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Cavendish Experiment

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Cavendish Experiment

Presented by Mark Reeher

Lab Partner: Jon Rosenfield

For Physics 521

- Historical Background
- Theory
- Experimental Setup and Methods
- Results
- Analysis of Results
- Uncertainties

- Conclusions

- 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

- 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

- 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

Fβ

Fα

- 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

Torsion balance enclosure

Large masses

Vacuum pump (oil)

He-Ne laser

Ametek plotter (converted)

Laser

Plotter

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

Fβ

Fα

Fα

Fβ

- 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

- 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

- 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

- General model:

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

- ri calculation (m)
- θ calculation
- Avg eo from “NM” values:
eo = 3.954” + 0.000177”

- Define xi = eo - ei

- 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

- Total Uncertainty relation for G:

000000000000

- 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:

- 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