# why is this? (gravitational potential)

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why does E=mV

Where E=gravitational energy and V=gravitation potential energy(? i think) and m=mass

I don't understand this equation.

Could someone please explain exactly what it is and what it describes.

Many thanks

Where E=gravitational energy and V=gravitation potential energy(? i think) and m=mass

I don't understand this equation.

Could someone please explain exactly what it is and what it describes.

Many thanks

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#2

(Original post by

why does E=mV

Where E=gravitational energy and V=gravitation potential energy(? i think) and m=mass

I don't understand this equation.

Could someone please explain exactly what it is and what it describes.

Many thanks

**Mr Tall**)why does E=mV

Where E=gravitational energy and V=gravitation potential energy(? i think) and m=mass

I don't understand this equation.

Could someone please explain exactly what it is and what it describes.

Many thanks

_{g})is gravitational potential. Not potential energy. The subscript g to indicate

*gravitational*potential.

It's the gravitational equivalent of electrical potential.

In the electrical case a charge q has energy in a field where the potential is V

The energy is E = qV

This comes from the definition of V

In a gravitational field the gravitational potential at a point is

**defined**as the energy required to bring a unit mass from infinity to that point.

So if 1kg needs energy V

_{g}

a mass m will need energy mV

_{g}

The only thing to understand is that it is a definition of what you mean by gravitational potential.

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(Original post by

V in that equation (it should be V

It's the gravitational equivalent of electrical potential.

In the electrical case a charge q has energy in a field where the potential is V

The energy is E = qV

This comes from the definition of V

In a gravitational field the gravitational potential at a point is

So if 1kg needs energy V

a mass m will need energy mV

The only thing to understand is that it is a definition of what you mean by gravitational potential.

**Stonebridge**)V in that equation (it should be V

_{g})is gravitational potential. Not potential energy. The subscript g to indicate*gravitational*potential.It's the gravitational equivalent of electrical potential.

In the electrical case a charge q has energy in a field where the potential is V

The energy is E = qV

This comes from the definition of V

In a gravitational field the gravitational potential at a point is

**defined**as the energy required to bring a unit mass from infinity to that point.So if 1kg needs energy V

_{g}a mass m will need energy mV

_{g}The only thing to understand is that it is a definition of what you mean by gravitational potential.

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#4

(Original post by

What does this have to do with -GM/r ? sorry im so confused!! thanks so much stonebridge !!!

**Mr Tall**)What does this have to do with -GM/r ? sorry im so confused!! thanks so much stonebridge !!!

That's the formula for the actual value of V

_{g}at a point a distance r from a mass M is

So the gravitational potential

*energy*of a mass m at that point is mV

_{g}

which comes to

or more usually written

note the similarity to the equation for the

*force*at a distance r which is

But then force and potential energy are related, aren't they? Potential energy is the result of the work done by the force moving the mass to that position from infinity.

The mathematical relationship, if you look closely, is that the one is derived from the other by differentiation or integration. I leave it to you to work out which is which.

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(Original post by

Everything.

That's the formula for the actual value of V

So the gravitational potential

which comes to

or more usually written

note the similarity to the equation for the

But then force and potential energy are related, aren't they? Potential energy is the result of the work done by the force moving the mass to that position from infinity.

The mathematical relationship, if you look closely, is that the one is derived from the other by differentiation or integration. I leave it to you to work out which is which.

**Stonebridge**)Everything.

That's the formula for the actual value of V

_{g}at a point a distance r from a mass M isSo the gravitational potential

*energy*of a mass m at that point is mV_{g}which comes to

or more usually written

note the similarity to the equation for the

*force*at a distance r which isBut then force and potential energy are related, aren't they? Potential energy is the result of the work done by the force moving the mass to that position from infinity.

The mathematical relationship, if you look closely, is that the one is derived from the other by differentiation or integration. I leave it to you to work out which is which.

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#6

(Original post by

thanks stonebridge, my understanding is better now! One last thing ... I am doing electric field questions and have been asked to find the KE of an electron. How do I do this without being given the velocity!? The next question actually asks me to find out the velocity so I presume we dont use ke=0/5*mv^2 to find the KE? What method do we use ? many many thanks stonebridge

**Mr Tall**)thanks stonebridge, my understanding is better now! One last thing ... I am doing electric field questions and have been asked to find the KE of an electron. How do I do this without being given the velocity!? The next question actually asks me to find out the velocity so I presume we dont use ke=0/5*mv^2 to find the KE? What method do we use ? many many thanks stonebridge

The energy gained (which is all kinetic) by the electron is eV where V is the pd and e the charge.

So it usually involves putting ½mv² for the electron = eV

So you don't need v or m for the electron if you know the pd it's been accelerated through.

If you are given m you can actually then calculate v if needed.

Without the specific question you are doing I can only guess this is what you mean.

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