Problem Solving:

Objectives:

1.    Write conversion factors from given unit equalities.

2.    Explain how conversion factors are used in dimensional analysis.

3.    Name and describe the four steps of problem solving strategy.

4.    Explain why graphs are often used to display experimental data.

Key Terms:

dimensional analysis    percent error    conversion factor

Web Resources:

Notes:

Dimensional Analysis:

Dimensional analysis is the name given to the process of converting units.

Example:  Convert the following to SI units.  75km/hr (Remember SI for length is the meter and SI for time is the second.)

75km x 1000m x    h      = 75000m = 20.8333m/s or 2.1x101m/s (2 significant digits)

h   x    km    x 3600s       3600s

The above problem was solved taking advantage of conversion factors or what is called unit equalities. (1km = 1000m)  Dimensional analysis is simply the method of organizing the unit equalities into an equation.

Strategies:

1)    Always place your given amount (75km/h) on the left side of the problem.

2)    Next place the units that you want to end up with  last and orient them so that the units that you don't want will cancel out.  In the case of the problem above I wanted to end up with m/s so I started with the unit equalities 1000m = 1km and 1h = 3600s.
 Notice that I placed the meters and seconds in the appropriate orientation for my desired answer. Place units to cancel on a diagonal so that they cancel out completely

3)    Check your setup by canceling any unwanted units.

4)    Solve the entire upper and lower portions of the equation.

5)    Reduce the final amount and round to the appropriate significant digits.