Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric...
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Transcript of Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric...
![Page 1: Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric system to make measurements. SI units: System International.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ec05503460f94bcb5f3/html5/thumbnails/1.jpg)
Dimensional Analysis
Conversions of Units
![Page 2: Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric system to make measurements. SI units: System International.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ec05503460f94bcb5f3/html5/thumbnails/2.jpg)
UNITS
• The world-wide scientific community uses the metric system to make measurements.
• SI units: System International d’Unites
• SI units are related by powers of 10 (making it easy to convert between)
![Page 3: Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric system to make measurements. SI units: System International.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ec05503460f94bcb5f3/html5/thumbnails/3.jpg)
Fundamental Units
• Time: seconds (s)
• Length: metres (m)
• Mass: kilograms (kg)
• Other quantities can be described using these three units. Derived units are combinations of fundamental units.
• i.e. Speed: m/s
![Page 4: Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric system to make measurements. SI units: System International.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ec05503460f94bcb5f3/html5/thumbnails/4.jpg)
Definitions
• Note: You are NOT responsible for these definitions! They are just for knowledge sake!
• Distance (m): “The metre is the length of the path travelled by light in a vacuum during a time interval of 1/299 792 458 of a second.”
![Page 5: Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric system to make measurements. SI units: System International.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ec05503460f94bcb5f3/html5/thumbnails/5.jpg)
Definitions
• Note: You are NOT responsible for these definitions! They are just for knowledge sake!
• Mass (kg): “The kilogram is equal to the mass of the international prototype of the kilogram.”
![Page 6: Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric system to make measurements. SI units: System International.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ec05503460f94bcb5f3/html5/thumbnails/6.jpg)
Definitions
• Note: You are NOT responsible for these definitions! They are just for knowledge sake!
• Time (s): “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.”
![Page 7: Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric system to make measurements. SI units: System International.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ec05503460f94bcb5f3/html5/thumbnails/7.jpg)
Why do we need to convert units?
• They are EXACT so we can compare worldwide (even the USA).
• They are used by the scientific community and have been used since 1960.
![Page 8: Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric system to make measurements. SI units: System International.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ec05503460f94bcb5f3/html5/thumbnails/8.jpg)
Dimensional Analysis
• Identify the given or known data (information).
• Identify the unknown. • Plan the solution or calculations by either:
– setting up a series of conversion factors OR– using a formula
• Check your work by cancelling out units.
![Page 9: Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric system to make measurements. SI units: System International.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ec05503460f94bcb5f3/html5/thumbnails/9.jpg)
Example 1: Conversion within Fundamental SI units
• A space shuttle orbits the Earth at an altitude of 300 000 m. What is its altitude in:
• A) mm
• B) km
![Page 10: Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric system to make measurements. SI units: System International.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ec05503460f94bcb5f3/html5/thumbnails/10.jpg)
Example 2: Conversions between SI units and non-SI units
• Calculate the number of cm in 20 inches if you know that 1 inch = 2.54 cm.
![Page 11: Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric system to make measurements. SI units: System International.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ec05503460f94bcb5f3/html5/thumbnails/11.jpg)
Example 3: Multiple step conversions
• A person on a diet might lose 2.3 kg per week. Express the mass loss rate in mg per second.
![Page 12: Dimensional Analysis Conversions of Units. UNITS The world-wide scientific community uses the metric system to make measurements. SI units: System International.](https://reader036.fdocuments.in/reader036/viewer/2022082611/56649ec05503460f94bcb5f3/html5/thumbnails/12.jpg)
Questions for you…
• How many seconds are in 1 year? (note: 1 year is 365.25 days …)
• Both the 100 yard and the 100m dash are used in track events. Which is longer and by how much? (note: 1 yd = 0.9144 m)