A mass is dropped into a hole bored along the diameter of earth. What is the type of motion with the mass?
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Answer:
Well, you'd fall a long ways. Because the tunnel was full of air, you'd only be able to reach a certain, slightly disappointing speed, and you'd reach it after falling just a few hundred feet. You'd fall for a long time! Geologists would very much envy the view.
I guesstimated how long it would take to reach the center of the Earth, ignoring some pretty major factors. I came up with 33 hours? It doesn't matter though, because one major factor I ignored was, you'd start slowing down as you got deeper. You'd slow down continuously until you'd barely be moving when you fell down past the center if the Earth, than up and down would get switched around and you'd float slowly back down toward the center again. You'd come to rest pretty quick, then it would be a miserable 4,000 mile climb to get home. Luckily, the core of the earth is thousands of degrees of red hot molten iron and nickel, so you'd have died from the heat long ago and you wouldn't have to climb it.
The speed problem is, air resists your movement as gravity pulls you down. The two forces balance out when you reach "terminal velocity" which is something like 200 km/hr (120 mph).
The other speed problem is, when you're standing on the surface you have 100% of the mass beneath your feet, all cooperating to pull you in one direction. As you fell, you'd have less and less earth below you, and more and more above, and the Earth would start arguing about which way you should be pulled. The closer you got to the center, the less downward acceleration you would experience. At the center, the earth would finally agree that you should be pulled equally in all directions at once, so you'd go nowhere.
The other other speed problem is, as gravity pulled on you less and less, there would still be air resistance slowing you down the whole time. Terminal velocity for 1% of earth's gravity in one atmosphere is a snail's pace. Without actually doing any arithmetic, I'm guessing you'd fall for closer to 33 days than 33 hours.
The other other other speed problem is, the air would be getting thicker as you went deeper, so the terminal velocity would be more like a gimpy snail's pace. It would also make the core of the planet an even more effective convection oven, so you'd be mercifully melted long before you got down to such a boring speed.
That was no fun after all, so to fix the speed problem let's suck all the air out of the tunnel, and also fix the heat problem. Line the tunnel with duct tape maybe.
The more I think about it, the less sure I am. Well, I'm going to plow onward anyway. Please bear in mind how wrong I might be. And don't try this at home.
So. Now when you jumped in the hole, if you remembered to bring a space suit, there would be no air to resist you, and no terminal velocity. You would continue to accelerate the whole way down to the center. The acceleration would decrease as you fell deeper and the earth started disagreeing about which way was up, but you wouldn't slow down a bit. It's totally more fun this way. If the earth didn't argue, you'd fall toward the center for 800 seconds, and pass the center at about 30,000 km/hr. (If you were an American, it would only be 18,000 mph.) That's about as fast as the Space shuttle.