Unit 0.2 Powerpoint – Dimensional Analysis

Example 2002

• Estimate the potential reduction in petroleum consumption (in gallons of gasoline per year) that could be achieved in the United States by introducing electric vehicles under the following assumptions:

• 1. The mileage rate for the average car is 25 miles per gallon of gasoline

• 2. The average car is driven 10,000 miles per year. • 3. The united states has 150 million cars • 4. 10 percent of the United States cars could be

replaced with electric vehicles.

Step 1

• Determine the final units

– Hint they gave it to you in the question

– This is not always the case

Step 1

• Determine the final units

– Hint they gave it to you in the question

– This is not always the case

– Final units: gallons/year

Step 2

• Write the equation, using the units as you go along as a guide:

– A) pick one of the final units as your starting point:

– 25 miles per gallon, we can write it as

25 miles OR gallons

gallon 25 miles

• B) now we have gallons on top and miles on the bottom, we need to cancel miles use 10,000 miles per year, the miles will cancel and we get year

10,000 miles

year

• C) we now include all the cars

150 million

1

• D) now include the 10% of cars being replaced

10%

1

• Solve for the math:

400 x 150 = 4 x 15 (add 3 zeros after the multiplication) = 60 (add three zeros) = 60,000 then the units = 60,000 million = 60 billion

Assignment

1. Your car's gas tank holds 18.6 gallons and is one quarter full. Your car gets 16 miles/gal. You see a sign saying, "Next gas 73 miles." Your often-wrong brother, who is driving, is sure you'll make it without running out of gas. You're not so sure and do some quick figuring:

Answer

Sample APES Math #2

• A group of AP Environmental teachers were sitting around the table discussing the full coal cars heading east to several big cities and the empty cola cars returning to the mines in the west. They were wondering how much energy was in each coal car and how long the coal would last. In addition, they discussed the environmental impact of mining the coal across vast lands.

• A) A large, coal-fired power plant produces 48 million kilowatt-hours of electricity each day. Assume the following, 10,000 BTU’s is required to produce 1 kWh of electricity, 1 pound of coal produces 5,000 BTU’s of heat, each coal car can hold 120 tons, 1 ton is 2000 pounds.

• i) Determine how much heat in BTU’s is needed to produce the power each day.

• ii) How many coal cars will be needed to operate the power plant for the day.

• Iii) How many trains will be needed to power the plant for a day if the train pulls 100 coal cars

• B) Coal mines in the west tend to be strip mines. Describe how strip mines are mined to obtain coal. Discuss one environmental impact of strip mining.

• Strip top mining is a practice where coal companies literally strip the surface of an area until they reach the mineral/material that they are after. This is used in areas where the “overburden” i.e. material that is not used or needed is thin and the material that is wanted is fairly close to the top of the ground.

• This practice leads to major erosion and flooding in areas. Strips the land of habitats and natural vegetation necessary for organisms of that region. Reclaiming the land post strip mining it is a positive practice but still typically does not involve native vegetation but rather quick growing plants that don’t support the biodiversity of the area.