# What would happen if an iron sinks on the ocean? Velocity

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1. Dec 30, 2015

### CollinsArg

if I throw a ball of iron on the ocean, the velocity in which it will sink will be lower at the beginning and higher getting near the deepest part of it? As it may be forced by the pressure of water? (the weight of water)

2. Dec 30, 2015

### SteamKing

Staff Emeritus
Remember, when the ball is totally submerged, there is pressure forcing it to the surface, as well as pressure forcing it to the bottom. According to Newton's law of motion, it's the net force acting on the ball which causes it to move. How to figure this net force? Apply Archimedes' principle to the ball.

3. Dec 31, 2015

### jambaugh

The pressure of the water applies a force to all sides of the ball of iron, including the top and bottom. It is the difference in pressure that matters. The pressures at the top and bottom of the iron ball will be different but their difference does not change (much) with depth. (Try picturing a cube instead of a ball so the pressure forces are only in the cardinal directions. This makes the reasoning a bit simpler.)

What you may observe is that since there is still a net downward force on the ball, it will accelerate downward until the fluid drag of its downward motion is sufficient to match the net force of weight minus buoyancy.

If you do all the book keeping on this difference in pressure and the directions of the forces and such you end up recalculating Archimedes principle of buoyancy. The weight of the iron ball will be reduced by the weight of the water it displaces and only the water it displaces. The amount of water above and below do not factor into this directly and so to first order approximations the net weight of the ball will not change as the ball sinks.

There are some very minor corrections to this however. There will be slight compression of the water, deeper water is denser, and so ignoring compression of the iron you will get an increase in the buoyancy of the iron ball. Of course iron will compress too but not nearly as much as water so the net effect will, in so far as it can be measured at all, a very slight increase in buoyancy with depth so ultimately the iron ball will slow slightly as it sinks.

Now something you can play with to see buoyancy in action is a Cartesian diver: https://en.wikipedia.org/wiki/Cartesian_diver . If you consider a bubble of air rather than an iron ball then it is much more compressible than the water around it so with higher pressure it compresses, displaces less water, and thus becomes less buoyant. I used to play this in large scale with plastic buckets and weights in our swimming pool when I was younger. I could balance the weight so that the bucket floated at the surface but would stay on the bottom if I pushed it down. But the Cartesian diver is a small example of this in a (modern version) flexible bottle. Squeeze the bottle to increase pressure and compress the air bubble within the little diver and it sinks. Release it and it floats.

4. Dec 31, 2015

### A.T.

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