**Date:** Thu, 2 Dec 2004 16:11:04 -0800

**Author:** Paul Doherty

**Subject:** Re: buoyancy

**Post:**

Hi Wolfgang

Think of the simpler static experiment a partially hollow wood ball

floating in a beaker of water on the

earth, then the Moon

The ball floats exactly half submerged.

On earth The buoyant force on the ball is equal and opposite to the weight

of the ball. (This happens when the ball displaces a volume of fluid with a

weight equal to the weight of the ball.)

On the moon the buoyant force is equal and opposite to the weight. The

acceleration of ggravity on the moon is 1/6 the acceleration of gravity on

the surface of the earth. So the same mass ball has 1/6 the weight. The

force required to float the ball is 1/6 the force on the earth. However,

this happens when the same volume (mass) of fluid is displaced because the

weight of the fluid is decreased by the same 1/6 as the weight of the ball.

The upward force is indeed less yet the ball still floats 1/2 submerged

same as it did on earth.

Another way to look at it.

The pressure of the fluid increases with depth. Integrate the vertical

component of the fluid pressure over the submerged hemisphere on earth to

get the upward net buoyant force. Do the same integral on the moon. The

pressure with depth goes up 1/6 as rapidly with depth on the moon as it

does on earth. The net force is 1/6. but the weight of the ball is also

1/6, so it all works out.

Now move to the accelerating frame...

Paul D

>I have a conceptual question pertaining to buoyancy in an accelerated

>frame (for example, Dick Berg's demo found under

>http://www.physics.umd.edu/lecdem/services/demos/demosf2/f2-22.htm

>I understand the argument why the buoyant force of a floating object

>increases by the same amount the the object's weight increases in the

>accelerated frame, and therefore the object doesn't float any

>differently than when it's sitting still. My problem is visualizing

>the mechanism of what's going on to accelerate the floating object.

>The container of fluid is accelerated by some outside force and that

>force has to be communicated to the floating object by the liquid it's

>floating in so that it too accelerates by the same amount. But the

>only force of the liquid on the object is the buoyant force. So

>doesn't the buoyant force have to be a little different from the

>apparent weight of the floating object to produce an acceleration?

>Where is my thinking hanging up? -- Wolfgang

From jowelch@cabrillo.edu Thu Dec 2 19:09:03 2004