Cavendish Experiment
From High School Online Collaborative Writing
Sir Henry Cavendish (1731-1810)
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[edit] The Cavendish Experiment a.k.a. The Torsion Bar Experiment : An Introduction
Pretty much everyone knows that gravity is a constant force which pulls us towards the center of the earth. But not everyone knows that it was Henry Cavendish who found this constant value of G through experimentation from 1797 to 1798. Henry Cavendish, an english scientist, conducted an experiment using torsional balance to find this constant force of gravity. In the experiment that Cavendish conducted, two weighted spheres were attached to a wire and it was their attraction which caused the wire to bend slightly. Cavendish wanted to find this constant value of gravity in order to measure the mass of the earth.
A Diagram of the torsional balance appartus used to find the value of G:
[edit] The History of The Cavendish Experiment
Issac Newton (1642-1727) was not the founder of The Cavendish Experiment. He did however play a key role in it's creation. Newton discovered the force of gravitation and the equation to solve for it. Part of the equation that Newton created is the constant value of gravity. He did not solve for this because he thought it was impractical. Henry Cavendish (1731-1810) decided to take on this experiment of solving for G (the constant value of gravity) in 1783. Cavendish started by writing a letter to his friend Rev. John Michell discussing his theories on how to go about with the experiment. Upon recieving Cavendish's letter, Rev. Michell turned to the work of French scientist Coulomb to find the weight of the earth. This weight would then lead them to find the constant value named G. Coulomb's work suggested that using torsional balance would be appropriate. Coulomb had devised the appartus of two sphere shaped masses connected by a middle rod, but died before he brought the appartus into the lab for experimentation.
Charles Coulomb (1736-1806)
[edit] Newton's Law of Gravity (and why this is relevant)
To find constant gravity and ultimately the mass of the earth, we can use the equation:
F = GMm / R^2 which is more commonly known as Newton's theory of gravitation. or Force of Gravity = (Gravitational Constant * Product of the mass of the spheres) / (Distance between spheres)^2
This theory involves the mass of the objects, the distance between the objects and the gravitational constant. Because Newton thought that the gravitational constant was probably too small to be of importance, it wasn't until Cavendish adopted the experiment that this constant value was found.
[edit] Using The Cavendish Experiment (The Theory behind it all)
The theory behind The Cavendish Experiment is not as complicated as one might think. First off, picture the two sphere masses held together by a rod. This should look somewhat like a dumbell used for lifting weights. Now the torque of the oscillating masses is proportional to the angle of it. The torque is given by the equation:
Torque = -K * Theta
(In which K is a constant)
To find the period of the oscillating spheres, simply use the equation:
Period of Oscillation = 2 Pi * The Square root of (The Rotational Inertia of the Apparatus / K)
(In which K is a constant)
And the equation for the Rotational Inertia is:
Rotational Inertia = 2m (d^2 + 2/5 r^2)
d= distance r= radius of sphere mass and m= mass
By using these equations to find k (the spring constant) and because you know values such as M (the mass of the spheres), you can solve for G, the natural gravitational force.
[edit] Practice Problems
These problems deal with mass, gravity and weight. Henry Cavendish dealt with these variables when finding the weight of the earth and the value of G.
What is the constant value for the acceleration due to gravity on Planet Earth?
answer: 9.8 m/s^2
On the surface of a distant planet, a 5kg mass weighs 20N. What is the acceleration due to gravity there?
answer: 4 m/s^2
The weight of an apple is approximately how many Newtons?
answer: 1N
On Planet Gamma, a 4 kg mass experiences a 24N gravitational force. What is the acceleration due to gravity on planet Gamma?
answer: 6 m/s^2
What combination of fundamental units can be used to express the weight of an object?
answer: kg * m/s^2
The acceleration due to gravity on Planet X is 19.6 m/s^2. If an object on the surface of the planet is 980N, what is the mass of the object?
answer: 50kg
[edit] References
The following websites were referenced:
http://saeta.physics.hmc.edu/Courses/p23a/Experiments/Cavendish.html
http://fas.harvard.edu/~scdiroff/lds/NewtonianMechanics/CavendishExperiment/CavendishExperiment.html
http://www.leydenscience.org/physics/gravitation/cavend.htm
Glencoe Physics: Principles and Problems
Notes from GK's Physics Class: Newton, Gravity and Mass
[edit] Resources
http://saeta.physics.hmc.edu/Courses/p23a/Experiments/Cavendish.html This site has background information and gives you a procedure for the actual experiment.
http://mattson.creighton.edu/History_Gas_Chemistry/Cavendish.html This site is a little bio on Sir Henry Cavendish
http://www.stmary.ws/physics/home/review/review_all.htm This site has self-grading quizzes with topics such as Gravity and Weight (It is a useful site for Regents Preparation and even SAT Physics Subject test Preparation)
