• Categories

  • Most Popular Questions

  • Recently Viewed Questions

  • Recent Answers

    Daigrepont on Can an earthquake cause air tu…
    Benedict on How did God come into exi…
    joshua on How does the human body g…
    Ian on How did God come into exi…
    Sidra on How did God come into exi…
  • Recent Questions

  • Blog Stats

    • 2,167,541 hits
  • Visitors since 11-3-08

    counter create hit
  • Terms and Conditions

  • Warning

    We are doing maintenance on this site, so some posts may disappear for a short time. Sorry. Normal service will soon be resumed...
  • Pages

  • March 2008
    M T W T F S S
    « Feb   Apr »
     12
    3456789
    10111213141516
    17181920212223
    24252627282930
    31  
  • Archives

  • Meta

What would happen if you fell into a shaft through the earth?

If a shaft was possible from the surface of the Earth, through the centre, and re-emerged on the other side (heat etc notwithstanding) what would happen if you fell down it?
Simon Wright from South Yorkshire (Age: 35-44)

Advertisements

One Response

  1. Actually, as long as you don’t melt (and if air resistance is negligible) what would happen is that you’d oscillate back and forth from one side of the earth to the other ad infinitum. This is a rather unusual example of “simple harmonic motion”, the underlying principle behind many types of oscillations in the physical world, such as a pendulum.

    The reason is as follows. At the “top” of the earth, gravity will accelerate you downwards. Your speed will increase, until you reach the centre of the earth. At the centre of the earth, you’ll feel gravity equally above and below you, so acceleration on you will be zero. However, you don’t stop. All the potential energy you had at the top of the earth has been converted to kinetic energy, and you’re travelling downwards at a significant velocity! Newton’s second law dictates that because gravity is zero exactly at the centre, your speed won’t change, and you’ll keep on going!

    As you carry on going, and you get closer to the “bottom” of the earth, there is more earth above you than below you, and in balance, the gravity will begin pulling you back up to the top again, making you decelerate and slow down. Without air resistance, you’ll find that exactly at the point that you come out the other side, you come to an instantaneous standstill, and then get pulled back into the shaft again.

    And how do we know that you’ll stop exactly as you emerge from the other side of the earth? Well, that’s easy if you consider energy conservation. All your energy at the top of the earth is in potential energy, and by the time you’re at the centre of the earth, it’s been entirely converted to kinetic energy. You know the Earth is symmetric, so that means you’ve got exactly enough energy to carry on and reach the bottom of the Earth before gravity wins and you get pulled back again. You don’t lose any energy though, and when you’re at the bottom of the earth, you’re in the same situation as you were at the top of the earth. This means that you keep on bouncing back and forth for ever!

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: