Measurements in Physics

Historical Perspective Ancient Civilizations and Monarchies “Cubit” local customs were used Use of length foot to standardize measurement a king’s foot 1700’s Scientific Renaissance. France metric system, units of 10. 1960’s SI system is adopted worldwide Present Day: USA, Liberia, and Burma (or Myanmar) still use Empirical System of Measurement (inches, feet, pounds). The United Kingdom uses both systems. The solution is a rod or bar, of an exact length, kept in a central public place. From this 'standard' other identical rods can be copied and distributed through the community. In Egypt and Mesopotamia these standards are kept in temples. The basic unit of length in both civilizations is the cubit, based on a forearm measured from elbow to tip of middle finger. When a length such as this is standardized, it is usually the king's dimension which is first taken as the norm.

Physical Quantities Physical quantity: a physical property that can be measured (height, volume, temperature, and other physical properties). It is described by both a number and a unit of defined size. 61.2 kilograms number unit The number along isn’t useful without a unit. If you asked how much blood an accident victim had lost, the answer “tree” wouldn’t tell you much. Three drops? Three milliliters? Three pints? Three liters? (By the way, an adult human has only 5-6 liters of blood). Your car speed: 30 mi/hr, or km/hr, or m/s? All these values could give you completely different speed.

SI Units SI units: units of measurement defined by International System of Units; standard units agreed upon by scientists Mass is measured in kilograms (kg), length is measured in meters (m), volume is measured in cubic meters (m3), temperature is measured in kelvins (K), and time is measured in seconds (s). Any physical property can be measured in many different units. For example, a person’s height might be measured in inches, feet, yards, meters, or many other units. To avoid confusion, scientists from many countries have agreed on a system of standard units, called by the French name Systeme International d’Unites (International System of Units), abbreviated SI.

Metric System SI units are closely related to the more familiar metric units used in all industrialized nations of the world except the United States.

Comparing SI and Metric Units Some SI and Metric Units and Their Equivalents Quantity SI Unit (Symbols) Metric Unit (Symbol) Equivalents Mass Kilogram (kg) Gram (g) 1 kg=1000 g = 2.205 lb Length Meter (m) 1 m= 3.280 ft Volume Cubic meter (m3) Liter (L) 1 m3=1000L=264.2 gal Temperature Kelvin (K) Celsius Degree (⁰C) 1K = 1⁰C 1⁰C=1.8⁰F Time Second (s) ----- Although SI units are now preferred in scientific research, metric units are still used in some fields. In addition to these units, many other widely used units are derived from them. Speed, for example, is a distance covered in a given time and expressed in units of meter per second (m/s).

SI prefixes Prefix Symbol Meaning (fraction form) (decimal form) Example kilo- k 1000 1 kilogram (kg) = 1000 g hecto- h 100 1 hectogram (hg) = 100 g deka- da 10 1 decaliter (daL) = 10 L deci- d 1_ 0.1 1 deciliter (dL) = 0.1 L centi- c 0.01 1 centimeter (cm) = 0.01 m milli- m 1__ 0.001 1 milligram (mg) = 0.001g micro- μ 1____ 1000 000 0.000 001 1 micrometer (μm) = 0.000 001 m One problem with any system of measure is that the sizes of the units are often too large or too small for the problem at hand. A biologist describing the diameter of a red blood cell (0.000 006 m) would find the meter to be too large. However, astronomer measuring the average distance from the earth to the sun (150,000, 000, 000 m) would find the meter to be too small. For this reason, metric and SI units can be modified by prefixes to refer to either smaller or larger quantities. SI unit for mass – the kilogram – differs by the prefix kilo- from the metric unit gram. Kilo- indicates that that a kilogram is 1000 times larger then a gram. 1 kg = 1000 x 1g = 1000g Small quantities are often reported in milligrams (mg). The prefix milli- shows that the unit gram has been divided by 1000, which is the same as multiplying by 0.001: 1 mg = 1g/1000 = 1/1000 x 1g = 0.001 x 1g = 0.001g

Fundamental SI Units Fundamental SI units: Standard units agreed upon by scientists Mass: kilograms (kg) A measure of an object inertia or resistance to change in motion Length: meter (m) Distance between two points Time: seconds (s) How long?

