B Gravitational attraction of 2 equal masses

[dyn]

Hi.
If 2 equal masses are placed at rest ( an arbitrary distance apart ) on a horizontal friction-less surface do they accelerate from rest towards each other until they collide ?
Thanks

 

[anorlunda]

What do you think? Here are the two equations you need.F_1,2=m₁m₂G/r²

F=ma

 

[Geofleur]

It might be a tough experiment to do outside of one's head though, as frictionless surfaces (air hockey tables notwithstanding) are hard to come by. Also, you might be waiting a long time for the masses to collide :)

 

[dyn]

I think the answer is yes. I just wanted someone to confirm that for me

 

[Geofleur]

We have a habit here of asking people to think through things using equations.

 

[dyn]

I understand the equations. Its just that most examples use the attraction between the Earth and an object so the Earth is assumed not to move. I just wanted a confirmation that I was correct about the hypothetical situation that I described ?

 

[Geofleur]

That first equation that anorlunda put up applies to any two masses in the universe. So, yes, you are correct :)

 

[dyn]

Thank you

 

[PeroK]

I understand the equations. Its just that most examples use the attraction between the Earth and an object so the Earth is assumed not to move. I just wanted a confirmation that I was correct about the hypothetical situation that I described ?

You might be interested in this:

https://en.wikipedia.org/wiki/Cavendish_experiment

 

[dyn]

In reality if I place 2 identical masses close to each other on a real table I see no movement towards each other. Is the lack of movement entirely due to friction between the masses and the table ?

 

[DaveC426913]

In reality if I place 2 identical masses close to each other on a real table I see no movement towards each other. Is the lack of movement entirely due to friction between the masses and the table ?

Well, technically, yes.
Objects small enough to sit on a table have a very small gravitational force between them (like 10^-11 Newtons), but it's not zero.

To actually observe this, you'd have pretty tough time eliminating other factors, such as even the gentlest of air currents. Not sure how long you'd have to wait.

[ EDIT ] Looks like you'd be waiting several days, depending on the masses and their distance.

 

[profbuxton]

Didn't some one already do this experiment(Cavendish?) with two large(maybe tons) weights suspended on flex cables and measured to force between them to calculate the gravitational attraction. I believe he had to actually do the observations from another room using a telescope to avoid any draft effects Thats how the force of gravity was calculated a per above equation. Been replicated a few times since then.

 

[sophiecentaur]

Didn't some one already do this experiment(Cavendish?) with two large(maybe tons) weights suspended on flex cables and measured to force between them to calculate the gravitational attraction. I believe he had to actually do the observations from another room using a telescope to avoid any draft effects Thats how the force of gravity was calculated a per above equation. Been replicated a few times since then.

Yes. By using a cable suspension, instead of a flat table, the effects of frictio n were greatly reduced and gave them a chance of isolating the effect of the gravitational force. There was also an experiment done, using a Scottish mountain, Schiehallion was known to be very dense, being composed largely of Iron Ore. The mountain is fairly isolated so the local gravitational field was reckoned to be significantly dominated by the presence of this big mass. (Gravitational Anomaly, in modern terms) They looked at the altered deflection of a pendulum bob due to the attraction of the mountain's mass.The experiment (in 1774 - a long time ago!) was basically to find the mass of the Earth so it was not an exact parallel of the OP's thought experiment but the results were astoundingly good for their time. I think the main error in their result can be put down to the effect of another massive mountain, not too far away.
The Cavendish experiment was around the same time and directly measured G. As with the Schiehallion experiment, the two bodies involved were not equal but the theory does not exclude equal masses.

 

[Andrew Mason]

If you want to use equal masses, the acceleration toward each other will be proportional to the mass you use. But no matter what mass you use, you will have very slow accelerations to measure. In order to create greater acceleration, Cavendish used small masses on the torsion balance and much more massive stationary lead balls.

The difficulty, however, will be to remove the effects of other matter and the effect of the Earth's motion on the experiment. You could use small masses suspended in a vacuum chamber and far from mountains.

AM

[Edit: I realized after posting that I made an error in thinking that the acceleration would be the same for all masses, which by doing the math one can see is not the case]

 

[sophiecentaur]

If you want to use equal masses, the acceleration toward each other is independent of the mass you use. No matter what mass you use, you will have very slow accelerations to measure. In order to create greater acceleration, Cavendish used small masses on the torsion balance and much more massive stationary lead balls.

So you could use small masses suspended in a vacuum chamber. The difficulty, however, will be to remove the effects of other matter and the effect of the Earth's motion on the experiment.

AM

Experimentally, it must be a nightmare. Slamming doors in the same building could upset everything. The Cavendish experiment finds the local g field using the same principle as a pendulum can be used to find the Earth's g. Amazing accuracy for 1783!