skill in this experiment. x Ball shown on table with pa- per beneath. 1) Calculation of the average value: x= x i i=1 N ! N Physics 215 - Experiment 1 Measurement, Random Error & Error analysis The xi’s are simply the meas- ured values for x for the different trials. A comparison of this value with the true distance from the table edge to the line shows whether or not the results are consistently too short or too long. 2) Calculation of the standard deviation: This quantity gives an indication of the consistency of the trials. Write your result as: ! 2 = x i " x( ) 2 i=1 N # N "1 3) Plot of the distribution of hits versus position (i.e., a histogram): Draw a graph of the number of times the ball hit within a specified distance from the line versus the distance from the table in centimeter intervals. Include on the graph: 1) The average value of the measured value of x ( the arith- metic average). 2) The true value of x (actual position of the line). 3) The calculated standard de- viation. Part 2 Equipment: Compressed Pills Digital Balance (0.001g resolution) Procedure: Measure the mass of at least 30 of these compressed pills and calculate: a) the average value of the mass b) the standard deviation of this distribution c) plot the distribution of mass versus number for the pills in your measurement set. Questions: 1. Compare the graph of your data with the sample graph. Ex- Physics 215 - Experiment 1 Measurement, Random Error & Error analysis plain the differences in the distri- butions observed. How could you reduce the value of σ if the ex- periment were repeated? 2. If a die were tossed twice, what can you say about the av- erage value of the number thrown? If the die were tossed 100 times, what would be the average value of the number thrown? Why are your answers different? 3. What can you say about the dose delivered by a pill in your measurement set. How does this experiment help to describe the variability or consistency of the production process producing this medication?