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One liter $\left(1000 \mathrm{cm}^{3}\right)$ of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick just one molecule thick, with adjacent molecules just touching, estimate the diameter of the oil slick. Assume the oil molecules have a diameter of $2 \times 10^{-10} \mathrm{m}$ .

$3 \times 10^{3} \mathrm{m}$

Physics 101 Mechanics

Chapter 1

Introduction, Measurement, Estimating

Physics Basics

University of Washington

Hope College

University of Sheffield

Lectures

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One liter (1000 cm$^3$) of…

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our question states that one leader or 1,000 cubic centimeters of oil is spilled onto a smooth lake. If the oil spreads out uniformly until it makes an oil slick, just one molecule thick with adjacent molecules touching. Estimate the diameter of that oil slick. Assume the oil molecules have a diameter of two times 10 to the minus 10 meters. Okay, so I wrote down here what we have given in the question. It tells us the thickness of the oil, which is the diameter of the molecules. And I wrote that thickness is tea, which is equal to two times 10 to the minus 10 meters. The volume of the oil in question is 1,000 cubic centimeters, which I convert to cubic meters by multiplying it by the conversion between meters and centimetres, where one meter is equal to 100 centimetres. You cube that because we're dealing with volume and we want cubic meters from cubic centimeters. This gives us a 0.1 cubic meters. Question then, is how big is the diameter of this oil slick? If we're assuming it's spreading out and a spiritual or circular, a manner, well, the volume of the oil is equal to the area of the oil multiplied by the thickness of the oil. Okay, well, the area is equal to pi r squared, right? And then that's gonna be multiplied by the thickness of the oil. Because Pyrrhus squared is the area of a circle, well, are is equal to diameter. So the radius is equal to half the diameter, right? So we know what our is equal to its equal to pi r is equal to de divided by two the diameter divided by two squared times the thickness. So now we have our equation for volume is equal to pi times the diameter divided by two squared times the thickness Well, we know the volume and we know the thickness so and pious just a constant. So we need to solve for the diameter and we will be able to calculate our question or, ah, the solution. Your question. So the diameter squared will just leave it a squared. For now. Excuse me. Diameter squared is equal to, um the volume. Right. So you have the volume on one side of the equation. You need divide that by the thickness. So it's equal to the volume divided by the thickness. You also need to divide the volume by pie. So one over pi and then the two squared is on the bottom on the right hand side of the equation. So when you're putting it in, terms of d'you need to multiply of the volume by two squared to square, just being four. Okay, so now we can again rewrite this in terms of D by taking the square root of each side so D is equal to the square root of four times the volume divided by the thickness terms play Okay, So if you plug in everything that you would need for this equation which we already have the volume A 0.1 cubic meters and the thickness is two times 10 to the minus 10. You get 2,000 500 in 23 approximately, and there's a couple of decimal places there, Right, this is approximately, but in the question, we're given the thickness as two times 10 to the minus 10. This has one significant figure so well, our maximum accuracy. We can report to his one significant figure so we can round this to 3,000 or Mrs Meters. Excuse me. I forgot dimensions. Three, 3,000 or three times. 10 to the third meters. Go ahead box than it.

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