Why is escape velocity given when total mechanical energy is zero?

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Discussion Overview

The discussion revolves around the concept of escape velocity and its relationship to total mechanical energy, specifically when that energy is considered to be zero. Participants explore the implications of gravitational potential energy and kinetic energy in this context.

Discussion Character

  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants explain that in a gravitational field, potential energy is negative, with the zero point defined at infinity, leading to the conclusion that energy must be supplied to reach this point.
  • One participant asserts that at infinity, all kinetic energy (KE) is converted to gravitational potential energy (GPE), resulting in a total energy of zero at that point.
  • Another participant agrees with the previous point but introduces the idea that GPE is a relative value, suggesting that it can be defined differently depending on the context, such as at the surface of the Earth.
  • It is noted that if an object's velocity exceeds escape velocity, its total energy (KE + GPE) would be greater than zero, indicating a potential disagreement on the implications of escape velocity.

Areas of Agreement / Disagreement

Participants express some agreement on the relationship between kinetic and potential energy at infinity, but there are competing views regarding the definitions and implications of gravitational potential energy and escape velocity.

Contextual Notes

Participants highlight the dependence on the definition of potential energy and the relative nature of kinetic energy, which may lead to different interpretations of the conditions under which escape velocity is defined.

jsmith613
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can someone please very briefly explain why the escape velocity of an object is given when the total mechanical energy (KE + potential energy) on an object is zero

Thanks
 
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masses in a gravitational field have negative potential energy. The zero of potential energy is taken to be at infinity. To get to infinity energy must be supplied therefore objects must have negative potential energy. (if you have to add energy to get to zero...)
The energy supplied must total zero !
 
truesearch said:
masses in a gravitational field have negative potential energy. The zero of potential energy is taken to be at infinity. To get to infinity energy must be supplied therefore objects must have negative potential energy. (if you have to add energy to get to zero...)
The energy supplied must total zero !

ok so to clarify:
all the KE is converted to GPE at inifnity
at this inifinity point, GPE is zero (as anything/infinity) = 0
As total energy at the end = zero
total energy at ALL points is zero

is this correct?
 
In a word...Yes, unless... you know different.
 
truesearch said:
In a word...Yes, unless... you know different.

:)
thanks
 
jsmith613 said:
all the KE is converted to GPE at infnity, at this inifinity point, GPE is zero
PE is a relative value between two points in space. KE is relative to some (inertial, non-accelerating) frame of reference. GPE is zero at infinity only when it's defined that way. For simple physics problems, GPE is often defined as zero at the surface of the Earth (GPE = m g h).

Even if you define GPE as zero at infinity, (and KE relative to the source of a gravitational field such as a planet) if velocity of an object is greater than escape velocity, then it's total energy (KE + GPE) is greater than zero.
 
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