Dimensional AnalysisDimensional Analysis

How to do dimensional analysisHow to do dimensional analysis

1.1. Identify the “given” and the “getIdentify the “given” and the “get

2.2. Create a “mini road map”Create a “mini road map”

3.3. Identify the conversion factors you will use Identify the conversion factors you will use based on your “mini road map”based on your “mini road map”

4.4. Set-up your equationSet-up your equation Start with the given, followed by the conversion Start with the given, followed by the conversion

factors, ending with the getfactors, ending with the get

5.5. Cancel units, calculate and report the answer Cancel units, calculate and report the answer to the correct number of significant figuresto the correct number of significant figures

What are conversion factors?What are conversion factors?

Values that are equivalent to each other, but Values that are equivalent to each other, but have different unitshave different units

Conversion factors are used to convert from a Conversion factors are used to convert from a certain unit to a different unitcertain unit to a different unit• ie. 1 ft = 12 inie. 1 ft = 12 in• 100 cm = 1m100 cm = 1m

How do you make a conversion How do you make a conversion factor?factor?

Determine two values that are equal to Determine two values that are equal to each other then put one over the other…each other then put one over the other…numeratornumerator

denominatordenominator

examplesexamples

QuestionsQuestions

1.1. How do you know which factor to put in How do you know which factor to put in the numerator and which to put in the the numerator and which to put in the denominator?denominator?

AnswerAnswer

It depends…you want the units to cancel It depends…you want the units to cancel out, so line up the factors so that they out, so line up the factors so that they cancel outcancel out

How many inches in 3.10 miles?How many inches in 3.10 miles?

How many seconds in 1.00 year? How many seconds in 1.00 year? (not a leap year) (not a leap year) (3.15 x 10(3.15 x 1077 sec) sec)

Worksheet: DA part I #1-6Worksheet: DA part I #1-6

1. A plane skids 8,345 inches on the 1. A plane skids 8,345 inches on the runway before coming to a stop. How runway before coming to a stop. How many miles is this?many miles is this?

2. A jogger runs 5.0 x 102. A jogger runs 5.0 x 1055 cm each morning. cm each morning. How many kilometers is this? How many kilometers is this?

                 

3. An outboard motor requires exactly two 3. An outboard motor requires exactly two cups of oil to be mixed with gasoline for cups of oil to be mixed with gasoline for each tankful. How many gallons is this?each tankful. How many gallons is this?

4. A pretzel factory orders salt by the half ton. 4. A pretzel factory orders salt by the half ton. How many ounces of salt are there in 0.50 ton of How many ounces of salt are there in 0.50 ton of salt?salt?

5. A person ingests 1,500 mg of vitamin C each 5. A person ingests 1,500 mg of vitamin C each day. How many kilograms is this?day. How many kilograms is this?

6. An active dog travels 2.5 miles on his run 6. An active dog travels 2.5 miles on his run everyday. How many inches is this?everyday. How many inches is this?

Worksheet: DA part 2Worksheet: DA part 2

1. A cross country runner travels 3.75 kilometers 1. A cross country runner travels 3.75 kilometers through the woods. How many miles is this?through the woods. How many miles is this?

2. How many miles long is a 1,600 meter 2. How many miles long is a 1,600 meter race?race?

3. How many fluid ounces are there in a 2.0 3. How many fluid ounces are there in a 2.0 liter bottle of soda?liter bottle of soda?

4. A one-cup measure contains 8.0 fluid 4. A one-cup measure contains 8.0 fluid ounces. How many milliliters is this?ounces. How many milliliters is this?

5. Fruits and vegetables are sold by the half 5. Fruits and vegetables are sold by the half kilogram in Europe. How many pounds are there kilogram in Europe. How many pounds are there in 0.50 kg?in 0.50 kg?

6. A rectangular container measures 2.0 cm by 3.0 6. A rectangular container measures 2.0 cm by 3.0 cm by 4.0 cm. How many fluid ounces can it hold cm by 4.0 cm. How many fluid ounces can it hold if filled to capacity?if filled to capacity?

Worksheet: DA Part IIIWorksheet: DA Part III 1. The velocity of light in a vacuum is 3.00 x101. The velocity of light in a vacuum is 3.00 x101010

cm/sec. How many miles per hour is this?cm/sec. How many miles per hour is this?

#2 A bicyclist is traveling 12 miles/hr down a #2 A bicyclist is traveling 12 miles/hr down a country road. How many meters per second is country road. How many meters per second is this?this?

#3 A car travels on the freeway with a velocity of 3.8 x 10#3 A car travels on the freeway with a velocity of 3.8 x 1033 cm/sec. Is it likely to get a ticket?cm/sec. Is it likely to get a ticket?

#4 A faucet drips 5 drops of water each second. How #4 A faucet drips 5 drops of water each second. How many gallons of water will it drip in one year (if left without many gallons of water will it drip in one year (if left without interruption and it is not a leap year). ( 20 drops = 1 mL)interruption and it is not a leap year). ( 20 drops = 1 mL)

#5 An assembly line produces 22 gaskets per #5 An assembly line produces 22 gaskets per second. How many packages-of-100 gaskets can second. How many packages-of-100 gaskets can be made each hour?be made each hour?

#6 Apples cost 79 cents per pound. At the same #6 Apples cost 79 cents per pound. At the same rate of cost, how many dollars will these same rate of cost, how many dollars will these same apples cost per kilogram?apples cost per kilogram?