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37

Thanks a lot for your votes for the "answer" below. Unfortunately I think now the solution does not work. It is great for two slices, but that is the end. There is another solution that should give 3 slices, which is still a bit short. And I am afraid I do not see how to use the two available steps to start building a recursion :-) Why ? It is clearly ...


35

Petroleum engineers would all provide you with the same answer "use Compton scattering", as this is how the mass density of rock formations gets measured deep in oil wells. A more complete answer is: Compton scattering can provide you with a measurement of the bulk density of your head. Combine this with a volumetric measurement (dipping your head in a ...


33

Step 1: Take a trip to deep space (space suit recommended; means of transportation left as an exercise for the reader). It is important to compute the Hill sphere of your body to make sure it is large enough at this stage. Really it's a Hill-roughly-person-shaped-spheroid-blob, but feel free to assume a spherical you to simplify the calculation. Step 2: ...


31

I don't know if it qualify as home experiment, but you can use the internet to get access to thousands of kilometres of optical fibres for free. It allows you to measure the speed of light in the fibres, which is c/n, where n is the refractive index of glass, i.e. 1.5. This corresponds to 2×10⁸ m·s⁻¹. Using ping, you measure a roundtrip time, that is it ...


24

I would do it like this: The muscles of the neck have to be as relaxed as possible so that it approximates a flexible linkage, such that at some point along this linkage (which we can identify as the division between the head and the body, and thus the mass of the head includes a portion of the neck), if we separate the body into two free-body diagrams, ...


23

There is a trick I have heard about before but never tried. The basic idea is to put a mars bar in a microwave oven for a short amount of time. First you remove the turntable, so the chocolate bar stays stationary. Then you turn the microwave on just long enough for the chocolate to start to melt. It should melt at the nodes of the standing field. You simply ...


21

One common way of making these measurements is gravitational lensing. Basically, astronomers look at some distant object which is located directly behind the galaxy in question. Since the galaxy is so massive, it bends the light from the more distant object around it, so we see an image of the object displaced by some angle from where it actually is in the ...


21

Method The method is based on measuring variations in perceived revolution time of Io around Jupiter. Io is the innermost of the four Galilean moons of Jupiter and it takes around 42.5 hours to orbit Jupiter. The revolution time can be measured by calculating the time interval between the moments Io enters or leaves Jupiter's shadow. Depending on the ...


18

Let me first list all of the possibilities I considered that I later rejected. This is far from exhaustive, and I'm looking forward to seeing other people's creativity. Bad Ideas Sit on a tire swing with the fan pointing to the side. Point the fan up, measure speed of rotation of the system on the tire swing. Get a laser or collimated flashlight. Point ...


17

Eureka! As Archimedes said, according to legend. In principle, "TheMachineCharmer's" answer is feasible, but I would recommend recording the change in the volume of water instead (if you need an accurate measurement), because (1) it could be difficult to measure the volume of the spilled water, and (2) it is also a little less accurate to do so. (Some water ...


16

If you believe wholeheartedly in Mach's principle, then there is no way to test empirically for rotation of the universe as a whole, since there is nothing else for it to be rotating relative to. However, general relativity is not very Machian, and it offers a variety of ways in which an observer inside a sealed laboratory can detect whether the lab is ...


15

It depends on your definition of "any memories". If you don't remember what a second is, there is no solution. If you remember the "old" definition (a day has 24 h on 60 minutes, each of it is 60 s), and live on Earth not to far from now, you can rebuild an approximate time standard. If you remember the modern definition, i.e. (the duration of ...


15

You send the box and liquid towards a barrier equipped with a gauge to measure force. The setup looks like: When the box hits the barrier it stops, but the liquid inside it keeps moving. A short time later the liquid hits the side of the box and it too stops moving. So when you record the force at the barrier as a function of time you will get two peaks, ...


13

The set of irrational numbers densely fills the number line. Even assuming that quantum mechanics doesn't disable the preimse of your question, the probability that you will randomly pick an irrational number out of a hat of all numbers is roughly $1 - \frac{1}{\infty} \approx 1$. So the question should be "is it possible to have an object with rational ...


