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THE solution TO Weekly difficulty 1: A pound of Ants and the ability of clever Biomass
Posted by DrJeff top top June 1st, 2009
Filed under 1.1. Dr. Jeff"s Weekly Challenge, 1.2. Options to Weekly Challenges, 1.3. Driving through Jordi, 4. The Earth, 4.1. Environment and also Climate Change, 4.2. General Biosphere
This short article is a solution to a Dr. Jeff’s Weekly Challenge.
You are watching: How many ants is a pound
For those of friend that check out last week’s Weekly challenge 1 and also are now waiting ~ above the sheet of your seats because that the answers, well here they are. Because that those that you the haven’t yet review Weekly challenge 1, DON’T LOOK! Go directly to the challenge and read it first, do not pass go, and also do no collect $200.
And currently the answers—
1. How plenty of ants in a pound of ants?
Hint: over there is no solitary answer since there are numerous different varieties of ants. So perform some research study on ants, figure out an answer, and see if her answer drops in the variety I’ll give you following week.
1.5 MILLION ants in a lb of ants! (Great inquiry Jordi—it stunned her daddy.) This presume an average-sized species of ant, and also that we’re talking around worker ants. (Isn’t there constantly a disclaimer for solution to a simple question?)
Depending on the ant species, over there are almost everywhere from 190,000 come 7.5 MILLION ants in a pound of ants! check out the “How did ns come up with the answers?” section below.
2. How much does the human being race weigh?
Hint: you’ll require to know how plenty of humans space on the planet. Here friend go, courtesy of the U.S. Census Bureau.
With around 6.8 billion of us on Earth, below is the weight of the human being race—
english system: 440 million lots (1 ton = 2,000 lbs)
metric system: 410 million metric lots (1 metric ton = 1,000 kg)
See the “How did ns come up v the answers?” section below.
WOW!! ns think I’m impressed. But … wait a second. That’s just a big number. I have NO proviso what that big number means. If I’m to truly recognize it (you also in cyberspace), climate I need to develop a bridge to the familiar. Therefore let’s go on to the third part of ours challenge.
3. Wait, i hear Ellen in Detroit saying, “but Dr. Jeff, I’d rather recognize the full volume the the human being race, in various other words, how huge a volume of an are would you require to simply fit the whole human race?” great thinking Ellen! it is another great way come look at it. Therefore let’s do this a third component of the challenge. As soon as you calculation 2 above, number out the full volume that the human race.
Hint: you have the right to assume the we human beings are made largely of water, and every 1,000 kg that water takes increase 1 cubic meter of space. For those of girlfriend who choose to conceptualize utilizing the English system of units, 1 ton that water (2,000 lbs) takes up 32 cubic feet of space.
The entire human race—the varieties that can adjust the setting on a planetary scale—can comfortably fit into a box just 1/2 mile top top a side (0.75 km on a side). Watch the “How did ns come up v the answers?” section below.
If you recognize Washington, DC, that’s about the volume of room equivalent come the size of the national Mall filled to the optimal of the Washington Monument.
If girlfriend know new York City, that’s a around the volume of space equivalent come the dimension of main Park filled to the optimal of the Flatiron Building.
Isn’t this simply so unbelievable SMALL? have the right to you figure out an indistinguishable volume in a city near you?
THE necessary LESSON THIS WEEK
In this box of humanity is—mostly water. Also in this box is a species that is self-aware, intelligent, and also driven to know and do anything and everything, and also a varieties that has actually the ability to imagine, design, and BUILD tools. How does such a tiny box of clever biomass adjust the planet? TECHNOLOGY. Through hydraulics and explosives we have the right to move mountains. Through power plants and also engines to develop energy native fossil fuels we deserve to heat the entire planet, advanced the oceans, and change weather ~ above a worldwide scale. Ns CANNOT think of a better argument for the require for scientific research and an innovation education. We together a nation, we together a people must make informed decisions about how we usage our modern technology so that we can be an excellent stewards of the planet.
And now—how did ns come up v those answers?
The secret piece of details is the load of a solitary ant. You could do your conventional google search and find one answers-to-everything net site. This is probably exactly how you obtained your answer. Let’s compare it to mine.
