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Imagine you've lost somewhere in the wild due to some catastrophic event, and don't have any measurement tools with you. How do you find approximate meter, millimeter, etc. with materials like sticks and stones?

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closed as too broad by Kyle Kanos, Jon Custer, sammy gerbil, tom, stafusa Apr 9 '18 at 12:06

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ If you do not expect a return to civilization, just take any stick and declare it is one meter long. This is all only a convention anyway. If you still need to measure in proper, well-defined, meters, then you are not completely lost. $\endgroup$ – Stéphane Rollandin Apr 3 '18 at 9:46
  • $\begingroup$ Let's say I'd like to return to civilization someday, but until this will become possible, I'd like to stick to familiar and proper units, this why I'm asking this. All of this of course hypothetical thought experiment, or how do you call a question like this. $\endgroup$ – baldrs Apr 3 '18 at 10:17
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    $\begingroup$ Well maybe remember how tall you are, or how long your arms are (or how long an adult wolf is, if you expect to meet one). You need to transport some sort of reference, because there is nothing in nature itself that will tell you what a meter is, as it is purely a human convention. Nature does not measure itself, so it does not need measurement units. $\endgroup$ – Stéphane Rollandin Apr 3 '18 at 10:22
  • $\begingroup$ As @V.F. answer shows though, if you are lost in the wild on Earth you will still have at least a measurement tool: the sun. It gives you the length of a day, from which you get the hour unit, from which you can get the meter (with a pendulum thanks to another measurement tool valid on Earth only: the constant of gravity). $\endgroup$ – Stéphane Rollandin Apr 3 '18 at 12:20
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    $\begingroup$ Bonus points for answers that involve using a barometer. $\endgroup$ – The Photon Apr 3 '18 at 16:33
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Make a pendulum and compare its period to your heartbeat. Adjust the length until the period is two heartbeats. The length of the pendulum will be approximately one meter.

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    $\begingroup$ This shifts the problem from recovering a unit of length to recovering a unit of time. Since the answer here is to remember how long two heartbeats are, it is not different from directly remembering how long your arms are (the latter having the added benefit that it does not depend on your emotional state..). $\endgroup$ – Stéphane Rollandin Apr 3 '18 at 12:03
  • $\begingroup$ @StéphaneRollandin, you don't have to "remember how long two hearbeats are". You can put your fingers on your other wrist to measure it. $\endgroup$ – The Photon Apr 3 '18 at 16:32
  • $\begingroup$ ... and hope you weren’t just walking. $\endgroup$ – ZeroTheHero Apr 5 '18 at 22:23
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If you are insistent on a meter, take a stone and drop it from rest. The position of the stone is given by $$ x=\frac{1}{2}gt^2 $$ where $g=9.8 m/s^2$. Thus, after $t=\sqrt{2/g}\approx 0.452$ second (assuming you have a watch), the stone will have dropped by $1m$.

In practice you might want to try different starting position above grounds until you find one for which the stone takes $\approx 0.452$second to hit the ground. Once you found a position with this drop time, you can declare that this height is $1m$ and go from there.

Alternatively, since $0.452$ is quite a short time interval, you might want to time a fall of $2m$, which would take $\approx 0.639$second.

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  • $\begingroup$ You don't have any measurement tools with you. How will you measure 0.452s or 0.639s? $\endgroup$ – sammy gerbil Apr 5 '18 at 10:52
  • $\begingroup$ @sammygerbil The question wan’t very clear and I understood you did not have any tool for measuring length. $\endgroup$ – ZeroTheHero Apr 5 '18 at 11:08
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    $\begingroup$ The question says clearly that you do not have any measurement tools, the only things you can use are sticks and stones etc. $\endgroup$ – sammy gerbil Apr 5 '18 at 11:14
  • $\begingroup$ @sammygerbil and my answer clearly states that having a watch is an assumption. $\endgroup$ – ZeroTheHero Apr 5 '18 at 11:47
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Ok, since this is a physics forum, we'll assume that you are not going to rely on your height and you don't have a dollar bill in your pocket.

Out of million ways to do it, with various levels of precision, I'd just give one example and I bet you'll be able to better it.

You make a pendulum and keep it going all day long (24 hours that is). If you manage not to fall asleep and not to lose count, by the end of the day you'll have your clock.

Then you climb up on a tall tree (or the tower of Pisa, if it happens to be around) and drop a rock.

By the time the rock hits the ground, you should know your meter.

Improvement (added per suggestion from Nicolas, below): don't climb a tree (unless you really like to do it) - just use the fact that the period of a pendulum is defined by its length.

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    $\begingroup$ well, the period of a pendulum is a function of its length… $\endgroup$ – Nicolas Apr 3 '18 at 11:28
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    $\begingroup$ @Nicolas Yes, that's why you have to count the number of periods over 24 hours to find what it is. $\endgroup$ – V.F. Apr 3 '18 at 11:37
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    $\begingroup$ If you already have the period of the pendulum, wouldn't it be easier to just get length directly from that instead of using that to do a separate experiment to measure time? It seems like this would compound the errors. $\endgroup$ – JMac Apr 3 '18 at 13:18
  • $\begingroup$ @Nicolas Silly me. Correcting the answer. $\endgroup$ – V.F. Apr 3 '18 at 15:08

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