Hypothetical question. Let's say at the exact center of the earth, or any similarly sized planet, there was a void the size of a room or so. And you were in that void. What would happen? Gravity-wise, pressure-wise? The void could withstand the physical pressure of the earth bearing on it, but would gravity be stronger there? If it were, would you just be crushed, suspended in the center of the room? Or would it just be like space, where you could just float around? I need some help here, man.
Gravitational force at exact center would be 0 N.
True if: 1) the Earth is a perfect sphere (it isn't), 2) the Earth is also of uniform density (it isn't), and 3) the Earth exists in a void in which no external objects exert a gravitational force on it (theyd do).
1) Close enough, the assumption of a well defined "center" implies a sphere is which is enough to answer his question
2) As long as the density is only dependent on the distance from the center the variance in density doesn't matter
3) Yes the every other object in the visible Universe exerts a gravitational force as well, but I don't think ew2x4 wanted to include every possible other object in the visible Universe.
But yes you can successfully nitpick an infinitum if you want. You sure showed those EP1 profs a thing or two I bet!
1) The Earth isn't spherical, its basic shape is more that of a nonuniform oblate spheriod (those approximately 19 extra miles of mass around the equator are going to throw off your rather unclever assumption). And because your next unclever assumption is rather obvious: so will surface nonuniformities, you know, small things like continents, mountain ranges, etc.
2) The Earth's density is most definitely not a function only of the distance from "center" (another rather unclever assumption that prevents you from reaching the correct answer). Unless you, for example, believe that the air in Mammoth Cave has precisely the same density as the rock surrounding it. Similarly, since the material composition of the planet isn't uniform anywhere your assumption of uniformity is merely uniformly ignorant.
3) There exists an object with which you may be familiar, colloquially referred to as "The Moon" (take a few moments to familiarize yourself with it before we continue), that exerts sufficient gravitational force on the surface of the Earth to cause tides despite the roughly 238,000 mile distance between the bodies.
Suppose that, for the sake of argument, we move forward by assuming as true your false assumptions about the spherical uniformity and uniform density of the Earth. Even then your answer is wrong as the net gravitational force exerted on a body at the "center" of the Earth is still not zero. This is true for many reasons one of which is that the moon will exert a finite gravitational force on this body ... unless of course you believe that the gravitational force is somehow able to act at distance of approximately 238,000 miles but will not act at distance of approximately 242,000 miles. Your theory of gravitation must be fascinating, please do take the time to share it with us.
The question you answered was, "Hey what would happen to a point mass in a perfectly spherical void at the precise center of a perfectly spherical body made of a uniform material that is of precisely identical density at every point and which exists in a closed universe where no other masses or forces exist?" Unfortunately, for you, the OP asked about the Earth for which none of those assumptions even begins to hold.
EP was
but obviously you should have paid more attention.
