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# Cavendish Experiment PowerPoint PPT Presentation

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.

Cavendish Experiment

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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

• 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 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

• 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

Top View

### 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 Setup

Torsion balance enclosure

Large masses

Vacuum pump (oil)

He-Ne laser

Ametek plotter (converted)

Laser

Plotter

### Setup Diagram

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

### 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)

• 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

• 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

RMSE: 1.002

### Analysis

• I calculation

• Κ calculation

• Avg K = 2.60588 x 10-7+ 1.197 x 10-11 kg m/s2

### Analysis

• ri calculation (m)

• θ calculation

• Avg eo from “NM” values:

eo = 3.954” + 0.000177”

• Define xi = eo - ei

### 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

• Total Uncertainty relation for G:

000000000000

### 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

• 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