Comments on: Math problem: how many objects will fit into this glass jar
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Comments on Ask MetaFilter post Math problem: how many objects will fit into this glass jarSun, 22 Feb 2015 19:36:40 -0800Sun, 22 Feb 2015 19:40:45 -0800en-ushttp://blogs.law.harvard.edu/tech/rss60Question: Math problem: how many objects will fit into this glass jar
http://ask.metafilter.com/276306/Math-problem-how-many-objects-will-fit-into-this-glass-jar
I am trying to work how many 5 gram objects can fit into a 3 litre jar.
I struggle with conversions of grams to litres and finding the number of objects.
Can someone show me how to mathematically work it out. My mind is blank.
Thanks in advance :)post:ask.metafilter.com,2015:site.276306Sun, 22 Feb 2015 19:36:40 -0800nassepestimatingmathsBy: i_am_a_fiesta
http://ask.metafilter.com/276306/Math-problem-how-many-objects-will-fit-into-this-glass-jar#4008256
Grams are a unit of mass and liters are a unit of volume. In order to solve this problem, you need to know the density of the objects (mass/volume, or grams/liter) or the volume of each object.comment:ask.metafilter.com,2015:site.276306-4008256Sun, 22 Feb 2015 19:40:45 -0800i_am_a_fiestaBy: The Architect
http://ask.metafilter.com/276306/Math-problem-how-many-objects-will-fit-into-this-glass-jar#4008257
Grams are a unit of mass and liters are a unit of volume, so there is not going to be a direct conversion. Different things of the same size weigh different amounts. What are the 5 gram objects you are trying to calculate?<br>
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edit: on preview, what fiesta said.comment:ask.metafilter.com,2015:site.276306-4008257Sun, 22 Feb 2015 19:41:19 -0800The ArchitectBy: letourneau
http://ask.metafilter.com/276306/Math-problem-how-many-objects-will-fit-into-this-glass-jar#4008258
The missing piece of information here is the density of the objects (i.e. how much a cubic centimeter of material weighs, or vice versa, how many cubic centimeters a gram of material occupies). If we assume that the objects are as dense as water at room temperature, this becomes easy: one gram of room-temp water equals one cubic centimeter, so each object occupies 5 cubic centimeters (if our assumption about their density holds).<br>
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One liter is equal to 1000 cubic centimeters, so the jar is 3000 cubic centimeters in volume. Finally, with consistent units we can now divide 3000 by 5 to get the answer: 600 objects. (Note that this also assumes that the objects pack in perfectly with no wasted space.)<br>
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We can also use this 600 figure to scale the answer up or down if the objects' density is different from water's. If, for example, the objects have a density of (to pick a random value) 2.5 grams per cubic centimeter, the jar will hold 2.5 times as many (smaller, denser) objects as if we assumed the objects had a density of 1.0 grams per cubic centimeter (i.e. 1,500 objects). If the objects are less dense, say 0.4 grams per cubic centimeter, the jar will hold 0.4*600 = 240 (bigger, lower-density) objects.comment:ask.metafilter.com,2015:site.276306-4008258Sun, 22 Feb 2015 19:45:20 -0800letourneauBy: jeather
http://ask.metafilter.com/276306/Math-problem-how-many-objects-will-fit-into-this-glass-jar#4008260
The density of gold is about 19,300 g/l, so you could fit 11,580 pieces of gold weighing 5g each into a jar if you could pack them perfectly. The density of cork is about 250g/l, so you could fit 150 pieces of cork into a jar if you could pack them perfectly but not squish them (aka make them denser). Most things are less dense than gold and more dense than cork, so somewhere in that range probably.comment:ask.metafilter.com,2015:site.276306-4008260Sun, 22 Feb 2015 19:48:41 -0800jeatherBy: Cool Papa Bell
http://ask.metafilter.com/276306/Math-problem-how-many-objects-will-fit-into-this-glass-jar#4008264
Don't forget the shape of the objects may prevent a perfect amount to fill the jar.<br>
