General Physics, Accuracy and Precision, Summaries of Physics

Download General Physics, Accuracy and Precision and more Summaries Physics in PDF only on Docsity! ACCURACY AND PRECISION OF THE MEASUREMENT ACCURACY • is how close a measurement is to the correct value for that measurement. Two Types of Errors • Random Errors • Systematic Errors Random Errors • it is usually result from the experimenter’s inability to take the same measurement in exactly the same way to get exact the same number. Systematic Errors • the constant error occurs in the experiment because of the imperfection of the mechanical structure of the apparatus. The systematic errors arise because of the incorrect calibration of the device. Mean • is also known as the arithmetic mean of the given data. • The mean is the average or a calculated central value of a set of numbers and is used to measure the central tendency of the data. Standard Deviation • is the degree of dispersion or the scatter of the data points relative to its mean. • the standard deviation of a data set, sample, statistical population, random variable, or probability distribution is the square root of its variance. STANDARD DEVIATION FORMULA == THENUMBEROF = DATAPOINTS Di-.(%i- 2) n-1 X: sms: EACHOF THE VALUE j= omeoma S = x = memesnor Xj <> -3 -2 -1 1 2 3 NORMAL DISTRIBUTION CURVE The factors contributing to uncertainty in a measurement include: 1. Limitations of the measuring device. 2. The skill of the person making the measurement. 3. Irregularities in the object being measured. 4. Any other factors that affect the outcome (highly dependent on the situation). Percent Uncertainty • One method expressing uncertainty is as percent of the measured value. If a measurement A is expressed with uncertainty, δA, the percent uncertainty defined to be: x 100 Absolute, Fractional, and Percent Uncertainty Absolute Uncertainty | Fractional Uncertainty | Percent Uncertainty Uncertainty expressed as a Uncertainty expressed as a Uncertainty expressed as a number independent of the fraction of the original number percentage of the original number. original number Symbol: Symbol (and equation): Symbol (and equation): Aao Ab or Ac etc. Aa or Ab or Ac etc, |4&x100% or Ab x100% OF Ae x 00% a b c a etc. Example: Example: Example: 4+] 4 +0.25 4+25% Convert from absolute to fractional uncertainty: Convert from fractional to percent uncertainty: Divide the absolute 1 Multiply the fractional o, uncertainty by the —_ = 0.25 uncertainty by 100% 0.25 x 100% = 25 Yo number 4 Convert from fractional to absolute uncertainty: Convert from percent to fractional uncertainty: Multiply the fraction Divide the fractional §=— 950 by the number 0.254=1 uncertainty by 100% 2°=0.25 100% Solution Strategy First, observe that the expected value of the bag's weight, A, is 5 Ib. The uncertainty in this value, 6A, is 0.4 Ib. We can use the following equation to determine the percent uncertainty of the weight: éA % unc —— x 100%. 1.9 A Solution Plug the known values into the equation: 0.4 Ib % une = Sb x 100% = 8%. 1.40 Check Your Understanding • A high school track coach has just purchased a new stopwatch. The stopwatch manual states that the stopwatch has an uncertainty of ±0.05 s. The team's top sprinter clocked a 100 meter sprint at 12.04 seconds last week and at 11.96 seconds this week. Can we conclude that this week's time was faster? SIGNIFICANT FIGURES • The significant figures of a given number are those significant or important digits, which convey the meaning according to its accuracy. For example, 6.658 has four significant digits. • These substantial figures provide precision to the numbers. They are also termed as significant digits.