Cavendish's Gravity Experiment & the Value of G

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  • 0:02 What Is the…
  • 1:01 Cavendish Experiment
  • 2:47 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this lesson, you will be able to explain what the gravitational constant is and explain how the Cavendish Experiment can be used to figure out the value of big-G. A short quiz will follow.

What Is the Gravitational Constant?

There are two gravitational constants that people tend to get mixed up. The first is the acceleration due to gravity (or gravitational field strength), which is represented by g and is an average of -9.8 m/s^2 on Earth. But then there's G. G is the gravitational constant of the universe. In our universe, it's 6.67 x 10^-11 N(m/kg)^2, and it's the same everywhere in the universe.

G is the constant you find in Newton's Universal Law of Gravitation. The law of gravitation says that every object in the universe attracts every other object. And it can be represented by this equation, Fg = G x m1 x m2/d^2, where F is the force between two objects, M1 is the mass of one object, M2 is the mass of the other object and d is the distance between them. And this is where we use our value of G. Fg = G x m1 x m2/d^2.

Cavendish Experiment

In 1797, Henry Cavendish conducted the first successful experiment to find the value of the gravitational constant. The idea for the experiment was constructed earlier in 1783 by John Michell, who created the torsion balance apparatus that Cavendish used. Michell, sadly, died before completing his work, and so, the baton passed to Cavendish.

Cavendish experiment
equipment used in Cavendish experiment

The equipment looked something like this, though we can draw a simpler version to make it easier to understand. It is essentially a rotating balance. You have two small masses and two large masses, and you hang them like so:

Diagram of Cavendish experiment
diagram of Cavendish experiment

The small masses move because of the gravitational attraction of the larger masses, causing the torsion wire to rotate. The apparatus was also encased in a box to avoid any impact from air motions. The experimental set-up was super sensitive and could detect even tiny deviations using Vernier scales.

The specific way Cavendish calculated the value of G was a bit more complicated than it sounds. It involved finding the wire's torsion coefficient, the torque exerted per degree of twist. By timing the rate of rotation of the balance rod (which had a period of oscillation of around 20 minutes), combined with the mass and length of the balance, the torsion coefficient could be calculated. Cavendish had to make all these measurements while the equipment was continually moving - the equipment was incredibly sensitive and always in motion.

Cavendish's ultimate goal was to calculate the density of the earth. That is ultimately what motivated the experiment, but the first step in doing that was to calculate the value of G. The experiment was a huge success, and the accuracy of the value wouldn't be improved upon again for a hundred years.

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