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You know, it's funny, but when you say how many 5-gram objects can fit into a jar, the possible answers can be "none," if it's not very dense and hence too big, or "one," if it's just the right size to fit all by itself, or "infinite," if they're super-dense and tiny.comment:ask.metafilter.com,2015:site.276306-4008264Sun, 22 Feb 2015 19:55:56 -0800Cool Papa BellBy: jon1270
http://ask.metafilter.com/276306/Math-problem-how-many-objects-will-fit-into-this-glass-jar#4008277
<em>I struggle with conversions of grams to litres and finding the number of objects. </em> <br>
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Don't feel bad about struggling with this; it's simply not possible to figure this out from the information you've given here. Even if we knew the density, it would still be impossible unless the objects were basically gelatinous. If they are rigid solids then you'd need to know the shape of the jar, the shapes of the objects... it could get very complicated.comment:ask.metafilter.com,2015:site.276306-4008277Sun, 22 Feb 2015 20:17:50 -0800jon1270By: sammyo
http://ask.metafilter.com/276306/Math-problem-how-many-objects-will-fit-into-this-glass-jar#4008278
Just to make it worst, packing problems are some of the most intractable and actual research topics.comment:ask.metafilter.com,2015:site.276306-4008278Sun, 22 Feb 2015 20:19:34 -0800sammyoBy: palmcorder_yajna
http://ask.metafilter.com/276306/Math-problem-how-many-objects-will-fit-into-this-glass-jar#4008301
The good news is, if the objects have a simple, uniform shape, you can look up a "packing factor" for them, and then just multiply it in.comment:ask.metafilter.com,2015:site.276306-4008301Sun, 22 Feb 2015 21:40:30 -0800palmcorder_yajnaBy: aws17576
http://ask.metafilter.com/276306/Math-problem-how-many-objects-will-fit-into-this-glass-jar#4008313
The objects don't happen to be nickels, do they? (Pardon the idle speculation, but <a href="http://www.usmint.gov/about_the_mint/?action=coin_specifications">nickels weigh 5.000 grams</a> and seem like a reasonable thing to pack into a jar.)<br>
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You could pack just under 4,000 nickels into a 3-liter jar if they fit neatly in honeycombed layers.<br>
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On preview: you wrote "litre" so I am probably wrong. :)comment:ask.metafilter.com,2015:site.276306-4008313Sun, 22 Feb 2015 22:31:02 -0800aws17576By: yoyo_nyc
http://ask.metafilter.com/276306/Math-problem-how-many-objects-will-fit-into-this-glass-jar#4008342
This is a complex problem: https://en.wikipedia.org/wiki/Sphere_packingcomment:ask.metafilter.com,2015:site.276306-4008342Mon, 23 Feb 2015 02:15:00 -0800yoyo_nycBy: alms
http://ask.metafilter.com/276306/Math-problem-how-many-objects-will-fit-into-this-glass-jar#4008400
All the comments above are correct if you are talking about solid objects with a fixed shape made out of some unknown substance. If you ignore the shape fitting problem and answer the density question, then the problem is very simple.<br>
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Take, for example, 5 gram drops of water. 1 gram of water = 1 ml of water. 5 grams = 5 ml. 3,000/5 = 600 drops to fill the container.comment:ask.metafilter.com,2015:site.276306-4008400Mon, 23 Feb 2015 06:53:38 -0800almsBy: halhurst
http://ask.metafilter.com/276306/Math-problem-how-many-objects-will-fit-into-this-glass-jar#4008694
Identical round objects like marbles will fill 52% of the volume allotted. Therefore, for marbles, find the mass per volume of glass, and multiply by .52 times the volume of the container, treating it as a uniform substance, to find how much mass the container will contain. If you mix sizes, then it depends on what the sizes are, and it gets complicated, since now smaller objects can fill in the empty space between larger objects.comment:ask.metafilter.com,2015:site.276306-4008694Mon, 23 Feb 2015 14:22:13 -0800halhurst