How long does it take to fall to the center of the earth?

In summary, the conversation discusses the time it would take for a body to fall from the surface of the earth to its center, assuming only gravitational force is acting. The problem has been difficult to solve as only the acceleration as a function of distance is known, but not as a function of time. The conversation also suggests writing the gravitational force as a function of distance and seeing if it relates to any known concepts.
  • #1
raul_l
105
0
Let's assume that there are no other forces acting besides the gravitational pull of the earth. If a body started falling from the surface how much time would it take before it reached the center of the earth?
It seems like an easy problem, but so far I have had no luck. So far I have only found acceleration as a function of distance (which is quite easy), which would be [tex] a=\frac{4G\pi \rho}{3}(r-s) [/tex] (rho: Earth's density, r: Earth's radius, s: traveled distance)
But that doesn't help me since I need acceleration (or velocity) as a function of time and I have no idea how to proceed.
 
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  • #2
Write the gravitational force as a function of distance from the center. Then see if it reminds you of anything.
 
  • #3
[tex] F=\frac{4G\pi \rho m}{3}s [/tex]

still thinking...
 

1. How deep is the center of the earth?

The center of the earth is approximately 6,371 kilometers (3,958 miles) deep. This is the distance from the earth's surface to its core.

2. How long would it take to fall to the center of the earth?

The time it takes to fall to the center of the earth depends on several factors such as the initial velocity, air resistance, and the density of the medium you are falling through. However, assuming there is no air resistance, it would take approximately 42 minutes to reach the center of the earth from the surface.

3. What happens to a person's body when they fall to the center of the earth?

If a person were to free fall to the center of the earth, their body would experience increasing pressure and temperature as they get closer to the core. At the center, the person would experience intense heat and pressure that would likely be fatal. However, it is not possible for a person to reach the center of the earth due to the extreme conditions and the presence of the solid inner core.

4. Can anything survive the journey to the center of the earth?

No, it is not possible for anything to survive the journey to the center of the earth. The intense heat and pressure would destroy any living organism and even melt most materials.

5. Why is it not possible to dig or drill to the center of the earth?

Despite advances in technology, it is not possible to dig or drill to the center of the earth. The deepest hole ever drilled, the Kola Superdeep Borehole, reached a depth of only 12 kilometers (7.5 miles). This is because the earth's crust becomes increasingly hot and dense as you go deeper, making it impossible for any drilling equipment to withstand the extreme conditions.

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