# How cavendish determined the value of G

1. Aug 26, 2004

### Cyrus

Hi, I was wondering if anyone could explain how cavendish determined the value of G. I have read that he used a mirror on a small wire to determine the angle and from there determined the value of G. I do not see how you can detemrine G, since there are many unknowns. You have
$$G M m / r^2$$.

You know the two masses and their distance, but that is not enough to know G. A few books have said you also know w=mg = G m m/r^2, but this is not true, a cavendish does not factor in g, since the balls move side ways indepent of gravity g. Also, how come in this cavendish the two balls dont come together and touch and just sit there? Thanks, ( I hope Bobg replies :tongue2: )

2. Aug 27, 2004

### mu

You are right, distance and masses are not sufficient. From what I understand, the system is in equilibrium. This means the torque exerted by the masses is equal and opposite to the one exerted by the wire (the wire acts like a torsion spring, so by knowing the angle you know the torque). From there you can easily calculate the force and factor G from the gravitation law.

As I said, that's because the wire exerts a torque in the opposite direction, so your your system just 'stops' when the two are equal.

Someone correct me if I'm wrong or unclear

3. Sep 4, 2004

### ArmoSkater87

Cadendish used a laser to bounce off a mirror on the balls and see the angle that the light beam creates after the balls attract each other. I dont know how he exactly used this to calculate it, I've heard that Cavendish calculated G by accident, that he was origionally trying to calculate the density of the earth.

4. Sep 4, 2004

### Tide

Cavendish didn't have lasers to work with.

5. Sep 4, 2004

### ArmoSkater87

So, what did he use to bounce off the mirror?

6. Sep 4, 2004

### Tide

Probably a collimated light beam but he most certainly did not use a laser!

Schawlow and Townes first proposed the laser in their 1958 publication of their paper detailing the theory and the first working laser was created some years later - long after Cavendish did his experiments.

With regard to the original question, Cavendish measured the torque on a torsion bar supported by a wire. The bar had masses at its ends and those masses were pulled by two other masses to produce the torque. The torque (produced by the gravitational pull of the masses) is proportional to the deflection angle and, by measuring that angle, Cavendish was able to determine the force.

Last edited: Sep 5, 2004
7. Sep 5, 2004

### Cyrus

I actually solved this on my own. But cavendish, to my knowledge did not discover this by accident. As it was not even he who invented the experiment. (mitchell?) or some other guy actually invented the experiment. He was a geologist. But he died before he ever got it to work. Cavendish inherited this contraption, and the rest of the junk from this guys lab upon his death. Cavendish actually had to remake almost all of it as the wood had rotted and broken apart. When he did get it finally working he called it weighing the world. (or was it weighing the earth). He did not have a laser, but a focused beam of light which he measured outside the room using a teloscope. (as not to create air currents. ) He found the value of G. and from there he backed out the specific density of the earth relative to water i think, which he found to be like 5.5 or so. He actually made an error on his origional paper. As he put a number in the decimals place as .34 instead of .034. Those arent the actual numbers i just made something up off the top of my head to give you an idea. So his value of the earth was actually off, something ilke 5.3 instead of 5.5. But to my knowledge, he did know he was calculating G and did not stumble on it. As he needed g in order to find the mass of the earth.