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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


Derivation 1

Top View

Derivation - 1



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

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


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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