Dimensional Analysis

Dimensional Analysis

Appendix E

Converting to different units of measure.

Convert 12 feet into yards.

12 ft = 4 yds

because

1 yd = 3 ft

        1 yd
                      =     1
        3 ft

and multiplying by 1 does not change the value (property of real numbers).

        12 ft
                    x 1 yd   =   4 yds
           3 ft

the ft cancel to give answer in yds.

How to determine what is numerator and denominator.

What if we had

                 3 ft
   12ft x                   =    ?
                  1 yd

Does not give us the answer in yards because the ft do not cancel.

Exercise 1:

Change

40miles/hr into feet/min

1 mi = 5280 ft 1 hr = 60 min

Do one step at a time:

40 mi/hr x 5280 ft/mi = 40x5280ft/hr

40x5280ft/hr x 1 hr/60min = 40x5280ft/60min

= 3520 ft/min

How many feet will a car travel in 2 minutes if the car is going 40 mi/hr?

3520 ft/min x 2 min = 7040 ft.

Exercise 2:

Conversions are needed to change US standard system into the Metric system.

1 meter = 39.37 inches

1 kilometer = 1000 meters

find

1 kilometer = ? inches = 39370 inches

1 gram = 0.0022046 lbs

1 kilogram = 1000 grams

1 kilogram = ? lbs = 2.2046 lbs

Note: ever wonder why lbs represent pounds? ( The Latin word libras means stones used for measuring weight on scales)