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Measurement in Physics. Mark Lesmeister Pearland ISD. Mini-lab: Indirect measurements. In this lab, you will complete 3 lab stations involving indirect measurement. You will work in pairs at each station. You will only have two minutes at each lab station, so work quickly and efficiently.
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Measurement in Physics Mark Lesmeister Pearland ISD
Mini-lab: Indirect measurements • In this lab, you will complete 3 lab stations involving indirect measurement. • You will work in pairs at each station. • You will only have two minutes at each lab station, so work quickly and efficiently. • When I give the word, switch to the next lab station.
Objectives • List SI units and the quantities they describe. • Use scientific notation. • Distinguish accuracy and precision. • Use significant figures.
Dimension • In physics, dimension refers to the type of quantity being measured. • For example: • Both the height of a building and the distance from here to Dallas have the dimension of length, though they are usually measured in different units. • A football player’s age in years and the number of seconds he takes to run 40 yards are both measurements of the time dimension.
Measurement in Experiments All other units are called derived units because they are based on combinations of two or more of the SI base units.
Converting metric prefixes • Determine the units of the known and unknown quantity. • Write an equation between the two. • Write the equation as a fraction equaling 1. • Multiply the known by this fraction.
Practice with metric prefixes • A typical radio wave has a period of 1 ms. Express this period in seconds. • A human hair is approximately 50 mm in diameter. Express this diameter in meters. • The distance between the sun and the Earth is about 1.5 x 1011 m. Express this distance in kilometers.
Determine the units of the known and unknown quantity. Write an equation between the two. Write the equation as a fraction, with the unknown on top. Multiply the known by this fraction. meters (m) and mm 10-6 m = 1 mm Sample Problem 2
Determine the units of the known and unknown quantity. Write an equation between the two. Write the equation as a fraction, with the unknown on top. Multiply the known by this fraction. meters (m) and km 1000 m = 1 km Sample Problem 3
What are the units of the unknown? What is the value of the known? Write an equation between the known and unknown. Make a fraction with the unknown units on top. Multiply the known by the fraction. ml 37854120 l 1 l = 1000 ml Metric conversion practice: #1
What are the units of the unknown? What is the value of the known? Write an equation between the known and unknown. Make a fraction with the unknown units on top. Multiply the known by the fraction. km 3000 m 1 km = 1000 m Metric conversion practice: #3
#2 90,760 ms = 9.0760 x 104 ms 100,000 cm =1 x 105 cm #4 0.020 ks 0.1 km # 5 739 m #6 3033 m #7 6.250 A #8 62,400 cm Answers: Metric conversion
Discovery Lab: Accuracy and Precision • Please complete the Accuracy and Precision Mini-lab handout that you picked up on the way into class.
Accuracy and Precision • accuracy – how close a measured value is to the true or accepted value of the quantity being measured • precision – the degree of exactness with which a measurement is made and stated
Accurate, Precise, or Both • The following students measure the density of a piece of lead three times.The density of lead is actually 11.34 g/cm3. Considering all of the results,which person’s results were accurate? Which were precise? Were any both accurate and precise? • a. Rachel: 11.32 g/cm3, 11.35 g/cm3, 11.33 g/cm3 • b. Daniel: 11.43 g/cm3, 11.44 g/cm3, 11.42 g/cm3 • c. Leah: 11.55 g/cm3, 11.34 g/cm3, 11.04 g/cm3
Significant Figures or Digits • One way to express the precision of a measurement is to use significant figures or digits. • Significant figures or digits are those digits in a measurement that are known with certainty plus the first digit that is uncertain. • They are also called sig figs or sig digs.
Rules for Determining Significant Figures • All nonzero digits are significant. • Zeroes between other nonzero digits are significant. • Zeroes in front of nonzero digits are not significant; they are placeholders. • Zeroes at the end of a number and to the right of the decimal point are significant. • Zeroes at the end of a number but to the left of the decimal are not significant, but are important as placeholders, unless you are told they are measured.
How many significant digits? • 3.0025 • .0008 • .0430 • 4500
Rules for calculations with significant figures • In addition or subtraction, the answer should have the same number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal. • In multiplication and division, the final answer should have the same number of significant figures as the measurement with the fewest number of significant figures.
Compute using sig figs. • 72.4 +36.73 • 80.1 + 23 • 26 x .0258 • 15.3 / 1.1
Rules for Rounding • Leave the number alone when the digit following the last significant figure is 0, 1, 2, 3, or 4. • Round up when the digit following the last significant figure is 5, 6, 7, 8, or 9
Special Rules for RoundingThe Symmetric Rounding Rule • This rule is sometimes followed when the digit following the last significant figure is 5. This rule says to round to the nearest even number. This rule is often used to reduce average error due to rounding since the numbers are sometimes rounded up and sometimes rounded down. • Your text uses this rule.
