Dimensional Analysis Contents:•Handy things to know•Ways to convert•Whiteboard practice

Handy things to know:

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1 hr = 60 min = 3600 sec1 km = 1000 m .6214 mile1 mile = 5280 ft = 1760 yards 1610 m1 m 3.281 ft1 yard = 3 feet

Shortcuts:1 m/s = 3.6 km/hr 2.237 mph,1 mph 1.47 f/s (1.46666666…)1 f/s .682 mph (.6818181818…)

Ways to convert units:

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1. Unit cancellation2. Calculator’s built in (TI 85/86)3. Conversion factors4. Google

Unit cancellation: 30. mph to ft/s:

30. mi(5280 ft)( 1 hr ) hr ( 1 mi )(3600 s) = 44 f/s (note the units canceling)

Conversion factor: 30. mph to ft/s: (1 mph = 1.47 f/s)30. mph x (1.47) = 44.1 = 44 ft/s (slightly off - what’s the “real” conversion factor?)

Google: Type 30. mph in ft/s into the search bar

Calculator (TI 85/86)2nd CONV, MORE, MORE, SPEED, 30 mi/hr > ft/s

Whiteboards: Conversions1 | 2 | 3 | 4 | 5

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Convert 32 mile/hour to feet/second5280 ft = 1 mi3600 s = 1 hr

32 mi(5280 ft)( 1 hr ) = 46.933333 hr ( 1 mi )(3600 s)

47 f/s (2 sig figs)

47 f/s W

Convert 88.0 feet/second to mph5280 ft = 1 mi3600 s = 1 hr

88 ft( 1 mi )(3600 s) = 60 mph s (5280 ft)( 1 hr )

60.0 mph

60.0 mph W

Convert 27.2 m/s to km/hr1000 m = 1 km3600 s = 1 hr

27.2 m ( 1 km )(3600 s) = 97.92 km/hr s (1000 m)( 1 hr )

97.9 km/hr

97.9 km/hr W

Convert 110. km/hr to m/s1000 m = 1 km3600 s = 1 hr

110 km (1000 m)( 1 hr ) = 30.55556 m/s hr ( 1 km )(3600 s)

30.6 m/s

30.6 m/s W

Convert 110. km/hr to mph1 km .6214 mile3600 s = 1 hr ??

110 km (.6214 mi) = 68.354 mph hr ( 1 km )

68.4 mph

68.4 mph W