A million pennies and some math/science

Factual Questions
1

Inspired by the thread on how many m&m’s or other would fit in a jar…
http://boards.straightdope.com/sdmb/showthread.php?p=10248582#post10248582

A friend of mine wants to collect a million pennies for charity. She suggested that people save them, put them in milk jugs, and she’ll load them into the back of her truck to take to the charity.

How much would they weigh? I’ll put my calculations in spoiler.

[spoiler]Per Wikipedia, one penny weighs 2.50 grams. Wheat pennies were 3.11 grams, but they’re rare. So if we had a million, that would be 2.5 million grams.

I could divide by 454g/lb, but I used the Yahoo conversion calculator, since it might have a very precise equivalent. 2.5 million grams is equivalent to 5511.55655462 pounds. Imagine if they were all wheat pennies!

2.75 tons means your average F150 isn’t going to cut it—multiple trips are required.[/spoiler]

She googled and found

2L Soda Bottle=4363 or $43.63
Milk Jug (1 Gal.)= 6,000 or $60.00
Water Jug (5 Gal.)= 70,000 or $700

It’s interesting that in the thread that inspired this, they’re talking about “packing efficiency” as well. I.e. how much space is “wasted”—just air? For the milk jug especially, I’m not sure I can calculate that to corroborate. For one thing, part of the gallon is the handle…would pennies fit in there? If so, how much “wasted” space?

That aside, a stats prof in college said that pennies aren’t fair coins. He said that if magnified, their shape would reveal itself not to be truly cylindrical, that it’s shaped more like a bottle cap. Tossing the coin over and over and letting it land on a level floor, you’ll get more heads than tails.

IMO the milk jugs are a bad idea. The weight of 6000 pennies is much more

I calculate it’s just over 33 lbs

than the jug was designed to hold. If she hit a bump in the road, she might have 6000 pennies x number of broken jugs all over the bed of her truck.

I think 2 liter soda bottles would be the best. They’re designed to keep the soda carbonated, so they’re sturdier, thicker plastic. Notice I said “soda bottles” because there may be those designed for water etc. may not be designed to the same specs.

A dramatic demonstration of their strength: the dry ice bomb. Everybody and his brother in here has seen this, right? Kids (and the moronic at heart) go out and buy some dry ice. They put some water in a 2 liter bottle—maybe about 1/4 full. Then they add pellets of dry ice, screw the top on and get back.

Mild but possibly NSFW…expletives in the “soundtrack.”

http: //www.youtube .co
Look at how the plastic deforms at the top right before the explosion…man, that is insane!

Oh, and she better have bungee cords so that they can’t roll around in the bed, creating impacts like bowling balls.

Does my math check? What would you use to transport them? As disposable stuff goes, I think the 2L bottle is probably a pretty good piece of engineering, but maybe there’s something better.

2

6,273.6 pounds or 3.14 tons, so you’re not too far off.

Here’s a site with all the penny-ante information you’ll ever need.

3

To correct some misinformation in the OP: all pennies minted pre-1983 (except the steel pennies issued in '43 which massed 2.70 g) massed 3.11 g, not just the wheat ones. That’s when pennies changed over from all copper composition to copper-clad zinc.

4

Thanks for the info! So it’s even worse than I thought, weight-wise.

Here’s something weird…did you know the likeness of Lincoln appears in two places on the penny?

you can see him sitting ‘inside’ the Lincoln memorial on the back. File:20050228 200242 1 revers lincoln.999x989.jpg - Wikipedia

5

Not sure how you got your figure. Using the site’s peculiar number (over a million) and dividing out, I get 6250 pounds even.

I wonder if, per QED’s post, we have to assume a mixture of weights since some pennies will be pre-1983 and some post-1983, so it can’t be calculated a priori.
Sorry for the non-working link of the youtube CO2 bomb. Again, there’s some profanity in the soundtrack so I’ll mark this NSFW

I just love watching the top expand and expand until…

6

You can probably get close enough for government work by sampling 100 or so pennies and seeing how many are pre-'83 vs. post-'83. Just don’t use pre-rolled pennies for your sample, since they are likely to have come straight from a mint and will therefore all have the same year. Collecting change from several different stores will probably get you a sufficiently random sample you can call representative of the general circulation.

7

HERE it is!

http://vbxmaxima.8m.com/jetta.html

Remember this—ppl in Jetta decide they want to haul some home improvement supplies? I guess we can conclude that a Jetta can’t handle 3000 lbs. :smiley:

When I started this thread, in the back of my mind I was wondering: if you have a heavy duty truck like an F150 1) could you fit a million pennies in it, and 2) could it support a million pennies? I.e. if some uniformed person attempted it, would the results be disastrous/hilarious?

We already talked about weight, 6250 pounds ballpark. Shocks, struts, springs…could the axle survive?

http://www.kokogiak.com/megapenny/six.asp

says that number of pennies would make: *A wall five by four by one feet thick with a 9-inch cube stepstool *

20 cubic feet plus a bit. 6 foot bed, 3.5 wide=21 square feet, minus wheel wells etc.? Yeah, a mil would pretty much fit in the bed, especially if you choose containers that are tall and pack well.

