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

In summary, the two masses cancel out because the field strength is directed opposite to the potential energy.
  • #1
RSG_9
8
0

Homework Statement



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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 :)
 
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  • #2
Welcome to PF!

Hi RSG_9! Welcome to PF! :smile:
RSG_9 said:
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? :wink:
 
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  • #3


tiny-tim said:
Hi RSG_9! Welcome to PF! :smile: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? :wink:

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)
 
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  • #4
RSG_9 said:
The forces are equal but in opposite directions to one another?

Yes :smile:, but does that apply to one or both cases? :wink:
 
  • #5
tiny-tim said:
Yes :smile:, but does that apply to one or both cases? :wink:

Ahhhh I think I have it?

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

V1 + V2 = -2GM/r + -2GM/r
=-4GM/r
 
  • #6
yees :smile:

but why? :rolleyes:

why do they cancel for the field strengths, but not for the potentials? :wink:
 
  • #7
tiny-tim said:
yees :smile:

but why? :rolleyes:

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

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 :smile:)
 
  • #8
RSG_9 said:
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 :wink:
(btw, it's partly because i like being awkward! :biggrin:)
 
  • #9
tiny-tim said:
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 :wink:
(btw, it's partly because i like being awkward! :biggrin:)

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

1. What is the formula for calculating the gravitation field strength at the midpoint between two equal masses?

The formula for calculating the gravitation field strength at the midpoint between two equal masses is F = Gm/r², where F is the force of gravity, G is the universal gravitational constant, m is the mass of the two objects, and r is the distance between them.

2. How does the distance between the two masses affect the gravitation field strength at the midpoint?

The distance between the two masses has an inverse square relationship with the gravitation field strength at the midpoint. This means that as the distance increases, the field strength decreases proportionally.

3. Can the gravitation field strength at the midpoint ever be zero?

No, the gravitation field strength at the midpoint between two equal masses will never be zero. This is because gravity is a universal force that is always present between objects with mass, regardless of the distance between them.

4. How does the mass of the two objects affect the gravitation field strength at the midpoint?

The mass of the two objects has a direct relationship with the gravitation field strength at the midpoint. This means that as the mass increases, the field strength also increases proportionally.

5. Can the gravitation field strength at the midpoint between two equal masses be negative?

No, the gravitation field strength at the midpoint cannot be negative. This is because gravity is always an attractive force, meaning it always pulls objects towards each other. A negative value would indicate a repulsive force, which is not possible with gravity.

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