Posted: 5/13/2021 7:48:39 PM EDT
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I was trying to determine actual density of a copper wire for a project and the volume of insulated wire vs uninsulated (stripped same wire) isn't making sense. Wire with insulation diameter: 2.5 mm (1.25 mm radius) Wire length: 100 mm Wire volume: 491 mm^3 Wire without insulation diameter: 1.5 mm (0.75 mm radius) Wire length: 100 mm Wire volume: 176 mm^3 Ratio of diameters: 1.5/2.5 = 0.6 Ratio of volume: 0.36 Multiplying a number below 1 by itself results in a lower number, multiplying a number above 1 results in a higher number. I realize this is the cause but why are the two ratios not the same when the length is a constant? |
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Quoted: I was trying to determine actual density of a copper wire for a project and the volume of insulated wire vs uninsulated (stripped same wire) isn't making sense. Wire with insulation diameter: 2.5 mm (1.25 mm radius) Wire length: 100 mm Wire volume: 491 mm^3 Wire without insulation diameter: 1.5 mm (0.75 mm radius) Wire length: 100 mm Wire volume: 176 mm^3 Ratio of diameters: 1.5/2.5 = 0.6 Ratio of volume: 0.36 Multiplying a number below 1 by itself results in a lower number, multiplying a number above 1 results in a higher number. I realize this is the cause but why are the two ratios not the same when the length is a constant? The volume is a function of diameter^2. . |
| Take the unstripped wire, lower into a full container of water, measure the amount of displaced water, take the same wire, stripped, and lower into a full container of water, measure the amount of water displaced. The difference in volume of water displaced is the difference in volume between the two. |
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Quoted: The area of a circle increases at the square of its radius (or diameter). In your case one circle has a diameter of 1.5mm, the other has a diameter of 2.5. Divide 1.5 by 2.5 and you have 0.6. Square 0.6 and you have your 0.36. |
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Quoted: I think this is what others are saying as well but not as obviously. I assume you mean they aren't saying it as obviously? You know, internet text humanity filter and all. If so, good to know my way of explaining helped. Other than the treadmill comment and such, they were correct, though rather textbook. |
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Quoted: I was trying to determine actual density of a copper wire for a project and the volume of insulated wire vs uninsulated (stripped same wire) isn't making sense. Wire with insulation diameter: 2.5 mm (1.25 mm radius) Wire length: 100 mm Wire volume: 491 mm^3 Wire without insulation diameter: 1.5 mm (0.75 mm radius) Wire length: 100 mm Wire volume: 176 mm^3 Ratio of diameters: 1.5/2.5 = 0.6 Ratio of volume: 0.36 Multiplying a number below 1 by itself results in a lower number, multiplying a number above 1 results in a higher number. I realize this is the cause but why are the two ratios not the same when the length is a constant? A 50% increase is a 33% decrease, and you're talking percents. Start at 100. A 50% increase is 150. A 50% decrease of 150 is 75, a 33% decrease from 150 is 100. |
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Quoted: A 50% increase is a 33% decrease, and you're talking percents. Start at 100. A 50% increase is 150. A 50% decrease of 150 is 75. . . That has been a thorn in my side. People talk about a this and that percent decrease or increase, and I never know if that percentage is based on the total now, or the total then. They don't ever make it clear. I always figure that it's just one of the ways to lie with figures to the mass of people who don't look deeper. If there are 100 then and 300 now, there is a 300 percent increase. Or is it a 67% increase? Either number works depending on which end you calculate the percentage from. |
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Quoted: That has been a thorn in my side. People talk about a this and that percent decrease or increase, and I never know if that percentage is based on the total now, or the total then. They don't ever make it clear. I always figure that it's just one of the ways to lie with figures to the mass of people who don't look deeper. That's the point, you can't use the same ratio to increase one number and decrease another, and it's definitely a way people lie with numbers. A .36 ratio is just 36% - so you gotta know the baseline, and what direction the goal is moving. (Final part/whole)*100. (50/87)*100=57.4% decrease (87/50)*100=174% increase |
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Quoted: That has been a thorn in my side. People talk about a this and that percent decrease or increase, and I never know if that percentage is based on the total now, or the total then. They don't ever make it clear. I always figure that it's just one of the ways to lie with figures to the mass of people who don't look deeper. If there are 100 then and 300 now, there is a 300 percent increase. Or is it a 67% increase? Either number works depending on which end you calculate the percentage from. Quoted: Quoted: A 50% increase is a 33% decrease, and you're talking percents. Start at 100. A 50% increase is 150. A 50% decrease of 150 is 75. . . That has been a thorn in my side. People talk about a this and that percent decrease or increase, and I never know if that percentage is based on the total now, or the total then. They don't ever make it clear. I always figure that it's just one of the ways to lie with figures to the mass of people who don't look deeper. If there are 100 then and 300 now, there is a 300 percent increase. Or is it a 67% increase? Either number works depending on which end you calculate the percentage from. 100 to 300 is a 200% increase, or 300 to 100 is a 67% difference. |