13

1 Person A lays down on a carousel with its neck over the edge. Person B knocks A out. Person C spins the carousel. B clocks the time. Person D takes pictures of A's head as it goes around. 2 Measure the angle of the head by looking at the pictures. 3 Do the vector math.


11

Assume the body to be made of N sections $S_i$ of uniform linear density $\lambda_i$ and length $l_i$ and center of mass $r_i$ (from one end). Increase N as much as you want to get a more accurate reading. The sections need not be of the same length. Try to slice your body into approximately homogenous sections (homogenous with respect to mass-per unit ...


10

There are three relevant quantities involved here: the length of a meter, the duration of one second, and the speed of light. You only need to absolutely measure one of them, after which the other two can be defined in terms of the one that is measured. For technological reasons, we have chosen to make the measured reference quantity the length of one ...


10

Carbon-14 makes up about 1 part per trillion of the carbon atoms around us, and this proportion remains roughly constant due to continual production of carbon-14 from cosmic rays. The half life of carbon-14 is about 5,700 years, so if we measure the proportion of C-14 in a sample and discover it's half a part per trillion, i.e. half the original level, we ...


9

The best way of measuring the mass is in principle using gravitational lensing, as mentioned in the first posted answer to this question. However, applying this method has become feasible only relatively recently, partly because lensing is relatively rare and requires 'lucky' alignment of the source and the lens, and thus a large telescope survey to find ...


9

You could find a capacitor and read of its capacitance, alternately build one and measure it, and measure its dimensions. Now you can get a good estimate on the permitivity of vacuum, epsilon. There are possibly other intricate ways to measure this number. The speed of light is then given by a relation involving another number, the vacuum permeability, µ , ...


9

The Doppler shift in the light from the star tells you the period of the planet's orbit and also the velocity the star moves. You need to know the mass of the star, but this can be estimated to good accuracy from the star brightness and type. Once you know the mass of the star you can calculate the distance of the planet from it's period using: $$ r^3 = ...


8

You might also want to try the rotating mirror method, of Léon Foucault. It is detailed here and here. The only difficult part is the rotating mirror, but it could probably be done with a drill.


8

According to what I understand you will show as weighing more on a carpet than on a hard floor. From what I understand it is due to the way the hard floor affects the feet of the scales. Here is a article that explores that question: http://www.newscientist.com/article/dn2462-people-weigh-less-on-a-hard-surface.html


8

These days planes measure their speed (and position) using GPS. In the old days (my father used to fly Tiger Moth's!) they would measure air speed for a rough guide, but correct their speed by spotting landmarks on the ground. In poor visibility it was not uncommon for pilots to get lost, sometimes resulting in tragedy when they flew into mountains or ...


8

It seems we have reached the point where simple models are no longer satisfying. Rather than posing ad hoc DEs maybe it's time to try an actual physical model. Short of doing a full hydrodynamic simulation (definitely overkill here) we can try what is called a lumped capacitance model where we divide the system up into a number of "lumps" and energy flows ...


8

Method 1: The Chemist's method Firstly, take pictures of your head from at least $400^3=64000000$ different equally spaced out angles. Samples: Then load them onto the computer, and use some 3D visualising software (maybe Scientfic Computing.SE can help you with that. ) to intersect the images at different angles, to get good, but of course, approximate ...


8

You just do. If a calculation gives you $\pi$, then you just say it gave you $\pi$. It is a real number and it is as good as any rational in describing any numeric quantity: $$\text{all physical quantities are described by }\mathbb{REAL}\text{ numbers}.$$ If you must insist on what real numbers are and how we can even conceive of such a number as $\pi$, ...


8

The short answer is you can't, or at least not at all easily. Your detector has only a single detection plane, and almost all muons are minimum ionizing, so you get essentially the same energy deposition from every muon (well, there is a factor from the angle of incidence the detection plane). The usual mechanism for measuring the energy of a particle are ...


7

I can't think of a way to do it with "common household tools" but if you have an oscilloscope, a laser diode, a couple of photo-sensors, a beam splitter, you can do it. All of these things are readily available from science supply/hobby stores online, but not usually in most homes. Set up the laser diode to hit the beam splitter and be split into two ...



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