Penny Dropping in Water
Date: Spring 2013
At what rate will a penny fall through seawater? How long would it take a penny to drop from a boat to the bottom of the ocean (12,000 ft.)?
This is an extremely difficult question to answer. The rate of fall
depends on several things such as, is the penny falling edgewise or
broadside, or is it tumbling (spinning), and if tumbling, how fast is it
tumbling? Also, as the penny drops toward the bottom, 12000 feet
down, water density increases as depth and pressure increases. This
will gradually result in continuing to slow the rate of fall.
This is a fiendishly difficult fluid dynamics problem that is far to
complex to be answered by normal means. The answer will require the
use of a powerful computer running highly complex Computational
Fluid Dynamics (CFD) software.
Thanks for the question. It will be very difficult to know exactly at what rate a penny would fall through seawater since the penny will tumble and will experience viscous drag through the water. However, if we do know the rate at which the penny falls through water, we can use calculus to find out the time it would take to reach the bottom.
You can estimate the rate at which the penny will fall through the water: you can measure the time it takes the penny to reach the bottom of a shallow pool of water. Repeat this measurement for several heights of water and plot the data. You will see a trend in the data. I would recommend that you give this method a try as the first step in answering your questions. Note that this will give only a rough approximation.
I hope this helps.
This is difficult to say for one or more of the following reasons: (1) A penny is a flat disc. Its rate of fall in sea water, or any other fluid will depend upon how it tumbles. (2) The density of sea water at such a depth will change with temperature. That influences the rate of fall also. (3) The sea water is not stagnant. It is turbulent. These factors influence the rate of fall. (4) What is the initial velocity of the penny? All of these and other factors make a prediction difficult.
Interesting question, but I am afraid that an accurate prediction is not possible because:
1 the masses of pennies vary from country to country
2 the rate of sinking depends on the orientation of the penny (horizontal or vertical) (flat or standing up)
3 the orientation of the penny is subject to unpredictable localized current disturbances in the water as it sinks and changes in an unpredictable way.
But keep wondering about things like this. It is a good practice to think of all of the possibilities of a problem.
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