Physical science unit two measurement
- 1. Physical Science: Unit 2 MEASUREMENT
- 2. A STANDARD MEASUREMENT SYSTEM • Using SI as the standard system of measurement allows scientists to compare data and communicate with each other about their results. Si units are based on multiples of 10. • SI stands for the French phrase le Système International d’Unités. • Measurements consist of two parts: – The number – The unit • Measurements are meaningless without their units
- 3. Quantity Unit Abbreviation Length meter m Mass kilogram kg Time second s Temperature Kelvin K Electric current Ampere A Amount of substance mole mol Luminous intensity candela cd SI Base Units An SI base unit is a fundamental unit that is defined arbitrarily and not by combinations of other units.
- 4. SOME PREFIXES FOR MULTIPLES OF METRIC AND SI UNITS Prefix Symbol Multiple of base unit Example mega M 1,000,000 = 106 1 megameter (Mm) = 106 m kilo k 1000 = 103 1 kilogram (kg) = 103 g hecto h 100 = 102 1 hectogram (hg) = 100 g deka da 10 = 101 1 dekaliter (daL) = 10L deci d 0.1 = 10-1 1 deciliter (dL)= 0.1L centi c 0.01 = 10-2 1 centimeter (cm) = 0.01cm milli m 0.001 = 10-3 1 milligram (mg) = 0.001 g micro μ 0.000 001 = 10-6 1 micrometer (μm) = 10-6 m nano n 0.000 000 001 = 10-9 1 nanogram (ng) = 10-9 g pico p 0.000 000 000 001 = 10-12 1 picogram (pg) = 10-12 g femto f 0.000 000 000 000 001 = 10-15 1 femtogram = 10-15 g
- 5. LENGTH • Length is the distance measured between two points. • The meter is the SI unit of length. It is the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. • The origins of the meter go back to at least the 18th century. At that time, there were two competing approaches to the definition of a standard unit of length. Some suggested defining the meter as the length of a pendulum having a half-period of one second; others suggested defining the meter as one ten-millionth of the length of the earth's meridian along a quadrant (one fourth the circumference of the earth). In 1791, soon after the French Revolution, the French Academy of Sciences chose the meridian definition over the pendulum definition because the force of gravity varies slightly over the surface of the earth, affecting the period of the pendulum Common Conversions for Length 1 km = 1,000 m 1 m = 100 cm 1 m = 1,000 mm 1 cm = 10 mm 2.54 cm = 1 in
- 6. MASS • Mass is the amount of matter there is in a particle or object. The mass of an object measures the object's inertia. Inertia is the object's resistance to a change in motion. • The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram. • At the end of the 18th century, a kilogram was the mass of a cubic decimeter of water. In 1889, the 1st CGPM (Conférence Générale des Poids et Mesures) sanctioned the international prototype of the kilogram, made of platinum-iridium, and declared: This prototype shall henceforth be considered to be the unit of mass • Some scientists want to get away from defining the kilogram based on a hunk of metal. One possibility is using an electromagnetic device that consistently produces the same amount of force, from which the mass can then be calculated
- 7. MASS VS. WEIGHT Weight • Your weight is a measure of the force of gravity on you. • The force of gravity may be more or less on other planets or moons than on Earth. • You would weigh about one-sixth of your Earth weight on the moon. • The newton (N) is the SI unit, the pound (lb) is the English unit. Mass • Mass is the measure of the amount of matter an object contains. • Mass is not affected by gravity. • If you travel to the moon, the amount of matter in your body (your mass) will not change. • The kilogram (kg) is the SI unit for mass despite the base unit being the gram (g)
- 8. TIME • Time is a measure of events in a sequential order from past, to present, to future. (an interval of change) • The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom • The unit of time, the second, was defined originally as the fraction 1/86 400 of the mean solar day. However, measurement showed that irregularities in the rotation of the Earth could not be taken into account by the definition. Experimental work had, however, already shown that an atomic standard of time-interval, based on a transition between two energy levels of an atom or a molecule, could be realized and reproduced much more precisely. Considering that a very precise definition of the unit of time is indispensable for the International System, the 13th CGPM (1967) decided to replace the definition.
- 9. TEMPERATURE • Temperature is an expression of heat energy. Thermodynamically it is a measure of the kinetic energy in molecules or atoms of a substance. The faster the particles are moving the energy and the higher the reading on a thermometer. • The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. • There are three temperature scales in common use today: kelvin (K), centigrade or Celsius (C), and Fahrenheit (F).
- 10. Common conversions for Temperature 0°C = 273 K °C = (°F − 32) × 5⁄9 °F = °C × 9⁄5 + 32 K = °C + 273.15 °C = K − 273.15
- 11. ELECTRIC CURRENT • Electric current is flow of electric charge past a given point in an electric circuit, measured in Coulombs/second which is named Amperes. • The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length.
- 12. MOLE • The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is "mol." • When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles. • The mole is akin to other counting units as “a dozen eggs” “a herd of buffalo”, or a “bushel of wheat”.
- 13. VOLUME • Volume is the amount of space an object takes up. • Volume is not a base unit. It is a derived unit from the meter. • The SI unit of volume is the cubic meter (m3 ), but the more common unit of volume is Liters (L) or milliliters (mL). Common Conversions for Volume 1 L = 1,000 mL 1 L = 1,000 cm3 1mL = 1 cm3
- 14. VOLUME OF A LIQUID • Graduated cylinder • mL • Meniscus – curved surface at top of liquid, always record measurements using bottom of meniscus
- 15. VOLUME OF AN IRREGULAR SOLID: • Example – Rock • Submerge object in water in graduated cylinder and measure the displacement of the water VOLUME OF A RECTANGULAR SOLID • Example – cereal box • Volume = Length x Width x Height (V = L x W x H) • Remember to multiply numbers and units, so units will be cubed.
