Gravity at the center of the Earth?

From Tom Van Flandern:

Pressure is force per unit area. (But force is sometimes represented as a weight, making it look mass-like or volume-like, so we can measure it in non-standard units such as pounds per square inch or inches of mercury in a barometer.)

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Let's see that. Force is always a vector with a direction and a magnitude. Pressure p is defined as

dF=pds

where ds is an area vector. The pressure p can be a scalar quantity if and only if the force dF and the area ds vectors are parallel. Then, ds must be a vector with direction perpendicular to the area under consideration and magnitude equal to that area. If that's not a mathematical trick, so what is it?

More importantly, force is considered a cause or effect as in F=ma. What is exactly the cause and effect in the pressure equation? Certainly, ds cannot be an effect since it's there anyway. But p is a scalar quantity. Can we say a vector force affects a scalar pressure? As an example, in the Work equation, a force F and a dispacement vector dr cause a scalar product dW, which is fine. But, can we say that a pressure p, a scalar, times a vector ds results into a force. Which is which? Obviously, the force dF does not make the area, then pressure must the cause of force and not the force a cause of pressure. Any thoughts?

Time to fix some cars, pressure is mounting...

Also as the area is reduced the pressure must increase if the mass stays about the same. And as the center of mass is reached all the mass is above and resting at a point above the mass center. Assuming pressure peaks at some distance from the mass center where does one find the max pressure?

Now I see the problem Jim. When talking of pressure we always mean pressure difference. If we cut a sphere in half and place a manometer at the center then it will show a pressure for both halves. When the two halves are joint, the two pressures should cancel out according to the equation I gave above. Under the ocean is a different story but if you could find a spot where two diametrically opposed oceans are joint at the center of the earth, the pressure will be zero. No force then no pressure, equal force both sides then again no pressure. That's how I see it.

Time to fox some cars.

One of the problems is defining pressure in a container and a gravity field in the same statement. In a container pressure can be raised by adding small amounts of mass. In a gravity field pressure is mass per unit of area. The primary question in this forum is about the gravity field itself.

<BLOCKQUOTE id=quote><font size=2 face="Verdana, Arial, Helvetica" id=quote>quote:<hr height=1 noshade id=quote>[mechanic]: If we cut a sphere in half and place a manometer at the center then it will show a pressure for both halves. When the two halves are joint, the two pressures should cancel out according to the equation I gave above. Under the ocean is a different story but if you could find a spot where two diametrically opposed oceans are joint at the center of the earth, the pressure will be zero. No force then no pressure, equal force both sides then again no pressure.<hr height=1 noshade id=quote></BLOCKQUOTE id=quote></font id=quote><font face="Verdana, Arial, Helvetica" size=2 id=quote>

No, pressure is a scalar, not a vector. The force or gravity from the two sphere halves would cancel. The pressures from the two halves add. -|Tom|-

The splitting of a sphere into two equal masses can be done in many ways. Have you considered dividing the sphere into an inner and outer sphere of equal mass? Doing it this way it the inner sphere is attracted to the outer sphere and visa-versa. Would the force of gravity would be shifted from the center of mass?