Wish someone like Mythbusters would do it :smiley:

8

This is what I did. I happen to have $4.50 in pennies that I had collected and rolled over the past several months.

Using a postage scale that reads out to tenths of an ounce, I weighed all of them and got a total of 2 pounds, 10 ounces, or 42 ounces. The paper rolls I used are about .02 ounce each. (Ten of them weigh .2 ounce.) I subtracted .18 oz from the total and divided the result by 450. This yields an average weight per penny of 0.09293 ounces (2.6346 grams).

Thus, by my calculations one million pennies (a random mix of old and new styles) should weigh about 5,808 pounds, net. If you wrap them in paper tubes, add about 25 pounds for the 20,000 wrappers.

9

If n=number of pennies weighing 2.50 grams

2.50n + 3.11(450-n) grams=1190.7g
2.50n + 1399.5 -3.11n=1190.7g
-.61n = -208.8
x =342.29

Hmm, expected an integer. But I guess physical things like pennies aren’t going to be totally uniform and there’s the wear and tear factor.

Roughly 342/450 of the 2.50g penny—76% vs. 24% of the 3.11g version.

10

While I certainly find the theoretical/Math problem interesting, if your friend is planning this for real, please ask her if she wants to help the charity or sabotage it! Leaving the whole weight/transportation issue aside (which is a big aside), unless the charity has coin sorter-and-rolling-machine (which I somehow doubt), it will take countless volunteer man-hours to roll a million pennies, so the charity can pay it into the bank to use the money! (I leave it to the math people to calculate how long it would take manually to sort/roll a million pennies :))

And if the charity fobs this task off to a bank, won’t the bank take a fee (since they take fees for everything), which eats into the donated money?

Why not simply tell people to collect pennies and exchange for a dollar and so on - make changes with each bigger step?

11

Woohoo, I guess at 6000lbs with out doing any real math. I was pretty close.
Okay, there was a little math. I bring boxes of coins back to work from the bank all the time, I guessed that a box of pennies was about 30# or so, and just did a little math from there. $50/box, so we need 200 boxes, that would be 6000 pounds. Seems I was only off on the weight of a box by a pound or so.

When I get back to work later, I’ll have to see if I have a full box to weigh.

12

The F-150 is a ‘half-ton pickup’ which means its maximum carry weight – including people – is nominally 1,000 pounds, one-sixth the weight of the million pennies. I can’t think of any 3-ton pickups out there, a small dump truck, maybe. The F-150 (or similar sized Chevy, Dodge or Toyota) could tow a trailer with a 6,000 pound capacity, but it would take a Class 4 hitch to do so.

I remember as a wee lad seeing a movie where a gang of thieves robbed the Bank of England. They loaded a two-wheel horse cart with bullion and specie, not even up to the top boards on the cart, but it was still overloaded. When they were talking to a suspicious bobby, the bottom of the cart dropped to the ground, with coins rolling everywhere.

13

Nitpick: that isn’t totally correct - some 1982 pennies were primarily zinc, others copper. The only reason this is in my head is it was a past thread on here, and that I have one zinc and one copper 1982 penny upstairs somewhere.

http://www.usmint.gov/about_the_mint/fun_facts/index.cfm?action=fun_facts2

14

In my amusement park days we used coin counters and sorters to fill cloth coin bags, IIRC they were something like $50 in pennies per bag.

This would be more storage efficent as well as fairly manageable. IIRC there are mechanisms for depositing coins in this format as well where a bank would probably not want tons of rolled coins.

15

You might consider it a small dump truck since it can be outfitted as one, but the F-550 has a 12,000+ pound payload capacity.

16

All right, so it’s odd, I did my math wrong*, but it still wound up correct.
A box of pennies is $25 and weighs 15.04 pounds. That’s with the paper wrappers and the cardboard box they come in. Just throught I’d throw that in for an empirical/real world example.
*It’s odd since I had a brain fart and said a box of pennies is $50:smack:, it’s odd that I misjudged the weight so terribly that I thought it was 30# instead of 15. It’s a strange coincidence that my numbers still wound up being the same since $50 of pennies would be about 30#.

17

We did something like this a while ago with a mix of coins, but there was a spreadsheet that came out of the discussion which you could use to figure things out pretty easily. The numbers in that spreadsheet account for the packing factor, but the smaller the container is the more its edges will reduce the overall efficiency. The spreadsheet defines three mixes of coins: normal (all coins), no pennies, and “laundry mix” (no quarters). There’s also a section below with the masses of the old (pre-1965) coins. It’d be easy to replicate the method for just about any assumed mix of old and new pennies.

18

I was mulling that over as I was making the post. There certainly are trucks out there with the capacity, but I was thinking they are available only as chassis cabs – you get just the cab in front and a couple chassis rails in the back. You get the box, flatbed or whatever you else you want for hauling stuff from another vendor.

Wiki says the F-450 is available for the first time with a production pickup bed, but it’s capacity is 6,120 pounds, a tad shy. It would be a lot easier to make two trips.

19

I copied/pasted your post into an email to her…thanks!

20

Too bad we’re not in England. It’s easy for them to convert money to weight. That’s why they named it the pound.:stuck_out_tongue: