Topic 1 Physics and Physical Measurement 1.1 The Realm of Physics - Range of magnitudes of quantities in our universe.

1.1.1 State (express) quantities to the nearest order of magnitude. When dealing with very large or very small numbers we are often only interested in an approximate figure. For example, the remotest object we can detect is the quasar RDJ030117 located at a distance of 2.8X1022 km away. It is just as meaningful to say it is 1022 km from Earth. This is said to be its order of magnitude.

Order of magnitude The order of magnitude is the power of 10 closest to the number. However, when converting a number a number to its nearest base 10, the rule is: Numerals greater than 3.16 become 10 and those below 3.16 become zero. The reason for this is that 100.5 = 3.16

Try this quick quiz Measurement Dimension OM 1.9 x 1022 m 4.0 x 1016 m Distance to the Andromeda Galaxy 1.9 x 1022 m Distance to nearest star 4.0 x 1016 m Diameter of the Earth 1.3 x 107 m Thickness of a credit card 5.0 x 10-4 m Thickness of hair 2.8 x 10-5 m Mass of Hydrogen 1.67 x 10-5 kg

Calculations in OM’s When estimating the order of magnitude of a mathematical calculation, it is convenient to convert each number to its order of magnitude first. Example: Determine the order of magnitude of this calculation (3.0 x 1010)(8.4 x 106) Solution 3.0 x 1010 has an OM of 1010; 8.4 x 106 has an OM of 107 1010 x 107 = 1017 Note the full answer is 2.52 x 1017, which does have an OM of 1017.

1.1.2 State the ranges of magnitude of sizes, masses and times that occur in the universe, from smallest to greatest. Sizes—from 10-15 m to 10+25 m (subnuclear particles to extent of the visible universe). Masses—from 10-30 kg to 10+50 kg (electron to mass of the universe). Times—from 10-23 s to 10+18 s (passage of light across a nucleus to the age of the universe).

1.1.3 State and compare the order of magnitude of selected (significant) systems in the universe. Rounding the height of an ant, which is about 8 x 10-4 meters, to the nearest power of ten results in 10-3 meters. Another way of saying this is that the order of magnitude of the height of an ant is 10-3 meters. Now, if we compare the height of a human being (100 meters) with the height of an ant (10-3 meters), we come up with the ratio human height/ant height = 100/10-3 = 10 0 - (-3) = 103 = 1000. A human being is roughly 1000 times (or 103 times) taller than an ant. In other words, a human being is 3 orders of magnitude (3 powers of 10) taller than an ant.

Order of Magnitude of some Masses  Order of Magnitude of some Lengths  MASS  grams  LENGTH  meters  electron 10-27  radius of proton  10-15  proton 10-24  radius of atom  10-10  virus 10-16  radius of virus  10-7  amoeba 10-5  radius of amoeba  10-4  raindrop 10-3  height of human being  100  ant 100  radius of earth  107  human being 105  radius of sun  109  pyramid 1013  earth-sun distance  1011  earth 1027  radius of solar system  1013  sun 1033  distance of sun to nearest star  1016  milky way galaxy 1044   radius of milky way galaxy  1021  the Universe 1055   radius of visible Universe  1026

Great Web Sites Measurement (timeline form) http://www.alcyone.com/max/physics/orders/metre.html View the Milky Way at 10 million light years from the Earth. Then move through space towards the Earth in successive orders of magnitude until you reach a tall oak tree just outside the buildings of the National High Magnetic Field Laboratory in Tallahassee, Florida. After that, begin to move from the actual size of a leaf into a microscopic world that reveals leaf cell walls, the cell nucleus, chromatin, DNA and finally, into the subatomic universe of electrons and protons. http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html