MadSci Network: Physics |
The terminal velocity represents a balance of two effects
1) The gravitational force on an object (corrected for buoyancy if the density of the medium is not negligible), which depends on its mass.
2) the drag force on the object, which depends on the object's size and shape, the viscosity of the medium it is in, and also on its velocity through the medium.
As an object moves faster, the gravitational force remains the same, but the drag force increases. When the two forces balance, the net force is zero and the object no longer accelerates. This is terminal velocity. The relevant equations can be found in freshman college physics texts.
It is difficult to compute the terminal velocity for an irregularly shaped object (like a student). But it is pretty easy for a spherical object. There is a calculator on the WWW that computes terminal velocity in the atmosphere for a spherical object:
http://www.physics.qc.edu/~walt/wb.html
You should be careful with units when using this; they are a little wierd. Assuming a 60 kg object of 1 meter diameter, this gives a terminal velocity of about 52 meters per second. I've heard numbers like 150 or 200 miles per hour quoted as terminal velocities for skydivers, so this seems to be at least in the right ballpark. The more compact and streamlined the falling object, the greater the terminal velocity. Try dropping a tightly wadded piece of paper and one loosely crumpled up from a height and you should be able to see a difference.
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