Physics Challenge

[thecrecarc]

http://pages.physics.cornell.edu/~aalemi/challenge/

From the website:

The Problem

Your fantastic journey on the R.M.S. Titanic II was cut tragically short when the ship struck a polar bear and sank. You washed up on a desert island with nothing but the clothes on your back and the CRC handbook [a big book of experimentally measured numbers]. You're all alone and have some 60 years to kill, so you decide to continue on with your physics research. However, for the CRC to be of any use at all, you'll need to work on re-establishing standards for the meter, second and kilogram.
Your challenge is to design Macguyver-like experiments using only the materials readily accessible on some remote desert island to determine the meter, second and kilogram. Be sure to give estimates on your uncertainties. Bonus points if you actually carry out the experiments.
Naturally, you should assume that you don't have anything like a watch, clock, meter stick, ruler, or any sort of standard weight to start.
Update: 02/05/11 - We've had some interest from people outside Cornell. We are happy to accept submissions to the email. The more the merrier. Additionally, I'd like to emphasize the need for a qualitative estimate of the errors you expect from your method, in order to evaluate different submissions. Is your proposed meter good to 10%, 1%, 0.1%?

This is an interesting problem. A cheap-ish way is to assume the CRC book is standard, and derive the meter from that. Then, perhaps use something like a pendulum to determine the second, and water density to determine a kilogram, all with the help of your new meter. The accuracy is probably quite bad though.

 

[destrekor]

To help with mass, one could setup some crazy system to boil the saltwater, and use some kind of fashioned hood to collect the vapor (distilling the water a few times).
Then, of course this is using length measurements, find some way to hold a cubic centimeter (or cubic meter) of this distilled water. This would give you a fairly accurate standard of mass, though not a perfect gram or kilogram.

And this is ignoring the complexity needed to invent the ability to actually perfectly measure out a cubic metric container, and more importantly, the ability to scale the quantity to measure anything else. A scale experiment could give you a more dense and smaller quantity of equal weight, and repeated multiple times could land you something smaller and more portable that is determined to have 5 or even 10kg... but all those repetitions using only a scale setup would result in a less accurate unit of mass with eat repetition.

 

[Matthiasa]

I would find the meter, using your height if known in meters. From there getting a kg and a second shouldn't be hard.
Kg from a cube of water .1m in wide, then time from something dense and large(surface area increasing at the square of of width, while mass increases at the cube of it) falling a distance of 4.9 meters.
However any error in that measurement for a meter would cause a much larger one in the other two.

If you know your height all of those should be within at least~5-10%

Or for a meter, if the book has standard page sizes and you know what size that is in cm, just take a few pages out and get it that way.
If you know that, would be able to get within maybe 1% on everything.

Well unless desert island doesn't have stereotypical tree... cause making something to hold the water then becomes a lot harder.

 

[arkcom]

Shoe laces come in standard sizes. 27", 36", 45", 54". Convert to meters and go from there to derive the other units.

Don't know about seconds yet.

 

[silverpig]

The first thing to realize is that if you have any one of those measurements you can quite easily get the others. Your errors will propagate, so make your first measurement your best.

I have a couple of ideas... let me think about it.

 

[TallBill]

I would find the meter, using your height if known in meters. From there getting a kg and a second shouldn't be hard.
Kg from a cube of water .1m in wide, then time from something dense and large(surface area increasing at the square of of width, while mass increases at the cube of it) falling a distance of 4.9 meters.
However any error in that measurement for a meter would cause a much larger one in the other two.

If you know your height all of those should be within at least~5-10%

Or for a meter, if the book has standard page sizes and you know what size that is in cm, just take a few pages out and get it that way.
If you know that, would be able to get within maybe 1% on everything.

Well unless desert island doesn't have stereotypical tree... cause making something to hold the water then becomes a lot harder.

I'm pretty much exactly 2 meters tall, so I guess finding a meter would be relatively easy within 1%

 

[TraumaRN]

Shoe laces come in standard sizes. 27", 36", 45", 54". Convert to meters and go from there to derive the other units.

