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Cavendish Experiment

Cavendish Experiment. Presented by Mark Reeher. Lab Partner: Jon Rosenfield For Physics 521. Presentation Overview. Historical Background Theory Experimental Setup and Methods Results Analysis of Results Uncertainties Conclusions. Brief Timeline of Gravitational Physics.

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Cavendish Experiment

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  1. Cavendish Experiment Presented by Mark Reeher Lab Partner: Jon Rosenfield For Physics 521

  2. Presentation Overview • Historical Background • Theory • Experimental Setup and Methods • Results • Analysis of Results • Uncertainties • Conclusions

  3. Brief Timeline of Gravitational Physics • 4th Century B.C: Aristotle – tendency of objects to be pulled to Earth • 1645: Ismael Bulliadus - inverse square relation • 1665: Sir Isaac Newton - • 1798: Henry Cavendish – calculation of Universal Gravitation Constant, G • Early 1900s: Einstein- • Inertia-gravitation equivalence • General relativity

  4. Cavendish Experiment • John Michell – conception of experiment • Torsion Balance • Henry Cavendish – rebuilt balance and ran experiment in 1797-1798 • Basic Idea – directly measure Fg, find G • Found: G = 6.754 × 10−11 m3kg-1s-2

  5. Committee on Data for Science and Technology’s Value

  6. Theory – Experimental Design • Large masses brought near small masses • Gravitational force  movement in torsion balance • Study motion to determine Fg • With Fg, measure M, m, r • Newton’s gravitational equation • Result = calculated G

  7. Top View Derivation - 1 Fβ Fα

  8. Derivation - 2

  9. Small Angle Approximation • For simplicity, we assume θ is very small • Torque dot product • Tan θ = θ • This assumption confirmed by finding the largest possible angle of setup • θmax = 0.03884 = 2.226º • ~0.05% difference between tan θ and θ

  10. Experimental Setup

  11. Experimental Setup Torsion balance enclosure Large masses Vacuum pump (oil) He-Ne laser Ametek plotter (converted)

  12. Setup Diagram Laser Plotter

  13. Setup Diagram So we need to keep in mind, the plotter reacts to 2θ

  14. Fβ Fα Fα Fβ Setup Notes • Torsion enclosure pumped to ~100 mTorr • Data recorded automatically in Labview • Photodiode position vs time (4 s intervals) • Six total trials • 2 counter-clockwise (positive) torque • 2 clockwise (negative)torque • 2 no mass

  15. Results (Our Measurements) • Given in lab manual • m = 0.019 kg • Mrod = 0.031 kg (square cross section) • L/2 = 15.24 cm • Distance measurements (in inches) • Dd (mirror-diode) = 45 1/32” • ω and θ are found from Matlab data 1 2 4 3

  16. Analysis • Data from best fit: • General model: f(x) = a*exp(-x/b)*cos(c*x+d)+e • Coefficients (with 95% confidence bounds):        a =         131  (130.4, 131.6)        b =  1.029e+004  (1.006e+004, 1.051e+004)        c =    0.007577  (0.007575, 0.007579)        d =    0.004448  (0.0001244, 0.008771)        e =       682.1  (681.9, 682.3) • Goodness of fit:   SSE: 1000   R-square: 0.9986   Adjusted R-square: 0.9986   RMSE: 1.002

  17. Analysis • I calculation • Κ calculation • Avg K = 2.60588 x 10-7+ 1.197 x 10-11 kg m/s2

  18. Analysis • ri calculation (m) • θ calculation • Avg eo from “NM” values: eo = 3.954” + 0.000177” • Define xi = eo - ei

  19. Analysis • Now find θ from tan-1: • Finally… we find G (m3s-2): • Avg G = (3.89829 x 10-10+ 1.7129 x 10-11)/M

  20. Uncertainty • Total Uncertainty relation for G: 000000000000

  21. Uncertainty • Each of the four variables also had combined uncertainty in their calculation • All type A aside from distance measurements • In a few cases, values were averaged:

  22. Conclusions • M = 5.701 kg † • Gives us: • GCavendish = 6.754 × 10−11 m3kg-1s-2 • GCODATA = 6.67428 × 10−11 m3kg-1s-2 • Obvious setup interference • MEarth Accepted value = 5.97 x 1024 kg † conversation with Jose

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