Various expressions for the kinetic energy

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Homework Help Overview

The problem involves a theoretical scenario where an object is dropped through a hole drilled through the center of the Earth. The subject area is kinetic energy and gravitational potential energy, specifically examining the expressions for kinetic energy as the object passes through the center of the Earth.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply conservation of energy principles to derive the kinetic energy expressions, questioning why their derived expression does not match the provided options. Some participants question the assumption that potential energy is zero at the center of the Earth, leading to further exploration of the implications of this assumption.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of potential energy at the center of the Earth and its implications for the kinetic energy expressions. There is no explicit consensus yet, but the dialogue is productive in examining the assumptions involved.

Contextual Notes

Participants are considering the implications of gravitational potential energy and its behavior as the radius approaches zero, which raises questions about the validity of certain assumptions in the context of the problem.

hangainlover
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Homework Statement


Suppose that a hole is drilled through the center of Earth to the other side along its axis. A small object of mass m is dropped from rest into the hole at the surface of Earth, as shown above. If Earth is assumed to be a solid sphere of mass M and radius R and friction is assumed to be negligible, correct expressions for the kinetic energy of the mass as it passes Earth's center include which of the following?

the given choices are as follows:
a) (1/2) MgR
b) (1/2)mgR
c) (GmM)/(2R)

Homework Equations



Due to the conservation of energy, i said Potential energy = the final kinetic energy

So, on the surface of the Earth, the total potential energy = -(GmM)/R
this should equal kinetic energy




The Attempt at a Solution



I thought the answer should be (GmM)/R but none of them matches my answer.
 
Physics news on Phys.org
You assumed that the potential energy is 0 in the centre of Earth. Is it true?

ehild
 
yes cause GMm/R^2 R approaches 0
 
If R approaches 0 your expression goes to infinity.

ehild
 

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