Thread: Torsion balance question

Can anybody explain to me how the torsion balance works? The actual mechanical device. I tried understanding the concept from wikipedia/google but I can't figure it out in regards to the gravitational force. I understand how you could record an electromagnetic force but not gravity.

How do you use a torsion balance to record the force of gravity?

Anybody?

Are you asking how it would be used to measure the universal gravitational constant G, or how it was used to measure gradients in the earth's gravitational field? I ask because I don't want to explain something you already know, and besides I haven't quite figured out the second part.

How they measured G.

Newton's law of gravitation states that the force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between their centers of gravity.

F= GMm/r^2

Newton deduced this from the motions of the moon and planets but he never actually knew the value of G or the masses of the heavenly bodies.

To determine G is simple in concept but difficult to do. The formula works for any two objects, not just planets and moons. What you could do is get two heavy objects like lead balls, measure the mass of the objects M and m, the attractive force F between them and the distance r, then you solve for G. The problem is how tiny the force is compared to the gravitational attracation of the earth, friction, etc.

If you could manage to put the two lead balls on a completely frictionless table then all you would need to do is attach one firmly to the table attach a scale to the other, measure the distance between, and the attractive force. For your scale, you could use a spring scale that operates on the principle of Hooke’s Law F = -kx where x is the extension of the spring and k is the spring constant.

The problems with this are that you can’t eliminate the friction well enough and the spring scale is not sensitive enough.

The torsion balance solves these problems because the weight is hung by a thin wire, eliminating friction, and the spring is replaced by just the springiness of the wire as it is twisted. The torsion spring works the same way as a linear spring, except you replace force with torque and extension with angular displacement. Then Hooke’s law for a torsion spring becomes Torque = -k(angle). Instead of two weights you need four. The two movable weights are attached to the ends of a crossbar that hangs from the wire torsion spring. As they are brought near the fixed weight, there is an attractive force in accordance with Newton’s equation. To find the torque, multiply the force by the length of the lever arm.

Does this help?

Yes this does help, thank you.

I'm still a little bit confused about how the instrument is sensitive enough to measure the attraction between the balls though. I mean, how much gravitational force could a little thing like that have?

The original experiment by Cavendish used a 2 inch diameter 1.61 pound lead sphere attached to each end of the rod. Two 12 inch 348 pound lead balls were located near the smaller balls, about 9 inches away "The force involved in twisting the torsion balance was very small, 1.47 x 10–7 N, about 1/50,000,000 of the weight of the small balls or roughly the weight of a large grain of sand."

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

That's an impressive experiment. Thanks for the help.