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2540-66040Big G0Big G (4-page entry)Abstract: We will use a Cavendish torsional balance to determine the Universal Constant of Gravitation “Big G” by measuring the effect of the gravitational force of attraction (on the order of one ten-billionth of a pound!) between pairs of small lead masses. See Intro Video.364701734290ScreenLxθ2θmMMmdFinal PositionInitial Positionl/2Neutral PositionTop ViewSketch this.Note that when the pendulum swings through angle θ the beam sweeps through 2θ0ScreenLxθ2θmMMmdFinal PositionInitial Positionl/2Neutral PositionTop ViewSketch this.Note that when the pendulum swings through angle θ the beam sweeps through 2θSet-up/Theory: For a torsional fiber spring:τ=-κθ1546860193040I = =00I = =-104140193040T =00T =Find (“kappa”) for the fiber in terms of T2-10668085090 =00 =Find , using the small angle approximationIn terms of x and L.-10668062865 =00 =Now find the fiber restoring torque in terms of m, l, L, x, T and any necessary constants.Hint: sub in for and in the top equation…-55880130810 =00 =Find the total torque due to gravity. Use the law of universal gravity.-98425129540g =00g =Equate the torque magnitudes and solve for G.-9842582550G =00G =Point #t (m:s)t (s)x (cm)000014:372775729:0554511313:3547417:56567891054:3410911121314etcOscillation Data: First watch the time-lapse Oscillation video. Then see Beam Data (or the image below) to finish the table I started here in Excel. When you are done, paste the table back into your PJ here. Initial position oscillations coded in green, final position oscillations after external mass swing coded in red. Omit the data point 45:35?* 22330833661800* I got interrupted by a potentially life changing facetime announcement from one of my kids and lost track of the experiment momentarily!Make a big beautiful full-page Excel graph of x vs t. Do not use Excel to curve fit or connect the data points. Each data point represents the extreme end of each oscillation. Sketch in your own best fit curve to connect the points after printing the graph. Draw equilibrium lines through the initial and final oscillation sets. Measure x right on your graph. You should end up with something like this: Calculations:Calculate the period T using multiple cycles (>5) from your graph. Indicate the cycles you used on your graph. Show work here.Calculate G starting with your algebraic equation from above. Show all numerical substitutions (values from the table below.)Put all your data and results into this table. Use the accepted value of G to calculate % error.L (m)l (m)d (m)x (m) M (kg) m (kg)T (s)Gexp (Nm2/kg2)% E12.500.100.040From graph1.5000.015 Using the accepted value for G, calculate the force of gravity between one pair of masses a distance d apart. (M and m)Convert that gravitational force to lbs using 1 lb = 4.45 N.Conclusion: Quote your value for G and your % error. ................
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