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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

Cavendish Experiment

Presented by Mark Reeher

Lab Partner: Jon Rosenfield

For Physics 521

presentation overview
Presentation Overview
  • Historical Background
  • Theory
  • Experimental Setup and Methods
  • Results
  • Analysis of Results
    • Uncertainties
  • Conclusions
brief timeline of gravitational physics
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
cavendish experiment1
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

theory experimental design
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
small angle approximation
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
experimental setup1
Experimental Setup

Torsion balance enclosure

Large masses

Vacuum pump (oil)

He-Ne laser

Ametek plotter (converted)

setup diagram
Setup Diagram

Laser

Plotter

setup diagram1
Setup Diagram

So we need to keep in mind, the plotter reacts to 2θ

setup notes

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
results our measurements
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

analysis
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

analysis1
Analysis
  • I calculation
  • Κ calculation
  • Avg K = 2.60588 x 10-7+ 1.197 x 10-11 kg m/s2
analysis2
Analysis
  • ri calculation (m)
  • θ calculation
  • Avg eo from “NM” values:

eo = 3.954” + 0.000177”

  • Define xi = eo - ei
analysis3
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
uncertainty
Uncertainty
  • Total Uncertainty relation for G:

000000000000

uncertainty1
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:
conclusions
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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