Solving Problems with Dimensional Analysis
Dimensional analysis is a problem-solving strategy that used to check for errors or find
solutions (without knowing how to solve the problem!). It uses the fact that units must be
consistant to determine what is unknown by using what is known. It involves the
following five basic steps:
1) Unknown: Specify the dimensions (length, time, mass, etc.) of the desired quantity
(the unknown). These will become the target dimension for your equation
2) Knowns: Specify the dimensions of all the known values
3) Equation: Manipulate the the dimensions of the known (by multiplying and dividing)
on the left side of an equation to obtain the dimension of the unknown on the right side
4) Calculation: Now that you know what operations required, perform the calculations
by placing the values of the knowns and unknowns with their respective units.
Conversion factors might be required.
(1) Traffic accident investigators often discuss reaction time when trying to determine
liability for an accident. If a person’s reaction time is 1.5 seconds, how many meters will
his or her car travel before the brakes are activated if the car is traveling at 70 miles per
hour? (1 mile = 1600 m)
(2) In 1976 the United States successfully landed Viking1 on the surface of Mars.
Twenty years later, in 1997, NASA landed another robotic probe named the Mars
Pathfinder at a distance of 520 miles from the Viking1 landing site. Unlike the Viking
mission, the Pathfinder mission included a surface rover. Knowing the distances
between both landing sites, what would be the minimum number of hours required to
drive the rover to the Viking site assuming a top speed of 0.70 centimeters per second?
3) In Europe gasoline is sold by the liter. An average car fills up with 14 gallons, how
many liters will it take? (1L = 0.26 gallons)
4) The price of gasoline in Europe is about $2.20/L, how many dollars will it take to fill
the tank?