The Ecology of Hope

Science Workshop #3

Units & Estimation Problems



1) Estimate the number of people who are born in the world every day. (Hint: how likely is it that a woman of child-bearing age will give birth in a given year?)
 

2) For every gallon of gasoline burned by a motor vehicle, approximately 20 pounds of carbon dioxide is released into the atmosphere. Estimate the mass of carbon dioxide emitted by the vans we drove during last week's field trip.
 

3) Imagine you are given one dollar every second. How long would it take you to accumulate one thousand dollars ($103)? one million dollars ($106)? one billion dollars ($109)? one trillion dollars ($1012)? Express these times in the most convenient units applicable, i.e., hours, days, or years.
 

4) Express the speed at which your fingernails grow in miles per hour. (Hint: first estimate the speed in terms of units such as inches per month)
 

5) How many cubic feet are in one cubic mile? (1 mile = 5,280 feet)
 

6) Mercury is an exceptionally dense liquid. In metric units, its density is 13 g/mL. How many pounds would one gallon of mercury weigh? (1 pound = 454 g; 1 gallon = 3.78 L)
 

7) The annual volume of water that flows through the Columbia River at the Dalles is 133 million acre-feet. The height of Lake Celilo, which was formed by the Dalles dam, is 90 feet above the Columbia just downstream of the dam. Using the relationship, PE = mgh, what is the total potential energy (in joules) that is released in one year by water passing through the dam (g = 9.8 m/sec2)? (Hints: what is the definition of a joule?; 1 m = 3.3 feet; the mass of water can be obtained from its density, 1 kg/L; 1 ft3 = 7.5 gallons)

What is the average power, in watts, that this flow represents? (What is a watt?)

If the hydroelectric power could be stored, how long would it take to use the energy released in one year if it were used to light a single 100 watt light bulb?