- 16. DENSITY • Density is defined as the mass of a substance per unit volume. • D = m/v • another symbol for density is the Greek letter rho ρ = m/v • The SI unit of density is kg/m3 , other common units are g/cm3 and g/mL • Since density is made up of 2 measurements, it always has 2 units. One in the numerator and one in the denominator
- 17. DENSITY The density of a substance stays the same no matter how large or small a sample of the substance is. So a cup of water and a swimming pool of water will both have a density of 1 g/mL. Knowing an object’s density allows you to predict whether it will sink or float Densities of some common substances Substance Density (g/cm3 ) Air 0.001 Ice 0.9 Water 1.0 Aluminium 2.7 Gold 19.3 Iron 7.87
- 18. TABLES • Organizes data into groups by putting those groups into rows and columns. • Gives us an easy way to compare data • Data: are recorded facts, measurements and observations. • Observations can be – Qualitative: described in word (hot, cold, red, black, large, etc.) – Quantitative: described with numbers (10m, 26°C, etc.)
- 19. VARIABLES • Variable: a variable is any factor that can be controlled, changed, or measured in an experiment – Independent Variable: the one condition that you change in an experiment. – Dependent Variable: the one condition that is measured based on the independent variable being changed. • In a data table the independent variable is placed to the left of the dependent variable • In a graph the independent variable is placed on the x-axis and the dependent variable is placed on the y-axis. • Other variables in an experiment should be held constant. Independent Variable Dependent Variable Average Trials
- 20. TYPES OF GRAPHS • Line Graphs – are best for continuous changes. Data that change over a range are best represented by line graph. Good for visualizing increasing and decreasing trends.
- 21. TYPES OF GRAPHS (CONT.) • Bar Graph – is a diagram consisting of bars that represent the frequencies (or relative frequencies) for particular categories. The lengths of the bars are proportional to the frequency. • these are useful when you want to compare data for several individual items or events.
- 22. TYPES OF GRAPHS (CONT.) • Pie charts - circle divided so that each wedge represents that relative frequency of a particular category. The wedge size is proportional to the relative frequency and 360 degrees. The entire pie represents the total relative frequency of 100%. • Pie charts show parts of a whole
- 23. GRAPHS (CONT.) • Graphs include: – A title – Labeled axes – Proper scale and intervals – A legend or key (if necessary)
- 24. SCIENTIFIC NOTATION • Scientists express measurements in scientific notation when using numbers that are very large or very small • It takes the form of M x 10n where M < 10 and n represents the number of decimal places to be moved. Positive n means the standard number is larger than zero; negative n indicates a number smaller than zero. – The first digit is a number from 1 through 9 – The first digit is followed by a decimal point and then the rest of the digits. Example: 4,600,000,000,000 = 4.6x1012 0.000 954 = 9.54x10-4
- 25. SIGNIFICANCE OF MEASUREMENT • Precision is the degree of exactness of a measurement. For example, if you had two rulers and one is marked every 0.001m and the other is marked every 0.1m , the one marked every 0.001m would offer a more precise measurement. • Significant Figures are the digits in a measurement that are known with certainty. • Accuracy is the extent to which a measurement approaches the true (accepted) value. • Error is the difference between the true (accepted) value and the experimentally measured value. – Error = accepted value – experimental value • % Error is the absolute value of the error divided by the accepted value and then multiplied by 100. – % Error = 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 −𝑒𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 𝑥 100
- 26. SIGNIFICANCE OF MEASUREMENT (CONT.)
- 27. MAKING SIGNIFICANT MEASUREMENTS Look at the ruler on the right and estimate a measurement at the arrow. 1) We know for sure the object is more than 2 cm, but less than 3 cm. 2) We know for sure the object is more than 0.8 cm, but less than 0.9 cm. How do we know these two things? Look where the arrow is, it is to the right of 2, but short of 3. It is to the right of 0.8, but short of 0.9. So, I can say the object is more than 2.8 cm, but less than 2.9 cm. We can say this with complete confidence because of the markings on the ruler. Can I say anything more about the length? 1) Look at the gap between the 0.8 and 0.9 cm, where the arrow is and, mentally, divide that gap into 10 equal divisions. 2) Estimate how many tenths to the right the arrow is from the 0.8 cm. Let us say your answer is two-tenths. We then say the object's length as 2.82 cm. The first two digits are 100% certain, but the last, since it was estimated, has some error in it. But all three digits are significant. This issue of estimation is important. Experience tells us that the human mind is capable of dividing a short distance into tenths with acceptable reliability. However, there is error built in and it cannot be escaped. Since the reliability is acceptable, we say the digit is significant, even with the built-in error. However, the process stops there. ONLY ONE estimated digit is allowed to be significant. Make sure to always include the unit with the number.
- 28. PROBLEM SOLVING TECHNIQUES 1. Read the problem carefully and identify the a) Unknowns b) knowns 2. Plan a solution a) Use a formula b) Use conversion factors i.e. 60sec = 1min, 60min = 1hr, etc. 3. Do calculation always including units 4. Finish up a) Reread the problem b) Check the units c) Estimate the answer d) Give your answer clearly, put a box around your answer.