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

[jsmith613]

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

 

[truesearch]

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 !

 

[jsmith613]

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?

 

[truesearch]

In a word...Yes, unless... you know different.

 

[jsmith613]

In a word...Yes, unless... you know different.

:)
thanks

 

[rcgldr]

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.