Trying to work out what 1 million pieces of wire will weigh.
20 thousands of an inch diameter, 0.8 inches length.
The metal it’s made of is 600 lbs per cubic foot in weight.
I don’t need an accurate answer, just a rough one.
I got near 200 kg. Am I out by an order of magnitude?
Update. Problem solved, 40 kg or so. Thanks very much everyone.
Tim,
per length:
Diameter = 0.02 inches
radius = 0.01 inches
area =
Tim,
per length:
Diameter = 0.02 inches
radius = 0.01 inches
area = 0.00031416 sq inches
length = 0.8 inches
volume = 0.00025133 cubic inches
the density is 6oo lbs per cubic foot = 0.37422 lbs per cubic inch
mass per length = 8.7266*10-5 lbs
mass for a million lengths = 87.266 lbs = 39.584 kg
…so 200kg was nearly 1 order of magnitude out…
…but the question is: WTF???
Being offered some scrap metal in the day job. Needed to get to weight in order to work out whether it’s worth even looking at.
Thanks very much.
Yep, you’re off by an order of magnitude.
It will be about 2050 kg (4500) lb. I’m assuming you’re sure of the weight per cubic foot, so everything’s based off that. But if this wire is steel, that figure is wrong (steel is .283 lb/cu. in. – which would be 489 lb/cu. ft.)
Equations:
Area = (PI/4)*d^2 = .000314 sq.in.
Volume/piece = Area*length = .016 cu. in.
total volume = volume/piece*1,000,000
= 16,000 cu. in.
Total weight = density/cu.in. * total volume
Using your 600 lb/cu.ft. that gives density/cu.in. of .347, so your total weight would be 2518 kg (5552 lb).
If this were steel, it would .283 lb/cu.in., and the total weight would be 2054 kg (4528 lb).
Here’s some other metal densities, in case you start suspecting your density number:
lead = .410 lb/cu.in.
silver = .379 lb/cu.in.
copper = .324 lb/cu.in.
nickel = .322 lb/cu.in.
brass = .307 lb/cu.in.
tin = .264 lb/cu.in.
aluminum = .098 lb/cu.in.
gold = .698 lb/cu.in.
Hope this helps!
Yep, I found my error.
He’s right – by two orders of magnitude…lol I think one more round and we’ll have a six pack!
43.55 kg total weight (based on .382 lb/cu.in, or 660 lb/cu.ft.)
Valhall,
An order of magnitude means 10 times. So an estimate of 200kg is out by an order of magnitude if the real mass is either 20kg or 2000kg. The real mass of these million wires is about 40kg – so less than one order of magnitude out.
0.78(cwt)
With the numbers you give, Tim, the volume is 80 π cubic inches, or 5 π/108 cubic feet, for a mass in pounds of 250 π/9. For diameter d inches, length h inches, number N, denity ρ lbs per cubic foot, the general formula is mass = N d^2 π ρ h/6912.
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