Calculate mass of body based on fall time I'm participating a challenge that requires me to try and discover the mass of a person based on its fall time.
The rules are as follows:


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*You must use a smartphone

*You can't use any additional hardware besides the ones inside the smartphone


My first attempt was to read the phone's accelerometer constantly and check the vector sum of the acceleration of X, Y and Z. Based on the numbers produced by this equation I'm already able to detect if the phone is falling and when exactly it collides with a plane. Woot!
I need to do the same thing but with the smartphone on my lap and sitting on a traditional office chair. When I press the chair height knob, I should capture the starting and collision moments (unix timestamp) and based on that difference of milliseconds the challenge asks to come up with an approximation of the mass in kg of the person using the app.
Is there a way to discover the mass of a body based on its "falling time" like described above? I've been searching for this in the internet but all I was able to find was methods of discovering the distance traveled based on mass and velocity.
 A: We won't be able to give you an explicit formula for the relation of falling time and the mass of the person, since we do not know all parameters of your setup. As other have mentioned for free fall there should not be any real difference in falling time for different masses. However for the office chair you are not in free fall, since the chair slows down your fall. How the chair does this might be linear with your velocity, but can also be more complicated.
In physics (or science in general) one can also do experiments by doing a lot of measurements and try to see if there is any clear correlation between them and if so find a model that describes that. You can do this as well, by putting known masses (in the range of what the app should be able to predict) on the chair and measure their times.
Finding your model (assuming you do not switch chairs) will probably involve nonlinear regression, which I believe could be done in Excel. Once you have a model that fits your data you can use a measured falling time to predict the mass that is on the chair.
A: Office chairs contain a pneumatic cylinder. Your weight is supported by air pressure pushing up on a piston. Pressing the chair's height knob allows air to flow out of the cylinder into the surroundings.
The outflow rate from a cylinder has a complex dependence on the driving pressure. If you want to throroughly understand this, you will need to look at engineering resources like this. However, you will unavoidably need to make some measurements on the particular chair in question. With this in mind, you may as well measure the mass-time relationship empirically - start with a sensible guess like $t = \frac{c}{m - m_0}$, measure $(m,t)$ a few times and then use Excel to find the coefficients $c$ and $m_0$. If that doesn't give a good fit, try a more elaborate formula.
