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Phy 110 chapter 1

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Syahirah Suhalim
Syahirah Suhalim

1. The document discusses various concepts related to physical measurements including units, accuracy, precision, errors, and significant figures. 2. It explains different ways to express uncertainty in measurements using either estimated uncertainty with a 賊 sign or percentage uncertainty. Accuracy refers to how close a measurement is to the true value, while precision refers to the reproducibility of measurements. 3. The document outlines various units used in measurements like meters, kilograms, grams, seconds. It also discusses converting between different units using conversion factors.

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CHAPTER 1: PHYSICAL UNITS
1.1 Measurement
Uncertainty in Measurement There are 2 way to express uncertainty: Estimated uncertainty is written with a 賊 sign. If a ruler has precision of 0.1 cm, an object has length of 8.8 cm is written as 8.8賊0.1 cm. Percent uncertainty is the ratio of the uncertainty to the measured value, multiplied by 100:
Accuracy indicated how close a measurement is to the accepted value. It describes the nearness measurement to the standard or true value. Accuracy
Indicates how close together or how repeatable the result are. Is the degree to which several measurement provide answers that is very close to each other. The lesser the scatter, it gives a higher the precision. Precision
A measurement system can be accurate but not precise, precise but not accurate, neither, or both.
Figure 1 : Measuring the width of a board with a centimeter ruler. The uncertainty is 賊 1 mm.
Type of errors Random Errors are usually small and has equal probability of being positive or negative, example; parallax error (an error due to incorrect eyes position during the measurement), mistake in measurement, wrong count etc. Systematic Errors Constant error due to instruments, physical conditions of the surrounding or physical limitation of the observer.
Is an estimation of the difference between the measured value and the real value. It also known as error. Example: If the exact mass of an object is 5.0kg and you estimated mass between 4.8kg and 5.2kg. mass, m= 5.0kg Absolute error, m= 0.2kg Thus the mass, m= 5.0 賊0.2kg Absolute error
Is the ratio of the absolute error to the real/exact value of some measured quantity. Relative error
Example 1: If the exact mass of an object is 5.0kg and you estimated mass between 4.8kg and 5.2kg. Find the relative error and percentage error. mass, m= 5.0kg Absolute error, m= 0.2kg Relative error = m= 0.2= 0.04 m 5.0
Example 2: Find the percentage error of 3.16 賊 0.28 m.
Phy 110 chapter 1
The number of significant figures is the number of reliably known digits in a number. Significant figures
1) All nonzero digits are significant: i. 457 cm (3 S.F) ii. 0.25 g (2 S.F) 2) Zero between nonzero digits are significant: i. 1005 kg (4 S.F) ii. 1.03 cm (3 S.F) iii. 40500 (3 S.F) 3) Zero to left of the first nonzero digits in a number are not significant: 1) 0.02 g (1 S.F) 2) 0.0026 cm (2 S.F) 4) When a number ends in zeros that are to the right of the decimal point, they are significant: 1) 0.0200 (3 S.F) 2) 3.0 cm (2 S.F)
Phy 110 chapter 1
When two or more measured values are added, subtracted, multiplying or dividing the final calculated value must have the same number of decimal places as that measured value which has the least number of decimal places. Example: X = 12.658cm + 2.35cm = 15.01cm
A physical quantity can be measured using standard size called unit. For example: meter (m), kilogram (kg), etc. This unit is called SI unit. 1.2 Units and standard of measurement Units
SI unit is an International System of Units that is accepted by the Eleventh Conference of Weights and Measures in 1960. it is used in science and technology all over the world.
Anything that can be measured is called physical quantities. Measurement
Basic Quantities It cannot be derived from any physical quantities Basic quantities are the fundamental physical quantities.
Derived Quantities Derived quantities are constructed from a combination of several basic quantities. Quantities that can be obtained and expressed in terms of basic quantities. 22
23
Scientific Notation A way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation. In scientific notation, numbers are written in the form, An electrons mass is about 0.000 000 000 000 000 000 000 000 000 000 910 938 22 kg. In scientific notation, this is written 9.109822 x 10-31 kg.
Phy 110 chapter 1
1.3 Unit Conversion Conversion factor to remember : 1 km = 1000 m 1 m = 100 cm 1 cm = 10 mm 1 kg = 1000 g 1 h = 60 min 1 min = 60 s 1 h = 3600 s
Since any quantity such as length can be measured in several different units, it is also important to know how to convert from one unit to another. 1 L = 1000 cm3 1m = 3.28 ft 1 yd = 3 ft 1ft = 12 in 1 in = 2.54 cm 1 mi = 1.61 km
Example: 1) 1袖m = _________mm 2) 10袖m2 = _________m2 3) 17Mm = _________m
Conversion of Units 29
45 cm = ? km 30
Phy 110 chapter 1
Solution (i) : kmx km x m km cm m cmcm 5 1012 1000100 12 ) 1000 1 )( 100 1 (1212
Solution (ii):
35 km.hr-1 = ? m.s-1 Example
20 kg.m-3 = ? g.cm-3 35
Phy 110 chapter 1

