Hole straight through the Earth?

  • Context: High School 
  • Thread starter Thread starter Holocene
  • Start date Start date
  • Tags Tags
    Earth Hole
Click For Summary
SUMMARY

Dropping an object through a hypothetical hole straight through the Earth results in oscillatory motion due to gravitational forces, akin to a pendulum. The object would initially fall through the center, gaining kinetic energy, and then rise on the opposite side until it stops, only to fall back again. This cycle continues until air resistance and the Earth's non-uniform mass distribution dampen the motion, eventually causing the object to settle at the center of the Earth. Additionally, the Earth's rotation must be considered, as it would cause the object to collide with the tunnel wall during its descent.

PREREQUISITES
  • Understanding of gravitational forces and potential energy
  • Familiarity with simple harmonic motion concepts
  • Knowledge of Earth's structure and mass distribution
  • Basic principles of physics related to pendulum motion
NEXT STEPS
  • Research the effects of air resistance on oscillatory motion
  • Explore the concept of simple harmonic motion in depth
  • Investigate the implications of Earth's rotation on falling objects
  • Study gravitational force equations and their applications in physics
USEFUL FOR

Physics students, educators, and anyone interested in gravitational theories and thought experiments related to Earth's structure and motion dynamics.

Holocene
Messages
237
Reaction score
0
If a hole is somehow made to pass straight through the center of the Earth, and out on the opposite side, what would happen to an object dropped down the hole from one side?

Would it stop and "hover" at the center? Or would it fall straight through to the other side, and than fall back again and again?
 
Physics news on Phys.org
It will oscillate back and forward because there is a kinetic energy involved.
 
The action is similar to a pendulum. It will slow down only through friction (air resistance).
 
Oscillate back and forth through the center of the earth.
What will happen is when it will reach the center, it will possesses enough kinetic energy and will pass through the center.
Then it will slow down, building Potential Energy and will stop after emerging at the other side.
Then it will fall again, and the cycle will continue...

Important assumptions made are.
1)There is no air resistance.
2)Earth is a perfect sphere.
3)Mass is distributed homogeneously throughout the earth.

All are actually false and the first two will start affecting the motion and will start opposing its motion, so that, each time it stops before emerging out the other surface and will start slowing down.
This dampening will continue and after a huge amount of time, it will virtually stop at the center of the earth.
 
If you work out the force on the dropped object as a function of its distance from the center of the earth, you will find that it is a linear relationship (i.e., F = k * x), so it would be simple harmonic motion (this is, of course, neglecting air resistance).
 
It will hit the Eastern wall of the hole.
 
Granted this is a thought experiment, but Lurch mentions a wrinkle that I'm surprised no one else has: the Earth rotates. In the ~90 minute passage of the dropped object, the Earth will have rotated 22.5 degrees. The object will collide with the wall of the tunnel.

You'd have to do this experiment along the polar axis.
 
lurch mentioned a good point...
 

Similar threads

High School Hypothetical Gravity Question #2
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Equalizing airflow through multi-hole orifices
  • · Replies 3 ·
Replies
3
Views
2K
High School What sound frequencies can pass through a hole in a wall?
  • · Replies 31 ·
2
Replies
31
Views
4K
High School Thought Experiment from a Non-Physicist
  • · Replies 13 ·
Replies
13
Views
2K
Graduate Time to fall through a hole in Earth, but not through center
  • · Replies 1 ·
Replies
1
Views
2K
High School The inverse-square law: Gravitational force on two falling marbles
  • · Replies 23 ·
Replies
23
Views
2K
High School The Center of the Earth and Black holes and Gravity
  • · Replies 9 ·
Replies
9
Views
2K
High School Ignoring the motion of the Earth for energy vs. momentum conservation
  • · Replies 21 ·
Replies
21
Views
2K
High School Pressure through a curved hose - expected results?
  • · Replies 15 ·
Replies
15
Views
2K
High School Time to fall from 200 miles
  • · Replies 8 ·
Replies
8
Views
2K