If you dug a hole through the center of the earth,and jumped in, would you stay at the center because of gravi?
1. The person 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).
2. Terminal velocity of between 200-350 km/h would be reached in about 10 seconds or 500 meters. The terminal velocity is a function of G, mass of the falling object, and its coefficient of drag. Remember that air resistance is proportional to the velocity of the falling body squared. In other words, the faster you go, the more the air resistance. For an object to experience terminal velocity, air resistance must equal weight. The biggest variable in this case would be the amount of drag due to posture - if the person was falling head first (or feet first) to minimize aerodynamic resistance, or a belly flop position with arms and legs extended for maximum drag. Loose fitting thick clothes would also slow him/her down, as opposed to being naked (ouch!) or wearing some type of speed skaters clothing.
3. Once the person has fallen a few km, G would decrease because part of the mass of the earth would then be above the person. That means that the weight of the person 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 would be decreased. 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 the person is travelling faster than terminal velocity when drag starts to be greater than weight.
4. G would steadily decrease as the center of the earth was approached, until G is exactly zero at the center.
5. At the center of the earth, the person's actual velocity will still be faster than the calculated terminal velocity due to momentum. G is now zero, so the person's weight is zero (but mass doesn't change). Air pressure is now at its maximum.
6. The person would continue traveling past the center of the earth due to momentum, until the air resistance and gravitational force from the opposite side stopped him/her. Gravity would then pull him/her back toward the center in a "yo-yo" effect.
7. The person would oscillate back and forth a few thousand times, in ever decreasing movements due to the friction of air resistance. Every time the person passes through the center of the earth, s/he would be traveling a bit slower.
8. Air resistance would dampen the up and down (relative to the departure point) oscillations until a steady state of no movement was reached exactly at the center of the earth in a state of weightlessness and gravitational equilibrium. There is no gravity at the center of the earth because there are equal amounts of mass surrounding you.
Assuming of course there was no molten rock in the hole, and the person wasn't burnt to a crisp!
This question leads to a good study of the interaction between the various physical forces - motion, momentum, gravity, drag, mass, density, acceleration, and velocity - and the laws that apply to them including all three of Newton's three laws of motion.
I agree with the two previous answers - but if there was no friction you would oscilate back and forth from one side of the earth to the other forever (like a frictionless pendulum). Assuming friction you would eventually come to rest at the center.
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January 9th, 2009, posted by webmaster