I’m always careful to make sure info I research study is accurate. I commonly don’t also trust Wikipedia, yet often use it to allude me in the appropriate direction. In ~ the bottom the a Wiki web page there are regularly references to formal publication by scientists and engineers that have actually been the evaluation by …. Other scientists and also engineers. We call these “reviewed” or “refereed” publications, and are where you frequently find the best easily accessible information ~ above a subject.
So right here is the magic publication I found by Michael Kaspari, released in 2005 in the Proceedings that the nationwide Academy of scientific researches of the United says of America. Michael closely studied ant swarms at 49 various sites with various climates, and found 434 species of ants. I think we have the right to assume that is one ant expert. He created this write-up to tell various other scientists about what that found. If girlfriend look at what he composed it appears pretty technical, but it’s impressive that he defines the breadth the his research in beautiful information using 2 very an effective languages–english and also mathematics. Scientists and engineers must be good communicators if their research study is come be recognized by others. Yet no must read the article, I’ll analyze for you.
Michael found that the weight of a worker ant was anywhere from 0.06 milligrams to 2.34 milligrams. (A milligram is one thousandth the a gram, and a gram is one thousandth that a kilogram. A kilogram is 2.2 pounds.) The worker ant because that the largest species he studied was 40 times the load of the worker ant because that the smallest species! The mean was around 0.3 mg, i m sorry is what I’ll use. So here we go—
Weight of a single ant is 0.3 mg
The number of ants in a lb of ants = 1 pound separated by the weight of a single ant
To division you should use the exact same units: due to the fact that we have actually the load of an ant in milligrams, let’s do the mathematics in milligrams.
Convert 1 pound to milligrams: 1 lb = 0.45 kilograms = 450 grams = 450,000 milligrams
Now divide: 450,000 milligrams / 0.3 milligrams = 1.5 MILLION ants!
But WAIT! Let’s carry out this because that the types he studied with:
• the the smallest worker ant, just weighing 0.06 milligrams.
You obtain 7.5 MILLION ants in a pound of ants!
• the biggest worker ant, weighing 2.34 milligrams.
girlfriend still gain 190,000 ants in a lb of ants!
Here’s a cool question to lead us to the next component of the challenge. If you had actually as many ants as human beings on Earth, exactly how much would all those ants weigh?
(6.8 exchange rate ants) x (0.3 milligrams every ant) = 2,000 kg (or if you prefer the English system, around 2 tons)
2. Exactly how much go the human being race weigh?
Courtesy that the U.S. Census bureau I watch that right now there are around 6.8 BILLION people on the planet. Currently for the guess—I’m going to assume the average human being being weighs around 130 lbs (60 kg). It sound reasonable once I consider children, the distinction in weight in between men and also women, and also that most humans live in impoverished conditions.
The weight of the human being race is then:
english system: 6.8 billion x 130 lbs = 880 billion pounds =
440 million tons (1 ton = 2,000 lbs)
metric system: 6.8 billion x 60 kg = 410 exchange rate kg =
410 million metric lots (1 metric ton = 1,000 kg)
WOW!!!! Or possibly not.
3. How large a volume of an are would you need to just fit the entire human race?
Hint: you can assume the we people are made mainly of water, and every 1,000 kg that water takes up 1 cubic meter the space. For those of you who favor to conceptualize utilizing the English system of units, 1 ton that water (2,000 lbs) takes increase 32 cubic feet the space.
Yup, we are greatly water. In fact also water treats us like water. If we’re in a pool and we go underwater, we’re nice close to neutral buoyant—which method we don’t sink too fast or rise too fast. We’re about the thickness of water.
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So below is the volume that the human being race:
english system: 440 million loads x 32 cubic feet /ton = 14.1 exchange rate cubic feet
metric system: 410 million metric tons x 1 cubic meter every metric ton= 410 million cubic meters
NOW because that THE fun PART.
Let’s assume that we put the human being race in a box with the volume above. And let’s i think that package is a cube where the size = elevation = width. How big a box would contain the volume above?
Volume the a cube = (length of side) x (length that side) x (length the side)
= (length the side) 3
To obtain the length of a side you thus take the cube source of the volume, and also you get:
• english system: cube root of 14.1 billion cubic feet
length of next = around 2,400 feet = 0.45 miles!!!
• metric system: cube source of 410 millio cubic meters
length of side = about 750 meter = 0.75 kilometers!!
Permalink |June 1st, 2009