Thread: An odd request

1. An odd request

Google didn't give me satisfactory results, so I'm turning to the Playground for help: What's the density of a pumpkin (I'm trying to calculate the weight of one for a contest)? If you happen to have a (mostly spherical) one on hand, I could calculate it myself, but I'd need the weight or mass and the radius or diameter. Those, of course, wouldn't be quite accurate to the pumpkin I have to measure, but the density would be about the same. Then, I would just have to measure "my" pumpkin and calculate the volume of an ellipsoid.

2. Re: An odd request

based on some quick googling:

the average pumpkin weighs ~12 pounds, is 88cm in diameter, and 50 cm tall.

I don't, however, remember how to calculate density.

Also, your these numbers vary alot depending on the type of pumpkin. some breeds are small enough to hold in your hand, others can be over 20 pounds.

3. Re: An odd request

density=mass/volume. I wouldn't use average values, though: too many margins of error.

Or, you could cut a cube from a pumpkin and weight it*. The volume of a cube is easy to measure.

*Edit... well, you won't account for the difference between the pulp and the skin, but I think it's an approximation you could live with.

4. Re: An odd request

Plop it in some water. Since I'm pretty sure they will float, you know they're less than 1g/cm^3, but to get an estimate of how much less, eyeball how much of them stays above the water. If it's around 10% then you know it .9g/cm^3, 20% = .8g/cm^3 etc.

5. Re: An odd request

what are you going to use then? I don't have 100 pumpkins around to give you a nice sample size... Especially without specifying what type of pumpkin you want to know the density of - the rind to pulp ratio is going to be different for each breed, making the density different.

6. Re: An odd request

1: Work out the volume:

http://en.wikipedia.org/wiki/Archime...s.27_principle
(Get a bucket, fill it with water, push it under the water, and see how much water comes out)

2: Weigh it.

3: ????

4: Proffit (use D=M/V)

Don't forget there is a big old bubble of air in the middle of a pumpkin, so the density of a whole pumpkin is not the same as the density of punkin flesh!

7. Re: An odd request

The density of Pumpkins will vary, dependant mainly on their water content.

8. Re: An odd request

Plus the seeds will have a very different density to the flesh.

9. Re: An odd request

Chances are an intact, ripe pumpkin has a density around .85g/cc. Pumpkins float in water with a bit sticking out. Now, if you want the density of the rind, or the flesh, or the seeds, specifically, that's different.

10. Re: An odd request

Originally Posted by GnomeFighter

2: Weigh it.
He can't, from what I understand, he's trying to measure the weight by using the density...

11. Re: An odd request

Since all organic material is mostly water, it will be a good approximation that the pumpkin's density is approximately the same as water's.

12. Re: An odd request

Originally Posted by Zdrak
Since all organic material is mostly water, it will be a good approximation that the pumpkin's density is approximately the same as water's.
"Organic" means "made of carbon". All organic material is mostly carbon. Most organisms are made of mostly carbon but have a lot of water floating around in between. Counterexamples, just from the realm of living things: Wood generally has a density well below (though occasionally well above) water's. Muscle has a density rather above water's. Fat has a density well below water's. Counterexamples, including various other organic materials: Benzene has a density of .88g/cc. Ethanol has a density of .79g/cc. Nylon has a density of 1.15g/cc.

13. Re: An odd request

For purposes of estimation, I'd there are two approaches to take.
1) The flat stat method, where you calculate volume and weight of a bunch of pumpkins, and so their density, then fit some sort of regression equation. The problem is that it'll be risky to infer very far beyond your data values, and fitting the curve well is hard.

2) The physical model: Pumpkins can be broken into fairly discrete components: flesh, and the pulpy guts, seeds and air inside. The fleshy shell and the guts will have different densities. My suggested approach would be to buy a few pumpkins, weigh them, then carve them. After removing the guts, weigh the remainder, which will tell you the weight of the shell, and, by subtraction, the weight of the guts. You can also then figure out the radius of the interior and the total radius, which will allow you to estimate the volume taken up by the guts, hence it's density. Subtracting the volume of the guts from the overall volume will give you the volume of the shell, and hence you can calculate its density (although a better estimate is probably to carve off a cube of known dimensions and weigh that).

So now you know the density of the shell, and the density of the guts. Moreover you can calculate the proportion of the total volume that is guts, and the proportion that is shell by dividing the volume of each by the total volume. Multiply each of these by the density of the corresponding part, and you should have an estimate of the fraction of total weight due to each part.

Now calculate the volume of your target pumpkin. Assume the shell is the same proportion of radius as your observed case. Calculate the estimate of the volume of the shell, divide by estimated volume, and multiply by your shell density estimate from above. Do the same for the guts. Add them together. You now have an estimate of total weight.

(If you want to get really fancy, combine the above approaches: process and record several pumpkins. Fit a regression line for the proportion of total volume due to shell on total volume. Use this to predict the thickness of shell on your target pumpkin, then proceed as above. Although there's not particularly good controls so you'll have a lot of potential bias and high variation, this may not be worth the extra effort.)

14. Re: An odd request

Originally Posted by noparlpf
Counterexamples, including various other organic materials: Benzene has a density of .88g/cc. Ethanol has a density of .79g/cc. Nylon has a density of 1.15g/cc.
Nopt sure why this is a counterexample and what exactly is countered here, as all three are within what would be normally considered "approximately" the same as water.

15. Re: An odd request

Originally Posted by Zdrak
Nopt sure why this is a counterexample and what exactly is countered here, as all three are within what would be normally considered "approximately" the same as water.
I consider anything more than .1g/cc different to be significantly different, personally. 10% is a lot and 10% more or less mass per volume is significant.
The main point is that water has nothing to do with whether something is organic and that organic compounds usually don't have the same density as water anyway, so saying "it's organic, its density is probably 1g/cc like water" is inaccurate.

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