why is this? (gravitational potential)

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Mr Tall
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#1
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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
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Stonebridge
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(Original post by 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
V in that equation (it should be Vg)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 Vg
a mass m will need energy mVg

The only thing to understand is that it is a definition of what you mean by gravitational potential.
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Mr Tall
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(Original post by Stonebridge)
V in that equation (it should be Vg)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 Vg
a mass m will need energy mVg

The only thing to understand is that it is a definition of what you mean by gravitational potential.
What does this have to do with -GM/r ? sorry im so confused!! thanks so much stonebridge !!!
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Stonebridge
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(Original post by Mr Tall)
What does this have to do with -GM/r ? sorry im so confused!! thanks so much stonebridge !!!
Everything.
That's the formula for the actual value of Vg at a point a distance r from a mass M is

V_g = \frac{-GM}{r}

So the gravitational potential energy of a mass m at that point is mVg

which comes to

E = m \frac{-GM}{r}

or more usually written

E = \frac{-GMm}{r}

note the similarity to the equation for the force at a distance r which is

F = \frac{GMm}{r^2}

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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Mr Tall
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(Original post by Stonebridge)
Everything.
That's the formula for the actual value of Vg at a point a distance r from a mass M is

V_g = \frac{-GM}{r}

So the gravitational potential energy of a mass m at that point is mVg

which comes to

E = m \frac{-GM}{r}

or more usually written

E = \frac{-GMm}{r}

note the similarity to the equation for the force at a distance r which is

F = \frac{GMm}{r^2}

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.
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
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Stonebridge
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(Original post by 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
These questions usually ask for the KE of the electron after being accelerated from rest through a pd of so many volts.

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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