# A question regarding Potential Energy

#### brum

Let's say I lift a 50 pound weight with my arms to shoulder height (say, 4 feet). The "work" that I did to get the weight up there (the energy I put in) has now been converted to "potential energy" because it is perched in a position where it can then convert that into kinetic energy.

But, that potential energy is there only because of the Earth's gravity, right? If I were to let go of the weight, it would convert the energy I put in to lift it (potential energy) into kinetic energy -- falling towards Earth.

In other words, that potential energy exists only because of Earth's gravity.

....

Suppose I were to lift the weight 4 feet in the air, and then Earth disappeared or vanished or lost a lot of mass or whatever. Just say the earth went away. Wouldn't the weight then lose its potential energy (because the earth is no longer there)?

EDIT: How would this situation satisfy the Conservation of Energy rule?

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#### nbo10

If the earth just "disappeared", you wouldn't conserve energy, or mass.

JMD

#### drag

Originally posted by brum
Wouldn't the weight then lose its potential energy (because the earth is no longer there)?
Yes.
Originally posted by brum
How would this situation satisfy the Conservation of Energy rule?
It wouldn't (unless the Earth "dissapeared" at less than
the speed of light ).

Live long and prosper.

#### chroot

Staff Emeritus
Gold Member
The concept of potential energy depends upon a potential, which is nothing more than a way to express a field. Without a gravitational field, there is no such thing as gravitational potential energy.

- Warren

#### pmb

brum wrote
Let's say I lift a 50 pound weight with my arms to shoulder height (say, 4 feet). The "work" that I did to get the weight up there (the energy I put in) has now been converted to "potential energy" because it is perched in a position where it can then convert that into kinetic energy.

But, that potential energy is there only because of the Earth's gravity, right? If I were to let go of the weight, it would convert the energy I put in to lift it (potential energy) into kinetic energy -- falling towards Earth.

In other words, that potential energy exists only because of Earth's gravity.
In lifting the weight you have to move it obviously. Think of the force being constant and the velovity you lift it with constant as well. As soon as you let go the energy will be constant since you're no longer doing work on the system. The weight has kinetic energy since it was moving and it has a potential energy since you stopped applying the force at a non-zero height above the ground. The quantity

E = "Kinetic Energy (T)" + "Potential Energy (U)"

is constant. I.e.

E = T + U = constant

The force F can be written in terms of the potential energy U as

where "grad" is the gradient operator. In one dimension, say "z", that becomes (for one a potential with one variable)

F = -dU/dz

The gravitational field sometimes defined in terms of a "gravitational potential," Phi, defined as Potential Energy per unit mass. I.e.

Phi = U/m

So you're right. No gravitatiolnal fieldno potential energy.
Suppose I were to lift the weight 4 feet in the air, and then Earth disappeared or vanished or lost a lot of mass or whatever. Just say the earth went away. Wouldn't the weight then lose its potential energy (because the earth is no longer there)?

EDIT: How would this situation satisfy the Conservation of Energy rule?
If the Earth's gravitational field just turned off then it would violate the principle of the conservation of energy since there is energy associated with the gravitational field itself.

Hope that helps

Pete

#### HallsofIvy

Homework Helper
Brum, you have conclusively proved that, due to the conservation of mass and energy, the earth cannot simply disappear!

Whew, that's a relief!

#### STAii

Just say the earth went away
If it went away suddenly, and disappeared, it will be against the rules of conservation of mass and energy, but let's suppose the earth went away slowly (less than c), and for some reason you didn't stay on it.
In this case, this (moving the earth away from you) will need energy to be given to the earth to move away from you, and this will be a potential energy in the earth to you (well, and you will also have potential enery towards earth), so the law of conservation of energy will still be valid.

#### pmb

Originally posted by STAii
If it went away suddenly, and disappeared, it will be against the rules of conservation of mass and energy, but let's suppose the earth went away slowly (less than c), and for some reason you didn't stay on it.
In this case, this (moving the earth away from you) will need energy to be given to the earth to move away from you, and this will be a potential energy in the earth to you (well, and you will also have potential enery towards earth), so the law of conservation of energy will still be valid.
There's little cause to say that the earth is moving and not you. So what is the cause/reason that you don't move with it? There is work being done on you giving you energy

Pete

#### STAii

Well, you cannot know if actually the energy is yours or the earth's.
You see, when you have potential energy to earth, earth has potential energy to you too.
In my example, it could be that you are connected to the sun for example

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