Derived Units Derived Units: Combination of two or more fundamental units Volume: The cubic meter (m3) The amount of space occupied by an object Volume = length x width x height V = l x w x h Density: The physical property that relates the mass of an object to its volume Mass per unit volume: grams per cubic centimeter (g/cm3) for solids or grams per milliliter (g/mL) for liquids Density = mass (g) / volume (mL or cm3)

Measuring Mass Mass: A measure of an object inertia or resistance to change in motion A measure of the amount of matter in an object W eight: A measure of the gravitational force that the Earth, moon, or other large body exerts on the object. Mass and Weight: The amount of matter (mass) in an object does not depend on location. However, the weight of the object does depend on location. At the same location, two objects with identical masses have identical weights; that is, gravity pulls on both equally. Thus, the mass of an object can be determined by comparing the weight of the object to the weight of a known reference standard. Whether you are standing on the earth or on the moon, the mass of your body is the same. Your weight on earth might be 140 lb, but it would be 23 lb on the moon because the pull of gravity there is only about 1-sixth as great. We speak of “weighing” when we really mean that we are measuring mass by comparing two weights

Units of Mass Unit Equivalent 1 kilogram (kg) = 1000 grams (g) = 2.205 pounds (lb) 1 gram (g) = 0.001 kilogram (kg) = 1000 milligrams (mg) = 0.0035 27 ounce (oz) 1 milligram (mg) = 0.001 gram = 0.000 001 kilogram (kg) 1 ton (t) = 2000 pounds = 907.03 kilograms (kg) 1 pound (lb) = 16 ounces = 0.454 kilogram (kg) = 454 grams (g) 1 ounce (oz) = 0.028 35 kilogram (kg) = 28.35 grams (g) = 28,350 milligrams

Units of Mass The kilogram is a mass of platinum-iridium cylinder preserved at the International Bureau of Weight and Measures in France. It was defined as mass of one liter (1000 cubic centimeters) of water at the temperature at which it is most dense (4⁰C).

Measuring Length Length: Distance between two points The meter is the standard measure of length, or distance, in both the SI and metric systems. One meter is 39.37 inches, or about 10% longer than one yard. More commonly used measures of length are the centimeter (cm; 1/100 m) and the millimeter (mm; 1/1000 m) One centimeter is a bit less then half an inch = 0.3937 inch One millimeter is 0.039 37 inch, or about the thickness of a dime. One meter is a length that is much too large for many measurements

Units of Length

Units of Length

Units of Length 1 Meter: Was defined in terms of the distance from the North Pole to the equator. It equals approximately one ten-millionth of the distance from the North Pole to the equator. Equals the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second. This distance is close to 10 million meters.

Units of Time Time: The second is the SI unit of time Until 1956 it was defined in terms of the mean solar day. There were 86 400 seconds per day. Second was defined as 1/86400 of the mean solar day. However, the rate of rotation of the Earth is gradually slowing. In 1956 the mean solar day of the year 1900 was chosen as the standard on which to base a second. Since 1956, the second is defined as time taken by a cesium-133 atom to make 9 192 631 770 vibrations. One solar day was divided into 24 hours. Each hour was divided into 60 min and each min into 60 seconds.

Units of Volume Volume: The amount of space occupied by an object The SI unit for volume is the cubic meter, m3. It is so large that the liter (1 L = 0.001 m3 = 1 dm3) is much more commonly used. One liter has the volume of a cube 10cm (1 dm) on edge and is a bit larger then one U.S. quart. Each liter is further divided into 1000 milliliters (mL), with 1 mL the size of a cube 1 cm on edge, or 1 cm3

Units of Volume

Units of Volume