Gravitation field strength/Potential - Mid point between two equal masses.

[RSG_9]

Homework Statement

Homework Equations

g = GM/r^2

V = (-)GM/r

The Attempt at a Solution

I know the field strength at the mid point between two masses cancels out but I can't really get my head around the potential.
My instinct is telling me that it would also cancel out but I just want to check with somebody who knows more than me and could explain it :)

 

[tiny-tim]

Welcome to PF!

Hi RSG_9! Welcome to PF!

I know the field strength at the mid point between two masses cancels out but I can't really get my head around the potential.
My instinct is telling me that it would also cancel out but I just want to check with somebody who knows more than me and could explain it :)

Let's work it out …

as you know, both gravitational field strength and gravitational potential are additive

(gravitational potential, of course, is gravitational https://www.physicsforums.com/library.php?do=view_item&itemid=269" per mass).

So why should gravitational field strengths cancel when they add?

And why should gravitational potentials cancel when they add? ​

 

[RSG_9]

Hi RSG_9! Welcome to PF! Let's work it out …

as you know, both gravitational field strength and gravitational potential are additive

(gravitational potential, of course, is gravitational https://www.physicsforums.com/library.php?do=view_item&itemid=269" per mass).

So why should gravitational field strengths cancel when they add?

And why should gravitational potentials cancel when they add? ​

The forces are equal but in opposite directions to one another?

(Also, you're welcome, I stalk around here a little bit only just decided to join)

 

[tiny-tim]

The forces are equal but in opposite directions to one another?

Yes , but does that apply to one or both cases?

 

[RSG_9]

Yes , but does that apply to one or both cases?

Ahhhh I think I have it?

V from each mass is equal to -2GM/r

V1 + V2 = -2GM/r + -2GM/r
=-4GM/r

 

[tiny-tim]

yees …

but why? ​

why do they cancel for the field strengths, but not for the potentials?

 

[RSG_9]

yees …

but why? ​

why do they cancel for the field strengths, but not for the potentials?

Because field strength, Nkg^-1... i.e force so relatively act against each other where as potentials Jkg^-1 is energy so act 'with' each other?


(btw you're very helpful, usually people just give you the answer and think it's okay where as i like to understand things not just have to remember them )

 

[tiny-tim]

Because field strength, Nkg^-1... i.e force so relatively act against each other where as potentials Jkg^-1 is energy so act 'with' each other?

oooh, very woolly …

official reason: fields are vectors, so they obey the vector law of addition, and so they can cancel even if they have the same strength (ie magnitude)

but potentials (and potential energy) are scalars, which in the gravitational (though not electric) case are all the same sign ​

(btw, it's partly because i like being awkward! )

 

[RSG_9]

oooh, very woolly …

official reason: fields are vectors, so they obey the vector law of addition, and so they can cancel even if they have the same strength (ie magnitude)

but potentials (and potential energy) are scalars, which in the gravitational (though not electric) case are all the same sign ​

(btw, it's partly because i like being awkward! )

Ahh yeah, I understand that. Thank you very much for you help.