Don't know about seconds yet.

Use the shoe laces to build some sort of pendulum?

 

[busydude]

He can also use the length of his pant as a reference, but I guess the error may be pretty significant.

 

[arkcom]

Use the shoe laces to build some sort of pendulum?

an ~1m pendulum has a period of 2 seconds (1 second from on side to the other). So yes, that would work.

I guess you would just use the pendulum as your stop watch. What else would you do once you measured one second?

 

[Ika]

I'm pretty much exactly 2 meters tall, so I guess finding a meter would be relatively easy within 1%

higher than 1%, your height varies depending on time of day (i.e. spine elongation)
but I am nit-picking. either way this is a pretty lame method :awe:

 

[silverpig]

an ~1m pendulum has a period of 2 seconds (1 second from on side to the other). So yes, that would work.

I guess you would just use the pendulum as your stop watch. What else would you do once you measured one second?

Ever tried to measure time with a pendulum? They suck. Anything you build on an island will have a lot of friction and won't be accurate at all.

Once you measure distance, here's an easy way to measure time:

1. Find a coconut and crack it open. Eat the insides.
2. Drill a very very tiny hole in the coconut with a sharp rock. Make it so that water will drip out slowly.
3. Fill the coconut with water. It should drip out of the hole.
4. Raise and lower the coconut so that a drop leaves the coconut just as the preceding drop hits the surface below the coconut.
5. Once you have this set up, use your calibrated measuring stick to find the distance the water drop travels.
6. Use x = -0.5(g)t^2 with g = 9.81 and x as measured to find t. You now have a clock which measures time in those units.

Use trial and error until you get a coconut hole just the right size such that your measuring device measures time in seconds.

I still haven't figured out a good way to get distance.

 

[MikeMike]

okay, obviously the very first thing we have to do is figure out distance to figure out ANYTHING else...

something to do with right triangles?

 

[arkcom]

A piece of string doesn't have much friction. It's less effort to give the pendulum a swing than to refill a coconut.

Edit: besides, the goal wasn't to make a clock, but to measure a second.

Ever tried to measure time with a pendulum? They suck. Anything you build on an island will have a lot of friction and won't be accurate at all.

Once you measure distance, here's an easy way to measure time:

1. Find a coconut and crack it open. Eat the insides.
2. Drill a very very tiny hole in the coconut with a sharp rock. Make it so that water will drip out slowly.
3. Fill the coconut with water. It should drip out of the hole.
4. Raise and lower the coconut so that a drop leaves the coconut just as the preceding drop hits the surface below the coconut.
5. Once you have this set up, use your calibrated measuring stick to find the distance the water drop travels.
6. Use x = -0.5(g)t^2 with g = 9.81 and x as measured to find t. You now have a clock which measures time in those units.

Use trial and error until you get a coconut hole just the right size such that your measuring device measures time in seconds.

I still haven't figured out a good way to get distance.

 

[silverpig]

A piece of string doesn't have much friction. It's less effort to give the pendulum a swing than to refill a coconut.

Edit: besides, the goal wasn't to make a clock, but to measure a second.

I've done this before in a physics competition. The water method was accurate to within 3/10ths of a second in 46 seconds. That's about 0.6% and we only had 15 minutes to design, build and measure. I'm sure we could have done better if we had longer. All of the pendulum teams were lucky to be within 20%. Your internal clock is more accurate.

If you have an accurate clock, measuring a second is trivial. The goal is accuracy. I can measure a second just by counting. I doubt a shoestring pendulum would be any more accurate and it takes a lot less effort to count than it does to swing a pendulum.

 

[MikeMike]

A piece of string doesn't have much friction. It's less effort to give the pendulum a swing than to refill a coconut.

Edit: besides, the goal wasn't to make a clock, but to measure a second.

the goal still has the MAJOR issue of figuring out a standard unit of measure...

