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1.2 Physical quantities and units  (Page 5/18)

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Approximate values of length, mass, and time
Lengths in meters Masses in kilograms (more precise values in parentheses) Times in seconds (more precise values in parentheses)
10 − 18 Present experimental limit to smallest observable detail 10 − 30 size 12{"10" rSup { size 8{ - "30"} } } {} Mass of an electron 9 . 11 × 10 − 31  kg size 12{9 "." "11" times "10" rSup { size 8{ - "31"} } `"kg"} {} 10 − 23 size 12{"10" rSup { size 8{ - "23"} } } {} Time for light to cross a proton
10 − 15 size 12{"10" rSup { size 8{ - "15"} } } {} Diameter of a proton 10 − 27 size 12{"10" rSup { size 8{ - "27"} } } {} Mass of a hydrogen atom 1 . 67 × 10 − 27  kg size 12{1 "." "67" times "10" rSup { size 8{ - "27"} } `"kg"} {} 10 − 22 size 12{"10" rSup { size 8{ - "22"} } } {} Mean life of an extremely unstable nucleus
10 − 14 size 12{"10" rSup { size 8{ - "14"} } } {} Diameter of a uranium nucleus 10 − 15 size 12{"10" rSup { size 8{ - "15"} } } {} Mass of a bacterium 10 − 15 size 12{"10" rSup { size 8{ - "15"} } } {} Time for one oscillation of visible light
10 − 10 size 12{"10" rSup { size 8{ - "10"} } } {} Diameter of a hydrogen atom 10 − 5 size 12{"10" rSup { size 8{ - 5} } } {} Mass of a mosquito 10 − 13 size 12{"10" rSup { size 8{ - "13"} } } {} Time for one vibration of an atom in a solid
10 − 8 size 12{"10" rSup { size 8{ - 8} } } {} Thickness of membranes in cells of living organisms 10 − 2 size 12{"10" rSup { size 8{ - 2} } } {} Mass of a hummingbird 10 − 8 size 12{"10" rSup { size 8{ - 8} } } {} Time for one oscillation of an FM radio wave
10 − 6 size 12{"10" rSup { size 8{ - 6} } } {} Wavelength of visible light 1 size 12{"1"} {} Mass of a liter of water (about a quart) 10 − 3 size 12{"10" rSup { size 8{ - 3} } } {} Duration of a nerve impulse
10 − 3 size 12{"10" rSup { size 8{ - 3} } } {} Size of a grain of sand 10 2 size 12{"10" rSup { size 8{2} } } {} Mass of a person 1 size 12{"1"} {} Time for one heartbeat
1 size 12{"1"} {} Height of a 4-year-old child 10 3 size 12{"10" rSup { size 8{3} } } {} Mass of a car 10 5 size 12{"10" rSup { size 8{5} } } {} One day 8 . 64 × 10 4 s size 12{8 "." "64" times "10" rSup { size 8{4} } `s} {}
10 2 size 12{"10" rSup { size 8{2} } } {} Length of a football field 10 8 size 12{"10" rSup { size 8{8} } } {} Mass of a large ship 10 7 size 12{"10" rSup { size 8{7} } } {} One year (y) 3 . 16 × 10 7 s size 12{3 "." "16" times "10" rSup { size 8{7} } `s} {}
10 4 size 12{"10" rSup { size 8{4} } } {} Greatest ocean depth 10 12 size 12{"10" rSup { size 8{"12"} } } {} Mass of a large iceberg 10 9 size 12{"10" rSup { size 8{9} } } {} About half the life expectancy of a human
10 7 size 12{"10" rSup { size 8{7} } } {} Diameter of the Earth 10 15 size 12{"10" rSup { size 8{"15"} } } {} Mass of the nucleus of a comet 10 11 size 12{"10" rSup { size 8{"11"} } } {} Recorded history
10 11 size 12{"10" rSup { size 8{"11"} } } {} Distance from the Earth to the Sun 10 23 size 12{"10" rSup { size 8{"23"} } } {} Mass of the Moon 7 . 35 × 10 22  kg size 12{7 "." "35" times "10" rSup { size 8{"22"} } `"kg"} {} 10 17 size 12{"10" rSup { size 8{"17"} } } {} Age of the Earth
10 16 size 12{"10" rSup { size 8{"16"} } } {} Distance traveled by light in 1 year (a light year) 10 25 size 12{"10" rSup { size 8{"25"} } } {} Mass of the Earth 5 . 97 × 10 24  kg size 12{5 "." "97" times "10" rSup { size 8{"24"} } `"kg"} {} 10 18 size 12{"10" rSup { size 8{"18"} } } {} Age of the universe
10 21 size 12{"10" rSup { size 8{"21"} } } {} Diameter of the Milky Way galaxy 10 30 size 12{"10" rSup { size 8{"30"} } } {} Mass of the Sun 1 . 99 × 10 30  kg size 12{1 "." "99" times "10" rSup { size 8{"30"} } `"kg"} {}
10 22 size 12{"10" rSup { size 8{"22"} } } {} Distance from the Earth to the nearest large galaxy (Andromeda) 10 42 size 12{"10" rSup { size 8{"42"} } } {} Mass of the Milky Way galaxy (current upper limit)
10 26 size 12{"10" rSup { size 8{"26"} } } {} Distance from the Earth to the edges of the known universe 10 53 size 12{"10" rSup { size 8{"53"} } } {} Mass of the known universe (current upper limit)

Unit conversions: a short drive home

Suppose that you drive the 10.0 km from your university to home in 20.0 min. Calculate your average speed (a) in kilometers per hour (km/h) and (b) in meters per second (m/s). (Note: Average speed is distance traveled divided by time of travel.)

Strategy

First we calculate the average speed using the given units. Then we can get the average speed into the desired units by picking the correct conversion factor and multiplying by it. The correct conversion factor is the one that cancels the unwanted unit and leaves the desired unit in its place.

Solution for (a)

(1) Calculate average speed. Average speed is distance traveled divided by time of travel. (Take this definition as a given for now—average speed and other motion concepts will be covered in a later module.) In equation form,

average speed = distance time . size 12{"average speed = " { {"distance"} over {"time"} } } {}

(2) Substitute the given values for distance and time.

average speed = 10 . 0  km 20 . 0  min = 0 . 500  km  min . size 12{"average speed = " { {"10" "." 0" km"} over {"20" "." 0" min"} } =0 "." "500" { {"km"} over {"min"} } } {}

(3) Convert km/min to km/h: multiply by the conversion factor that will cancel minutes and leave hours. That conversion factor is 60 min/hr size 12{"60 min/hr"}{} . Thus,

average speed = 0 . 500  km  min × 60  min 1  h = 30 . 0  km  h . size 12{"average speed = "0 "." "500" { {"km"} over {"min"} } times { {"60"" min"} over {1" h"} } ="30" "." 0 { {"km"} over {h} } } {}

Discussion for (a)

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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