If a frictionless car on tracks descends into the hole by Earth's gravity from location A and comes out at location B, how long did it take to make the transit? Assume that density of the Earth's core is uniform.
2007-02-17 17:25:59 · 14 answers · asked by Scythian1950 7 in Science & Mathematics ➔ Physics
Points A and B are on the surface of the Earth.
2007-02-17 17:36:00 · update #1
Assuming that "frictionless" includes no wind resistance, and that the earth were perfectly spherical, the car will accelerate to the center at which point is begins to deccelerate until it arrives at the other side and just comes to a stop at the surface.
The trick is, as it travels, the acceleration due to gravity also changes. Consider that at the surface, the acceleration due to gravity is about 32 ft per second squared. At the very center, the earth's mass is uniformly distributed around the car, cancelling out to zero gravity (the car is "pulled" in all directions equally). The car's momentum is what carries it through to the other side as gravity then causes decceleration beyond the center point.
Because you have a continuously changing gravity, the calculation requires calculus to generate the answer. We had to do this in a physics class when I was an undergraduate.
The correct answer is approximately 91 minutes.
An interesting paradox, is that the direction of straight travel does not matter. The car could leave the surface at ANY angle and in a stright line and arrive at the surface in 91 minutes. Remember, NO friction, NO wind resistance and a perfect sphere.
2007-02-17 20:57:13 · answer #1 · answered by John E 3 · 0⤊ 0⤋
Consider a pendulum when there is no air resistance.
All the energy that is put into the car moving with the force of gravity must be expelled somewhere. Where can that energy be put other than propelling the car away from the center of the earth once it makes it there? Think about it. If there is no friction or resistance to absorb the energy, then the car will stop exactly at the very surface of the earth, where it started just in a different location.
2007-02-18 01:57:44 · answer #2 · answered by Sir Drew M 2 · 0⤊ 0⤋
Wouldn't it technically never fall out because the Earth's Gravity keeps it in. The earth's gravity is like a magnet in the center.
2007-02-18 01:29:52 · answer #3 · answered by Sahil 2 · 0⤊ 0⤋
It would take approxiamately 60 hours to reach the earths core. So 120 hours to make the whole trip... about ten days. I saw that on the History channel.
2007-02-18 01:29:56 · answer #4 · answered by backpackwayne 5 · 0⤊ 0⤋
It's velocity from the first half would Carry it approximately 1/3 of the way through the second half. then it would need enough power to propel it the rest of the way. so the time would depend on the weight and power. without those factors there can be no answer.
2007-02-18 01:41:21 · answer #5 · answered by oldmanwitastick 5 · 1⤊ 0⤋
I think that it will perform a simple harmonic motion.I remember the formula to be
T=2Ï[R^3/GM]^1/2 Or simply T=2Ï[R/g]^1/2
Where R=6.4*10^6 m
G=6.67*10^-11 Nm^2/kg^2
M=6*10^24 Kg
g=9.8 m/s^2
2007-02-18 01:34:08 · answer #6 · answered by Tariq M 3 · 1⤊ 0⤋
Gravitational force will not allow Car to travel through it. The Car may keep on moving like a pendulum.Since it's frictionless it will not stop.
but you can send objects with car and deliver them free of cost at both end.......lol
2007-02-18 01:31:49 · answer #7 · answered by pankaj s 3 · 0⤊ 0⤋
it will exit if and only if point B is the same distance or less from the earth's center as point A.
2007-02-18 01:34:43 · answer #8 · answered by Anonymous · 0⤊ 0⤋
No friction, so wouldn't it be stuck in the middle or stop shortly before hitting the other side?
2007-02-18 01:29:25 · answer #9 · answered by Anonymous · 0⤊ 0⤋
it will never make the transit.......cause once it passes halfway it is going against gravity.......
2007-02-18 01:29:19 · answer #10 · answered by PigPen 3 · 1⤊ 0⤋