Alright so say this is possible, we dig a hole in the Earth deep enough that it comes out the other side of Earth exactly in the center. So what would happen if we dropped something right down that hole like a penny? Assuming the magma wouldn't be there. Would it hit dead center of Earth and just float there due to gravity like it just hit the ground even though there wouldn't be a ground? That's what I always figured would happen. What exactly would happen?
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Assuming that it is possible to drill a 12,742 km deep hole and there was no Coriolis effect, the penny would ultimately end up motionless at the Earth's center of mass, but its a bit more complex than that. The penny was a veyr poor choice of objects to drop down the hole, as I will explain, but here is what would happen:
1. The penny would initially fall and accelerate at the rate of acceleration due to gravity (g), 9.8 m/sec/sec (exact g depends on latitude, density of surrounding rocks, and altitude). Potential energy will be at its maximum when you first dropped the penny.
2. Terminal velocity of between 200 km/h and 600 km/h would be reached in about 10 seconds or 500 meters. Kinetic energy is now at its maximum. The terminal velocity is a function of G, air density, density of the falling object, and its coefficient of drag or friction. Remember that air resistance is proportional to the velocity of the falling object squared. In other words, the faster the object moves through the air, the more the air resistance. For the penny to experience terminal velocity, air resistance must equal weight (not mass). The biggest variable in this case would be the attitude that the penny is falling - either flat (maximum resistance) or on edge (minimum resistance).
3. Once you have fallen a few km, g would decrease because part of the mass of the earth would then be above you. That means that your weight is decreased but the mass stays the same. Also the atmospheric pressure would increase, resulting in more drag. In other words, weight and g are decreasing but drag is increasing. Therefore terminal velocity is decreased as you approach the center of the earth. However momentum would ensure that the actual speed was slightly more than terminal velocity, so the net effect would be that velocity would lag behind the increased drag and decreased g, so that you are travelling faster than terminal velocity when drag starts to be greater than weight. The penny was a poor choice of objects to drop down the hypothetical drill hole because of these basic variables, never mind the aerodynamic effects if it wasn't perfectly flat or horizontal, and we'll ignore those possibilites to keep things relatively simple.
1. The penny would initially fall and accelerate at the rate of acceleration due to gravity (g), 9.8 m/sec/sec (exact g depends on latitude, density of surrounding rocks, and altitude). Potential energy will be at its maximum when you first dropped the penny.
2. Terminal velocity of between 200 km/h and 600 km/h would be reached in about 10 seconds or 500 meters. Kinetic energy is now at its maximum. The terminal velocity is a function of G, air density, density of the falling object, and its coefficient of drag or friction. Remember that air resistance is proportional to the velocity of the falling object squared. In other words, the faster the object moves through the air, the more the air resistance. For the penny to experience terminal velocity, air resistance must equal weight (not mass). The biggest variable in this case would be the attitude that the penny is falling - either flat (maximum resistance) or on edge (minimum resistance).
3. Once you have fallen a few km, g would decrease because part of the mass of the earth would then be above you. That means that your weight is decreased but the mass stays the same. Also the atmospheric pressure would increase, resulting in more drag. In other words, weight and g are decreasing but drag is increasing. Therefore terminal velocity is decreased as you approach the center of the earth. However momentum would ensure that the actual speed was slightly more than terminal velocity, so the net effect would be that velocity would lag behind the increased drag and decreased g, so that you are travelling faster than terminal velocity when drag starts to be greater than weight. The penny was a poor choice of objects to drop down the hypothetical drill hole because of these basic variables, never mind the aerodynamic effects if it wasn't perfectly flat or horizontal, and we'll ignore those possibilites to keep things relatively simple.
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