It would stay the same if there was no interference of if the gravitational pull of earth would not increase from the begining of it decent. Meaning I said the same thing you said. It would change if there were variables put into the equation.
Okay then, I'll write out an expression to show you how kinetic energy varies. The acceleration inside the solid Earth sphere would follow this equation:
F = mGM
Er/r
E3
Where F : The force acting on the ball
m : the mass of the ball
M
E : The mass of the Earth
r : the ball's position as a distance from the center of the Earth
r
E : the radius of the Earth
To find the gravitational potential, I integrate w.r.t. r:
U = mGM
Er
2/2*r
E3
Where U : Gravitational potential energy
Energy is conserved. Thus, since the ball begins with 0 kinetic energy at release, the kinetic energy at any point can be determined using the following equation:
U
i = U
f + K
f
mGM
Er
E2/2*r
E3 = mGM
Er
f2/2*r
E3 + K
(r
E2 - r
f2)*mGM
E/2*r
E3 = K
Doesn't look so 'the same' to me.
You can try some values for r
f if you want. For example, at r
E, K = 0. At r
f = 0 (the center of the Earth), then all potential energy has been transferred to kinetic energy. Anyway, I've probably lost you by now, and I don't even know why I'm explaining this, so I guess this paragraph is OVER!
So your telling me, that earths gravity increases as you go higher? and decreases as you go lower? That's not correct. You have 9.8 m/s ^2 at the crust and it increases to 10. something on the mantle boundary. Meaning it increases from 9 to 10 something in its gravitational pull on something.
If you're inside the sphere, then it increases as you approach the surface, and decreases as you approach the center. If you're outside the sphere, then it increases as you approach the surface, and decreases as you move away from it. What the hell are you talking about? D;
[...] only reaching net 0 when it is in the exact center. Wouldn't it?
Exactly.
Yea your right about that, but I was meaning that he said gravity decreases as you go deaper into the center of the earth which is not correct.
It IS correct.
Where did you read about this 10.7 m/s
2 acceleration? I can provide you with a proof about gravity being linearly dependent on distance inside a solid sphere, though, if you really want it.
[signs up for the Most Uselessly Descriptive Post Of The Year award]