Dimensional Analysis Worksheet

Dimensional Analysis Worksheet

Dimensional Analysis Worksheet

First identify the given value and the conversion factors.The given value almost always has only one unit. Example: 183 cm.

Conversion factorsalways have units in the form of a fraction: 2.54 or . Conversion factors may also be written as equalities: 2.54 cm = 1 inch, or 12 in = 1 ft,or they may be written in sentences: “There are 2.54 cm in one inch.”

Example: There are 2.54 cm per inch and 12 inches in a foot. How many feet are in 183 cm?

Step 1:Write the given value:183 cm

Step 2:Multiply by the first conversion factor so that cm will cancel and the remaining unit will be inches:

183 cm x (Note that you must invert the cm/inch conversion factor)

Step 3:Multiply by the second conversion factor so that inches will cancel and the remaining unit will be feet, then use your calculator to find the answer. Remember: after canceling units, “What’s left on the left you write on the right!”

183 cm x x = 6.00 ft

Problems

Write the following conversion factors in the form of fractions.

  1. 1 cal is 4.184 J
  2. There are 1,000 J in a kJ
  3. 1 Cal = 1,000 cal
  4. 1 Cal is the same as 1 kcal

Use the following given values to perform the conversions. Be sure your units cancel!

  1. Convert 10.0 cal to J
  2. Convert 10.0 J to cal
  3. How many cal is 86 Cal?
  4. Convert 120 Cal to joules.

Circle the given value in each problem. Then use dimensional analysis to perform the conversion. Show how units cancel.

  1. One pallet of bricks contains 1,020 bricks. How many bricks will you get if you buy
    6.5 pallets?
  2. A car gets 27 miles per gallon. How many gallons are required to drive from Sunnyvale to Berkeley, a distance of 52 miles?
  3. Gasoline costs $3.25 per gallon. How much does it cost to drive the 838 miles to Seattle if your car gets 27 miles per gallon?
  4. How far does light travel in 3.67 minutes? The speed of light 3.00 x 108 m/s.
  5. How many seconds are there in 7.00 days? There are 60 seconds per minute, 60 minutes in an hour and 24 hours in a day.
  6. You measure your heart rate at 65 beats per minute. How many times does your heart beat in one day?
  7. Your 76 pairs of chemistry students will be doing an experiment in which each pair will use a 0.100 g strip of copper. You know that a 1.00 cm strip has a mass of 0.0696 g. What length of copper strip do you need to buy?
  8. You are going to purchase $100 worth of gasoline for your boat. If gasoline is selling for $0.75/L and the density of gasoline is 0.750 kg/L, how much will the gasoline weigh?

Sometimes the given value will have two units in the form of a fraction and will look like a conversion factor.

Example: There are 1609 m in a mile. What is 100. km/h in mi/h?

100. x x = 62.2 mi/h

  1. What is the cost in dollars per liter of gasoline costing 3.25 dollars per gallon? There are
    3.785 L/gal.
  2. A satellite circling the earth is traveling at 7.44 km/s. What is this speed in miles per hour? There are 1.609 km in a mile.
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