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Phy 110 chapter 1

  • 3. Uncertainty in Measurement There are 2 way to express uncertainty: Estimated uncertainty is written with a 賊 sign. If a ruler has precision of 0.1 cm, an object has length of 8.8 cm is written as 8.8賊0.1 cm. Percent uncertainty is the ratio of the uncertainty to the measured value, multiplied by 100:
  • 4. Accuracy indicated how close a measurement is to the accepted value. It describes the nearness measurement to the standard or true value. Accuracy
  • 5. Indicates how close together or how repeatable the result are. Is the degree to which several measurement provide answers that is very close to each other. The lesser the scatter, it gives a higher the precision. Precision
  • 6. A measurement system can be accurate but not precise, precise but not accurate, neither, or both.
  • 7. Figure 1 : Measuring the width of a board with a centimeter ruler. The uncertainty is 賊 1 mm.
  • 8. Type of errors Random Errors are usually small and has equal probability of being positive or negative, example; parallax error (an error due to incorrect eyes position during the measurement), mistake in measurement, wrong count etc. Systematic Errors Constant error due to instruments, physical conditions of the surrounding or physical limitation of the observer.
  • 9. Is an estimation of the difference between the measured value and the real value. It also known as error. Example: If the exact mass of an object is 5.0kg and you estimated mass between 4.8kg and 5.2kg. mass, m= 5.0kg Absolute error, m= 0.2kg Thus the mass, m= 5.0 賊0.2kg Absolute error
  • 10. Is the ratio of the absolute error to the real/exact value of some measured quantity. Relative error
  • 11. Example 1: If the exact mass of an object is 5.0kg and you estimated mass between 4.8kg and 5.2kg. Find the relative error and percentage error. mass, m= 5.0kg Absolute error, m= 0.2kg Relative error = m= 0.2= 0.04 m 5.0
  • 12. Example 2: Find the percentage error of 3.16 賊 0.28 m.
  • 14. The number of significant figures is the number of reliably known digits in a number. Significant figures
  • 15. 1) All nonzero digits are significant: i. 457 cm (3 S.F) ii. 0.25 g (2 S.F) 2) Zero between nonzero digits are significant: i. 1005 kg (4 S.F) ii. 1.03 cm (3 S.F) iii. 40500 (3 S.F) 3) Zero to left of the first nonzero digits in a number are not significant: 1) 0.02 g (1 S.F) 2) 0.0026 cm (2 S.F) 4) When a number ends in zeros that are to the right of the decimal point, they are significant: 1) 0.0200 (3 S.F) 2) 3.0 cm (2 S.F)
  • 17. When two or more measured values are added, subtracted, multiplying or dividing the final calculated value must have the same number of decimal places as that measured value which has the least number of decimal places. Example: X = 12.658cm + 2.35cm = 15.01cm
  • 18. A physical quantity can be measured using standard size called unit. For example: meter (m), kilogram (kg), etc. This unit is called SI unit. 1.2 Units and standard of measurement Units
  • 19. SI unit is an International System of Units that is accepted by the Eleventh Conference of Weights and Measures in 1960. it is used in science and technology all over the world.
  • 20. Anything that can be measured is called physical quantities. Measurement
  • 21. Basic Quantities It cannot be derived from any physical quantities Basic quantities are the fundamental physical quantities.
  • 22. Derived Quantities Derived quantities are constructed from a combination of several basic quantities. Quantities that can be obtained and expressed in terms of basic quantities. 22
  • 23. 23
  • 24. Scientific Notation A way of writing numbers that accommodates values too large or small to be conveniently written in standard decimal notation. In scientific notation, numbers are written in the form, An electrons mass is about 0.000 000 000 000 000 000 000 000 000 000 910 938 22 kg. In scientific notation, this is written 9.109822 x 10-31 kg.
  • 26. 1.3 Unit Conversion Conversion factor to remember : 1 km = 1000 m 1 m = 100 cm 1 cm = 10 mm 1 kg = 1000 g 1 h = 60 min 1 min = 60 s 1 h = 3600 s
  • 27. Since any quantity such as length can be measured in several different units, it is also important to know how to convert from one unit to another. 1 L = 1000 cm3 1m = 3.28 ft 1 yd = 3 ft 1ft = 12 in 1 in = 2.54 cm 1 mi = 1.61 km
  • 28. Example: 1) 1袖m = _________mm 2) 10袖m2 = _________m2 3) 17Mm = _________m
  • 30. 45 cm = ? km 30
  • 34. 35 km.hr-1 = ? m.s-1 Example
  • 35. 20 kg.m-3 = ? g.cm-3 35