- #1
philipp2020
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To calculate the exact fall time of a mass, constant g is often used for a short distance
traveled as for example in this paper:
http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000044000009000855000001&idtype=cvips&doi=10.1119/1.10277&prog=normal
In this paper they come to a average time of 0.24470 for an object droped from 1 feet.
Now tried to calculate the exact fall time value including non consistant acceleration, but I couldn't come quiet close to the same values as with constant acceleration. My result shows it should take 0.8483364538s for the object to fall from one feet. As for mass of the Earth I was using 5.974*10^24kg and the radius of the Earth 6371000m. I don't think that the unprecise numbers for mass and radius are the reason for the different result, so there must be something wrong in my formula. Maybe someone could help me find the problem with my equations?
To calculate the falling time I used the following formula for non consistant acceleration and then solved for t at the end:
[itex]
a = \frac{-GM}{r^2}t [/itex]
[itex]v =\int_0^t \! \int_{0637100,348}
^{6371000} \frac {-GM}{r^2}t\,dt\,dr = -3.42\times \frac {1}{2}t^2[/itex]
[itex]S = \int v \,dt = \int_0^t
\frac{1}{2}t^23.42\,dt =\frac{1}{6}t^3\times-3.42[/itex]
Ps: Sorry for double post, forgot title in first one...
traveled as for example in this paper:
http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=AJPIAS000044000009000855000001&idtype=cvips&doi=10.1119/1.10277&prog=normal
In this paper they come to a average time of 0.24470 for an object droped from 1 feet.
Now tried to calculate the exact fall time value including non consistant acceleration, but I couldn't come quiet close to the same values as with constant acceleration. My result shows it should take 0.8483364538s for the object to fall from one feet. As for mass of the Earth I was using 5.974*10^24kg and the radius of the Earth 6371000m. I don't think that the unprecise numbers for mass and radius are the reason for the different result, so there must be something wrong in my formula. Maybe someone could help me find the problem with my equations?
To calculate the falling time I used the following formula for non consistant acceleration and then solved for t at the end:
[itex]
a = \frac{-GM}{r^2}t [/itex]
[itex]v =\int_0^t \! \int_{0637100,348}
^{6371000} \frac {-GM}{r^2}t\,dt\,dr = -3.42\times \frac {1}{2}t^2[/itex]
[itex]S = \int v \,dt = \int_0^t
\frac{1}{2}t^23.42\,dt =\frac{1}{6}t^3\times-3.42[/itex]
Ps: Sorry for double post, forgot title in first one...
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