Why Don't We Consider the Distance to the Earth's Center for Potential Energy?

[Karol]

Homework Statement

A mass of 3kg is 1m above the floor. the zero of the potential energy is chosen to be on the floor.
I understand that the 30j potential energy belongs to both the Earth and the mass, so, why don't i take into account also the distance to the center of the earth?
Why don't i take the distance to the center of the Earth as the potential energy? why is h₁ better than h₂ (see drawing)?
What does the zero line mean?

Homework Equations

$E_P=mgh$

The Attempt at a Solution

Is it related to the fact that only differences in potential energy count?

 

[Nathanael]

Is it related to the fact that only differences in potential energy count?

Yes, exactly.

There isn't any 'absolute gravitational potential energy'

It only makes sense to speak of gravitational potential energy relative to some other position.

The "zero line" is just the "some other position" (which we are measuring relative to)

h1 is arbitrary.

(I find it analogous to how kinetic energy only makes sense when measured relative to some other speed.)

 

[ehild]

The potential energy of a mass m that belongs to the gravitational force of the Earth is -GmM/r where G is the gravitational constant, M is the mass of the Earth and r is the distance from the Earth centre if r≥R, the radius of the Earth. In that case, the zero of the potential energy is at infinity.

Very near to the Earth surface, the change of the potential energy can be taken proportional to the change of height. It is an approximation, assuming constant gravitational force. The potential energy with respect to a chosen "ground" is U=mgh. But that is true only for distances which are much shorter than the radius of Earth.

ehild

 

[Karol]

Reply to Nathanel: i thought kinetic energy is fixed, has a meaning, i never learned that kinetic energy is relative to something, i am always asked "what is the kinetic energy of..."
Of course difference in kinetic energy means the energy is transferred elsewhere, but there is also meaning to absolute kinetic energy, no? because the momentum is related to kinetic energy and it's absolute.
I can also be asked what work will a mass of certain speed do and i use kinetic energy to answer

 

[ehild]

The kinetic energy of a particle depends on the frame of reference. If a particle moves with velocity v in a system traveling with velocity V, in the moving frame of reference its kinetic energy is 1/2 mv², but in the rest frame of reference the veleocity is v+V and the kinetic energy is 1/2 (v+V)².

ehild