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• ##### density of earth - H. Cavendish(0+ / 0-)

EXCERPT

Density of the Earth

Cavendish experiment

Following his father's death, Henry bought another house in town and also a house in Clapham Common, to the south of London. The London house contained the bulk of his library, while he kept most of his instruments at Clapham Common, where he carried out most of his experiments.

The most famous of those experiments, published in 1798, was to determine the density of the Earth and became known as the Cavendish experiment. The apparatus Cavendish used for weighing the Earth was a modification of the torsion balance built by Englishman and geologist John Michell, who died before he could begin the experiment. The apparatus was sent in crates to Cavendish, who completed the experiment in 1797–1798, and published the results.

The experimental apparatus consisted of a torsion balance with a pair of 2-inch 1.61-pound lead spheres suspended from the arm of a torsion balance and two much larger stationary lead balls (350 pounds), and Cavendish intended to measure the force of gravitational attraction between the two.

Cavendish noticed that Michell's apparatus would be sensitive to temperature differences and induced air currents so he made modifications by isolating the apparatus in a separate room with external controls and telescopes for making observations.

Using this equipment, Cavendish calculated the attraction between the balls from the period of oscillation of the torsion balance, and then he used this value to calculate the density of the Earth.

Cavendish found that the Earth's average density is 5.48 times greater than that of water. John Henry Poynting later noted that the data should have led to a value of 5.448, and indeed that is the average value of the twenty-nine determinations Cavendish included in his paper.

What was extraordinary about Cavendish’s experiment was its elimination of every source of error and every factor that could disturb the experiment and its precision in measuring an astonishingly small attraction, a mere 1/50,000,000 of the weight of the lead balls. The result that Cavendish obtained for the density of the Earth is within 1 percent of the currently accepted figure.

Cavendish's work led others to accurate values for the gravitational constant (G) and Earth's mass. Based on his results, one can calculate a value for G of 6.754 × 10−11N-m2/kg2,[14] which compares favourably with the modern value of 6.67428 × 10−11N-m2/kg2.[15]

Books often describe Cavendish's work as a measurement either of the gravitational constant (G), or of the Earth's mass.

Since these are related to the Earth's density by a trivial web of algebraic relations, none of these sources are wrong, but they do not match the exact word choice of Cavendish, and this mistake has been pointed out by several authors.

Cavendish's stated goal was to measure the Earth's density, although his result obviously calculates G in order to do so.

The first time that the constant got this name was in 1873, almost 100 years after the Cavendish experiment, but the constant was in use since the time of Newton. Cavendish's results obviously also give the Earth’s mass.

http://en.wikipedia.org/...

We’re enablers. We’ve become enablers. We can’t be that anymore. ~ Minority Leader Nancy Pelosi, D-CA

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• ##### gravity, magnetism and light(0+ / 0-)
EXCERPT

Gravity, magnetism and light

Michell conceived, sometime before 1783, the experiment now known as the Cavendish experiment. It was the first to measure the force of gravity between masses in the laboratory and produced the first accurate values for the mass of the Earth and the gravitational constant.

He invented and built, independently of co-inventor Charles Augustin de Coulomb, a torsion balance for the experiment but did not live to put it to use. His apparatus passed to Henry Cavendish, who performed the experiment in 1798.

In 1987, gravity researcher A.H. Cook wrote:

The most important advance in experiments on gravitation and other delicate measurements was the introduction of the torsion balance by Michell and its use by Cavendish. It has been the basis of all the most significant experiments on gravitation ever since.

We’re enablers. We’ve become enablers. We can’t be that anymore. ~ Minority Leader Nancy Pelosi, D-CA

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• ##### torsion pendulum(0+ / 0-)
EXCERPT

Torsion Balance

The torsion balance, also called torsion pendulum, is a scientific apparatus for measuring very weak forces, usually credited to Charles-Augustin de Coulomb, who invented it in 1777, but independently invented by John Michell sometime before 1783.

Its most well-known uses were by Coulomb to measure the electrostatic force between charges to establish Coulomb's Law, and by Henry Cavendish in 1798 in the Cavendish experiment to measure the gravitational force between two masses to calculate the density of the Earth, leading later to a value for the gravitational constant.

The torsion balance consists of a bar suspended from its middle by a thin fiber. The fiber acts as a very weak torsion spring.

If an unknown force is applied at right angles to the ends of the bar, the bar will rotate, twisting the fiber, until it reaches an equilibrium where the twisting force or torque of the fiber balances the applied force.

Then the magnitude of the force is proportional to the angle of the bar. The sensitivity of the instrument comes from the weak spring constant of the fiber, so a very weak force causes a large rotation of the bar.

In Coulomb's experiment, the torsion balance was an insulating rod with a metal-coated ball attached to one end, suspended by a silk thread. The ball was charged with a known charge of static electricity, and a second charged ball of the same polarity was brought near it.

The two charged balls repelled one another, twisting the fiber through a certain angle, which could be read from a scale on the instrument.

By knowing how much force it took to twist the fiber through a given angle, Coulomb was able to calculate the force between the balls.

Determining the force for different charges and different separations between the balls, he showed that it followed an inverse-square proportionality law, now known as Coulomb's law.

To measure the unknown force, the spring constant of the torsion fiber must first be known. This is difficult to measure directly because of the smallness of the force. Cavendish accomplished this by a method widely used since: measuring the resonant vibration period of the balance.

If the free balance is twisted and released, it will oscillate slowly clockwise and counterclockwise as a harmonic oscillator, at a frequency that depends on the moment of inertia of the beam and the elasticity of the fiber. Since the inertia of the beam can be found from its mass, the spring constant can be calculated.

Coulomb first developed the theory of torsion fibers and the torsion balance in his 1785 memoir, Recherches theoriques et experimentales sur la force de torsion et sur l'elasticite des fils de metal &c. This led to its use in other scientific instruments, such as galvanometers, and the Nichols radiometer which measured the radiation pressure of light.

In the early 1900s gravitational torsion balances were used in petroleum prospecting. Today torsion balances are still used in physics experiments. In 1987, gravity researcher A.H. Cook wrote:

The most important advance in experiments on gravitation and other delicate measurements was the introduction of the torsion balance by Michell and its use by Cavendish. It has been the basis of all the most significant experiments on gravitation ever since.

Torsional harmonic oscillators

Torsion balances, torsion pendulums and balance wheels are examples of torsional harmonic oscillators that can oscillate with a rotational motion about the axis of the torsion spring, clockwise and counterclockwise, in harmonic motion. Their behavior is analogous to translational spring-mass oscillators

(see Harmonic oscillator#Equivalent systems)

We’re enablers. We’ve become enablers. We can’t be that anymore. ~ Minority Leader Nancy Pelosi, D-CA

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