Measurements in Physics
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Just as physicists create simplified models to better understand the real world, they use the tools of mathematics to analyze and understand their observations
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Measurements in Physics
- 1. What do you think? What system of measurement is used in physics? Is a measurement of 2 cm different from one of 2.00 cm? − If so, how? What is the area of a strip of paper measuring 97.3 cm x 5.85 cm? How much should you round off your answer?
- 2. Measurements Dimension - the kind of physical quantity being measured − Examples: length, mass, time, volume, and so on − Each dimension is measured in specific units. meters, kilograms, seconds, liters, and so on − Derived units are combinations of other units. m/s, kg/m3, and many others Scientists use the SI system of measurement.
- 4. Prefixes
- 5. Converting Units Build a conversion factor from the previous table. Set it up so that units cancel properly. Example - Convert 2.5 kg into g. − Build the conversion factor: 103 g 1 kg − This conversion factor is equivalent to 1. 103 g is equal to 1 kg − Multiply by the conversion factor. The units of kg cancel and the answer is 2500 g. 103 g 2.5 kg × = 2500 g Try converting 1 kg − .025 g into mg − .22 km into cm
- 6. Classroom Practice Problem If a woman has a mass of 60 000 000 mg, what is her mass in grams and in kilograms? − Answer: 60 000 g or 60 kg
- 7. Accuracy and Precision • Precision is the degree of exactness for a measurement. − It is a property of the instrument used. − The length of the pencil can be estimated to tenths of centimeters. Accuracy is how close the measurement is to the correct value.
- 8. Errors in Measurement Instrument error − Instrument error is caused by using measurement instruments that are flawed in some way. − Instruments generally have stated accuracies such as “accurate to within 1%.” Method error − Method error is caused by poor techniques (see picture below).
- 9. Significant Figures Significant figures are the method used to indicate the precision of your measurements. Significant figures are those digits that are known with certainty plus the first digit that is uncertain. − If you know the distance from your home to school is between 12.0 and 13.0 miles, you might say the distance is 12.5 miles. The first two digits (1 and 2) are certain and the last digit (5) is uncertain.
- 10. Counting Significant Figures Examples − 50.3 m − 3.0025 s − 0.892 kg − 0.0008 ms − 57.00 g − 2.000 000 kg − 1000 m − 20 m Scientific notation simplifies counting significant figures.
- 11. Rounding Round to 3 figures: − 30.24 − 32.25 − 32.65000 − 22.49 − 54.7511 − 54.75 − 79.3500
- 12. Calculating with Significant Figures 97.3 + 5.85 123 x 5.35
- 13. Now what do you think? What system of measurement is used in physics? Is a measurement of 2 cm different from one of 2.00 cm? − If so, how? What is the area of a strip of paper measuring 97.3 cm x 5.85 cm? How much should you round off your answer?
Editor's Notes
- When asking students to express their ideas, you might try one of the following methods. (1) You could ask them to write their answers in their notebook and then discuss them. (2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups. The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
- Ask students to suggest other examples of dimensions, specific units, and derived units. You may also want to discuss the advantages of using a common system of measurement.
- This chart allows students to see the original standard and the current standard.
- It might be a good time to let students know which prefixes are more commonly seen, such as micro through mega. They will need to know these in order to convert units.
- When presenting the example, you may wish to ask students for the conversion factor before you show it. Be sure students know that they must set up the conversion factor such that the units cancel properly. To discuss this issue, ask students how we know that the conversion factor is 10 3 g /1 kg rather than 1 kg /10 3 g. Answers: 0.25 g = 250 mg, 0.22 km = 22,000 cm. Note that the second problem requires two conversions (if using the table), first km into m, and then m into cm.
- Show students how to get the conversion factor using the table (1 g / 1000 mg). The reverse (1000 mg / 1 g) will not work because the mg will not cancel out. Similarly, they need to find the conversion from g into kg. In order to make the grams cancel, the conversion factor is 1 kg / 1000 g.
- Point out to students the necessity of making sure your line of sight is directly over the measurement. Discuss measurement methods that improve precision and accuracy, such as: -not using the end of the meter stick (as was done in the picture on the last slide) -measuring a quantity several times and averaging the results -having different people measure the same quantity and averaging the results.
- Have students read the rule and then apply it to the two measurements to the right. (Each rule has two examples.) Give them some time to read the rules and try on their own to apply the rules. Then go over the answers with them (below) so they can see where they made mistakes. Answers: three, five, three, one, four, seven, one, one This activity also provides an opportunity to show them that converting the above numbers to different units does not affect the number of significant figures. For example, converting 0.892 kg into 892 g still yields three significant figures. Also show them that converting 57.00 g into kg yields 0.05700 kg and not 0.057 kg because the number must still have 4 significant figures. The zeros at the end are measured values and cannot be ignored.
- Have students practice rounding answers to the correct number of significant figures (three in this case). Answers: 30.2, 32.3, 32.6, 22.5, 54.8, 54.8, 79.4
- Have students apply the rule to the sample. (Answers are below.) Remind them often that “calculators do not keep track of significant figures.” Some students simply write down every digit they see on their calculator or round off in some arbitrary way. Students are very reluctant to take an answer such as 2540 m and round it off to 2500 m in order to get just 2 significant figures that the problem might require. However, many will simply take a number like 0.0821 m and call it 0.08 m even though the problem might require three significant figures in the answer. Answers: 103.2, 658
- Have students revisit the opening questions. They should now be able to answer as follows: -Physics uses the SI system of measurement. -A measurement of 2 cm is different from a measurement of 2.00 cm. The latter has three significant figures and is more precise than a measurement of 2 cm, which has just one significant figure. -The area should be rounded to three significant figures, 569 cm 2 .