Dimensional Analysis

1
Dimensional Analysis

• Solving Quantitative Problems
• 4 steps
• Step 1 Analyze
• List all given measurements.
• List the unknown measurements with units.

2
Dimensional Analysis

• Step 2 Plan
• Decide which conversion factors, and/or equations
  to use.
• Write out the complete setup, including units.
• If the units cancel to give the answer in the
  correct units, the setup is correct.

3
Dimensional Analysis

• Step 3 Compute
• Substitute the given information and conversion
  factors.
• Cancel units, calculate the answer and round off
  to the correct significant figures.

4
Dimensional Analysis

• Step 4 Evaluate.
• Estimate what the answer should be.
• Is your answer realistic?

5
Dimensional Analysis

• Example
• How many seconds are there in one year? Assume
  exactly 365 days per year.
• Step 1 Analyze
• Given 1 year
• Unknown ?seconds

6
Dimensional Analysis

• Step 2 Plan
• Year days hours mins sec
• 1 year x days x hr x min x sec
• year day hr min

7
Dimensional Analysis

• Step 3 Compute
• 1 yr x 365 days x 24 hr x 60 min x 60 sec
• 1 yr 1 day 1 hr 1
  min
• 31 536 000 seconds
• 3.1536000 x 10 7 s
• Step 4 Evaluate
• 300 x 20 x 60 x 60 21 600 000
• 2 x 107