Dimensional Analysis Practice Problems
Please set up your equations in the general form shown below, following the 3 steps for solving any unit analysis problem. Unit factors with the sign are defined (exact) quantities.
1) Write down the given units. 2) Write down the units asked for in the answer. 3) Apply one or more unit factor(s) to convert the given units to the units in the answer.
Units Given Unit Unit Unit Factor Factor Factor = Units Asked For
1) The rod and the furlong are both units of distance. Find the number of furlongs in 500 rods.
1 furlong 750 rods
1 furlong 500 rods = 0.667 furlongs 750 rods
2) Pharmacists work in units known as apothecary units. In this system of units, the typical aspirin tablet contains 5 grains of the active ingredient (acetylsalicylic acid). Express this weight in kilograms.
20 grains (gr) 1 scruple (sc); 3 scruples 1 dram (dr); 8 drams 1 ounce (oz); 1 ounce = 31.103 grams; 1 kilogram (kg) 1000 grams (g)
1 sc 5 gr 1 dr 1 oz 31.103 g 1 kg = 3 x 10-4 kg 20 gr 3 sc 8 dr 1 oz 1000 g
3) The distance run in a marathon is 26.2 miles. How long (in hours) would it take a runner to complete the race assuming an average speed of 425 centimeters per second (cm/s)?
1 foot (ft) 12 inches (in); 2.54 centimeters (cm) 1 in; 1 hour (hr) 60 minutes (min); 1 min 60 seconds (s)
12 in 26.2 mi 5280 ft 2.54 cm 1 sec 1 min 1 hr = 2.76 hrs 1 mi 1 ft 1 in 425 cm 60 sec 60 min
4) Approximately 40 billion kilograms of sulfuric acid, H2SO4 is produced annually in the United States. Express this rate of production in units of pounds per day.
1 ounce (oz) = 28.35 grams (g); 1 kilogram (kg) 1000 grams (g); 1 pound (lb) 16 ounces; 365 days (d) = 1 year (yr)
9 40 x 10 kg 1000 g 1 oz 1 lb 1 yr 2 x 108 lbs = 1 yr 1 kg 28.35 g 16 oz 365 days day
5) The acre was originally defined as the area of land that a team of oxen could plow in one day. Express this rate in square meters per hour using the following modern conversion factors.
1 acre 4840 square yards (yd2); 3 feet (ft) 1 yard (yd); 12 inches (in) 1 ft; 2.54 centimeters (cm) 1 inch (in); 8 hours (hr) = 1 working day (wd)
2 2 2 2 2 1 acre 4840 yd 3 ft 12 in 2.54 cm 1 m 1 day 1 day 1 acre 1 yd 1 ft 1 in 100 cm 8 hrs
506 m2 = hr