Cavendish Experiment

1 / 27

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.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

PowerPoint Slideshow about ' Cavendish Experiment' - damali

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

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
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)

Setup Diagram

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