1. Cavendish Experiment
Advanced Lab 2

2. Credit Josh Villatoro, Hunter Ash, Fall 2013
Seth Hodgson, Bailey Bedford, Catie Raney, Spring 2013
Darren Erdman, Mengfei Gao Spring 2010
Amanda Baldwin, Paul Wright, Thomas Kennington, Matt Whiteway, Chris Schroeder, Fall 2009
Dan Brunski, Sung Chou, Dustin Combs, Daniel White, Spring 2008
Susan Gosse, Daniel Freno,Jason Garman, Joshua Smith, Fall 2007

3. Overview History Theory of Measurement Apparatus Procedure Results
Derivations
Apparatus
Procedure
Results
Constant Acceleration Method
Equilibrium Position Method
Conclusions and Sources
Error Discussion
Procedure Appendix

4. Cavendish History Performed in 1797-1798 by Henry Cavendish
Primary result of experiment was to measure the density of the earth
“G” and the mass of the earth were derived by othersafter Cavendish’s death
Torsion balance method devised by John Mitchell in 1783
Mitchell died before the experiment could be performed
Apparatus was eventually passed to Cavendish, who rebuilt it
The apparatus was extremely large, with the heavy lead spheres weighing upwards of 348 lbs

5. Some illustrations and explanations for the original cavendish experiment

6. History of Measuring G Problems in Determining G
Experimenter
Year
Method
G Measurement
ΔG/G*10^6
Cavendish
Boys
Luther
Fitzgerald
Schwarz
Kündig
1798
1895
1982
1995
1998
2002
Torsion balance
Torsion pendulum
Free fall
Beam balance
6.75 ± 0.05
6.658 ± ± ± ± ±
7400 (stat.)
1000 75 90
1400
200
Problems in Determining G
Weakest of the four fundamental forces
Inconstancy of the torsional moment of suspension
Sensitivity to Environmental Oscillations
Sensitivity to temperature
Inability to shield gravity
Consequently, G is the least precisely measured fundamental constant

7. Recent Measurement of G
[Insert the table doohikie]

8. Compare with Coulomb Experiment
Gravitational force is much smaller than the coulomb force
Typical Coulomb force used in an experiment: 10-4 N
Typical Gravitational force used in an experiment: N
Coulomb experiment requires a correction factor of 1/(1 - a3/R3)
This accounts for the induced dipolarity in the spheres
a is the radius of the sphere and R is the distance between spheres

9. Compare with Coulomb Experiment
Cavendish experiment requires a correction factor of 1/(1 - ẞ) where ẞ = b3 /(b2 + 4d2)3/2
b is the distance between the small spheres
d is the distance between the small sphere and the center of the pendulum
The initial calculations account for the force of gravity between the near masses, and the correction factor accounts for the force between the further apart masses.
Near A A
Far from A

10. Theory of Measurement Two methods of measurement used
Method of equilibrium positions
Accuracy of ~5% according to PASCO
90 to 180 minute observation time
Involves finding equilibrium points for Positions I and II by observing oscillations, then taking the differences to determine G
Method of constant acceleration
Accuracy of ~15% according to PASCO
3-10 minute observation time
Uses acceleration of small masses during first minute after switching large mass positions to determine G

11. Constant Acceleration Derivation
Starting with the law of gravitation: F=Gm1m2/b2
Total force acting on the object: FTotal=FTorsion+FGravity
[insert illustration of flipping]
FTotal=2FGravity
=> G=b2a0/2m1

12. Constant Acceleration Derivation
The Law of Reflection implies that the arc length that we measure

13. Equilibrium Position Derivation
Graphical Method for measuring

14. Procedures
Make the set up more concise and refer to additional procedures
Calibration, rewrite, maybe eliminate. Knowing the equilibrium is unnecessary