How Big is the Oil Slick Created by Spilled Oil on a Lake?

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In summary, the problem involves estimating the diameter of an oil slick that forms when 1 liter of oil is spilled onto a lake and spreads out uniformly until it is three molecules thick. Using the equation V = (h)(pi)(r^2), the estimated diameter is calculated to be [sqrt 10m^3/(3)pi(2x10^-10)] *2.
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zelly15
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Homework Statement



One liter (1000 cm3) of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just three molecules thick, with adjacent molecules just touching, estimate the diameter of the oil slick. Assume the oil molecules have a diameter of 2 ✕ 10^-10m.

Homework Equations


V= (h)(pi)(r^2)

The Attempt at a Solution


[sqrt 10m^3/(3)pi(2x10^-10)] *2
 
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  • #2
You have a cube of oil 1000 cm^3 and once its dispersed you'll have a cylinder of oil whose height is 3 molecules thick.

Pay attention to units conversion as the cube's volume is in cm^3 whereas the diameter of the oil molecule is in meters.
 

1. Where does the three go?

The three refers to the number 3, and it can go in many different places depending on the context. In mathematics, it is commonly used as a digit in numerical operations. In language, it can be part of a word or phrase, such as "three blind mice." In a physical sense, it can be found as the third item in a sequence or the third point on a coordinate plane.

2. Why is the number three significant?

The number three has been considered significant in many cultures and belief systems throughout history. In mathematics, it is the first odd prime number and the only number that is both a triangular number and a perfect number. In religion and mythology, three often represents completeness or balance, such as the Holy Trinity in Christianity or the three Fates in Greek mythology. In everyday language, three is often used for emphasis or to create a pattern or rhythm.

3. How does the number three relate to patterns and cycles?

The number three is often associated with patterns and cycles because it is the smallest number that can create a repeating pattern. For example, a triangle has three sides and can be tessellated to create a pattern. In music, a chord is made up of three notes and can create a repeating melody. In nature, many cycles occur in threes, such as the stages of water (solid, liquid, gas) or the phases of the moon (new moon, full moon, waning moon).

4. Can the number three be divided evenly?

Yes, the number three can be divided evenly by 1 and 3. It is also a factor of many other numbers, such as 6, 9, and 12. However, it is not a factor of all numbers, as it cannot be divided evenly into odd prime numbers like 5 or 7. In mathematics, dividing a number by three is equivalent to finding one-third of that number, which can be represented as a decimal or fraction.

5. How is the number three used in measurements and time?

In the metric system, the number three is used as a prefix to indicate a value that is one thousand times larger or smaller than the base unit. For example, a kilometer is 1000 meters and a milliliter is 1/1000 of a liter. In time, three is often used to divide the day into three parts: morning, afternoon, and evening. It is also used to divide the year into four seasons, with each season lasting approximately three months.

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