 

[arkcom]

the goal still has the MAJOR issue of figuring out a standard unit of measure...

I gave my answer to that a few posts up.

It would be nice if the book had a line on the front page that said "this is a decimeter." Beyond that, I don't know.

 

[IcePickFreak]

I would rather spend the 60 years pondering how the ship sank from a polar bear, yet I washed up on a desert island. Divine intervention? Space aliens? Orcas?

 

[arkcom]

I would rather spend the 60 years pondering how the ship sank from a polar bear, yet I washed up on a desert island. Divine intervention? Space aliens? Orcas?

Desert island means nothing's there, not that it is a "desert" in the dry, sandy sense.

But that would be a very large bear.

 

[IcePickFreak]

Oh, a deserted island. I should of expected that when the problem was written by a physicist. Which makes me wonder if they can even spell their title. :awe:

 

[Ninjahedge]

You could also set up a slit to refract light. I believe you can make a rainbow from that, correct?

If you could get a ratio of the distance from the slit to the rainbow, and the relative width of the slit, I think you would have a basis of measurement strictly on the width of the banding you observe.

You do this several times and take the average and you will have your measutring standard.


Or, you could just use a rock and set that up as your mass unit and a strudy stick as your length unit and realize that everything in physics can be converted later.

Assume a new standard for each (Kilo-stones, milli-stones, centi-sticks and "moments") and you then start re-doing all your units.

Once you have a new set of constants (comparable to 32.2 ft/sec^2 vs 9.81 m/sec^2) you can then solve simultaneous equasions to compare one set to another and derive one conversion factor (moments to seconds for instance), then work it back through.

The specifics would be the hard part, as I do not know how many different standards you would need to set to get the necessary crossover to solve the system of simultaneous equasions......

 

[ussfletcher]

Build a pendulum with about the estimated length of a meter, and adjust until it takes about "one Mississippi" to make a swing one side to the other, now you have a reasonable approximation for a second and a meter. (Or if you have a good approximation of one, you can get the other by T=2pi*sqrt(L/g))

If you had a spring with a known K, you would be able to approximate the rest.

As for the mass, if you had a reasonable approximation for distance it would be trivial to find the weight of a CC of water.

If you want to get tricky, you could work the Eratosthenes method and solve backwards using the exact circumference of the earth.

Really, its almost trivial to get a reasonable approximation.

 

[JTsyo]

Oh, a deserted island. I should of expected that when the problem was written by a physicist. Which makes me wonder if they can even spell their title. :awe:

You can have cold deserts too. Desert is only defined by lack of rainfall. The largest desert is actually Antarctica.

Might be a regular size bear but a small boat.

Using things falling for time introduces the error from air friction but I guess it should be within 1%.
If you knew your latitude and time of year you could probably get a decent estimate of a meter from a sun dial. That would probably be over 1% though.

 

[silverpig]

You could also set up a slit to refract light.

That would work, but you'd need to measure the distance between the slit and the screen. There's a ton of ways to measure using trig, but you always need the length of one of the sides first.

 

[Ninjahedge]

You want a key?

It depends on whether or not you have any glassware or some way to heat a controlled volume of water.

You know what tempearature it boils at. You also know your body temp is fairly constant (I am assuming there is not freezing on this island). You now have a scale from 212 to 98.6 degrees based on the expansion of a known liquid. (You need to construct a thermometer though. Something roughly cylindrical and rather tall to get a pronounced expansion.) You have the expansion coefficient and the Delta T, you should be able to back calculate the relative expansion and get your unit of measurement. You could also do this with a metal bar, but immersing it in boiling water would be difficult, as would getting it to body temperature.....


The actual coefficient might be too small to get a noticable expansion though.....

Possibly find a way to seal up a container with a kind of light lid/gasket slider head and do this with gasses? (breathe in and out into it to get it to ~98, then do a boiking water bath and calculate the relative % expansion....)


I still feel like I am missing something though.....

 

[ussfletcher]

If you have access to glass, why not just make one of these then?