An evil scientist has constructed a shaft that passes through the center of the Earth to...

An evil scientist has constructed a shaft that passes through the center of the Earth to the other side as a way of getting

rid of his rivals. If he drops a rival who is an average height and weight male into the shaft, predict how far they make

it to the surface on the other side of the core. Would they emerge on the other side of the Earth? If they do not, what

is the fractional distance back to the surface they would make it? The Earth’s diameter is 12.72 million meters.

Assume the shaft is at ambient temperature.

Expert Solution

If the evil scientist drops a rival into the shaft that passes through the center of the Earth to the other side, first of all, the acceleration due to gravity is inversely proportional to the distance between the core of earth and surface. So the acceleration due to gravity progressively becomes smaller and smaller as you travel to the center of the earth.

So at the core center of the earth, the acceleration due to gravity will become zero and the person will be having net force due to weight 'Zero'. Assuming the air resistance is negligible in this flight to the center of the earth (so no energy dissipation due to friction).

This resembles a mass on a spring problem. This means the traveler would oscillate back and forth when he travels through the shaft.

The person will accelerate towards the center of the earth, feel zero force at the center of the earth, by taking a time of 119.18 / 2 = 59.59 minutes. And it oscillates back to the surface by taking 59.59 minutes. So the time period of oscillation will be 119.18 minutes. This is the case if we are neglecting the air resistance and frictional force.

but if we are considering the air resistance, assuming the journey started with zero velocity, jumping into the shaft, the velocity increases till the center of the earth, because of the high velocity he will not stop there, he will go to the opposite surface of the earth, since we are considering the air resistance, the velocity keeps on decreasing as he travels to the opposite surface and by the time he reaches the surface on the other side, the velocity will becomes zero (assuming constant air resistance) and he can stop at the surface eventually.

Amanda K answered 6 months ago

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