How Does Gravitational Attraction Affect Potential Energy of Spheres in Space?

[airkapp]

Two spheres with radius of .10 m and a mass of 25 kg are floating in deep space. Their gravitational attraction keeps them in contact. If we go in and manually separate these spheres to a large distance, by how much will the potential energy involved in their interaction increase.

Is there some special formula for solving potential energy w/spheres?

I tried this formula but it doesn't seem to be giving me the right answer..

-G(m1m1/r) ..but it does not seem to be giving me the right answer.
Can anyone help me? My book is so vague that I can't find anything to help me on this problem.
thanks
Jay

 

[airkapp]

I multiplied r by 2 and it gives me the right answer in the back of the book..but I still don't know why

 

[HallsofIvy]

Now I'm confused! What r did you multiply by 2? What values did you use in -Gm₁m₂/r ?

What is the potential energy of 2 25 kg point masses at a distance of 0.2 m apart (Oh- that's twice the radius of the two spheres- do you see whyh it works? A uniform sphere can be treated as a point mass at the center of the sphere. What is the distance between the centers of the two spheres?)

Do you know what the potential energy is when the two spheres are "infinitely" far apart?

 

[airkapp]

G = 6.67 * 10^-11 Gravitational Constant
m1,m2 = mass (25 kg)^2
r = distance (the .10 meters)

is this the right formula to use?

 

[airkapp]

Now I'm confused! What r did you multiply by 2? What values did you use in -Gm₁m₂/r ?

What is the potential energy of 2 25 kg point masses at a distance of 0.2 m apart (Oh- that's twice the radius of the two spheres- do you see whyh it works? A uniform sphere can be treated as a point mass at the center of the sphere. What is the distance between the centers of the two spheres?)

Do you know what the potential energy is when the two spheres are "infinitely" far apart?

hmm..do I use a different formula for that. V(r) = ke^2/r ?

 

[airkapp]

Do you know what the potential energy is when the two spheres are "infinitely" far apart?



hmm..do I use a different formula for that. V(r) = ke^2/r ?


so is that the right way to approach infinetely far apart..somebody?? or was that a trick question..ahh..physics.

 

[HallsofIvy]

No, use that formula! What is the limit of V(r) as r gets larger and larger?


What is the distance between the centers of two spheres, each of radius 0.1 m?

Physics doesn't have "trick" questions- it only requires that you think.

 

[airkapp]

No, use that formula! What is the limit of V(r) as r gets larger and larger?


What is the distance between the centers of two spheres, each of radius 0.1 m?

Physics doesn't have "trick" questions- it only requires that you think.

the limit is zero
the distance is zero..i think.

 

[K.J.Healey]

the initial potential the r is the distance from the center of mass of each of the objects. The center of mass is NOT their surface. What is its potential energy?

 

[airkapp]

okay I think this is all starting to click..as V(r) potential energy decreases..the distance increases. the two are inversely proportional, so when they are infinitely apart ..the potential will be zero.
the r is used to find distance..so if I line the spheres up together..and connect the centers..I can get a pretty good understanding of what goes in the denominator to multiply by r..or just leave r as it is depending on what the question is asking. I think I got it
someone correct me I'm wrong,
thanks.

 

[HallsofIvy]

Look at V(r) = ke^2/r . As r-> infinity, V(r) goes to 0. V will increase as r decreases (typically k is taken to be negative so that V is decreasing in the sense of becoming more negative).

The point every one has been trying to make is that, since the spheres can be thought of as point charges (or masses in gravity problems) concetrated at the center of the spheres, the question is '"what is the distance between the two centers?"- it should be obvious that that is 2r where r is the radius of the two spheres.
(If that is not obvious, draw a picture for goodness sake!)

Since the potential at a large distance apart (at infinity) the potential difference is just the potential when the two spheres are touching: ke²/(distance apart)= ke²/(2r).