Honors Physics
Review: Problem Solving By Dimensional Analysis
Directions: Solve the following problems on another sheet of paper. You must demonstrate your
ability to use Dimensional Analysis (Factor Label Method) in order to receive full credit. Show all
work, round all answers to the correct number of significant digits, and label answers with the correct
units.
1. During a recent baseball game, a pitcher threw a fastball that had a velocity of 93.7 mph. Calculate
the velocity in m/s.
? m/s = (93.7 miles/hr) ( 1 hr/3600 s) (1609 m/mile)= 41.9 m/s
2. Calculate how long it took the pitch in problem #1 to travel from the mound to home plate (60 ft 6 in).
Answer: 0.044 seconds
? s = (726 in) (1 ft/12 in) (1 mile/5280 ft) (1 hr/93.7 miles) (3600 s/ 1 hr) = 0.440 seconds
OR
? s = (726 in) (2.54 cm/ 1 in) (100 cm / 1 m) ( 1 s /41.9 m) = 0.440 seconds
3. If a student weighs 185 lb, what is his mass in µg? (1 kg = 2.21 lb)
? µg = (185 lb) (1 kg / 2. 21 lb) (1000 g / 1 kg) (1 x 106 µg/ 1 g) = 8.37 x 1010 µg
4. The density of the earth is about 3.5 g/cm3. If the earth has a radius of 7000 miles, what is its mass?
(V = 4∏r3/3) Volume = 4 (3.14) (7000)3 /3) = 1.44 x 1012 miles3
? g = (1.44 x 1012 miles3) ((1609 m)3/1 mile3) ((100 cm)3/1 m3)(3.5 g/cm3) = 2.1 x 1028 g
5. Which is less, 4 x 10-2 kg/cm3 or 4 x 10-1 mg/cm3? Answer: 4 x 10-1 mg/cm3
? mg/cm3 =( 4 x 10-2 kg/cm3 )(1000 g/1 kg) (1000 mg/1 g) = 40000 mg/cm3 > 4 x 10-1 mg/cm3
6. A parsec is an astronomical unit of distance. 1 parsec = 3.26 light years (or the distance traveled by
light in one year.) Light speed = 186,000 miles per second. An object travels 9.6 parsecs. Calculate this
distance in cm.
? cm =(9.6 parsecs)(3.26 years/1 parsec)(365 days/1 year)(24 hours/1 day)(3600 s/1 hr)
(186,000 miles/s)(1609 m / 1 mile)(100 cm/1 m)=3.0 x 1019 cm