Tuesday, May 5, 2009

Falling Objects

Objects fall to the earth because our friend gravity compels them to do so. This is true whether you are a bowling ball falling off a building or a human sinking in a vat of Jell-O. The rate at which an object falls determines how long it takes for the object to land wherever it’s going to land. This is physics.

We objects accelerate towards the earth until we reach terminal velocity. Terminal velocity is the rate at which surface resistance (friction between the surface of the object and the air, water, or Jell-O) cancels out the acceleration due to earth’s gravity. Once terminal velocity has been achieved, bowling balls, pennies, and people fall at constant rates of speed. To determine how long it would take my rock-self to reach the bottom of the deepest part of the ocean I needed to determine the terminal velocity of a rock falling through sea water.

The cute little equation below is called Stoke's Law. He's gonna help me figure out what I want to figure out. He says that terminal velocity (Vt) depends on the shape and density of the falling object (rock). Vt also depends on the density and viscosity of the fluid the object is falling through (sea water). I used him to do a quick and dirty calculation for the terminal velocity of a rock-like object falling through sea water.

I came up with a terminal velocity of 8 miles per hour. It's far from exact. I encountered a serious problem in my calculations because the viscosity and density of water vary according to temperature, pressure, and salinity. All three of these factors change quite a bit over the course of a 35,000 foot journey.

In Conclusion:

How long does it take for a rock dropped from the surface of the ocean to fall to the bottom 35,000 feet below?

About forty-five minutes.

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