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course phy 201
12-30 8:15
Gold Ball
How can we tell that there’s not a gold ball of diameter 1000 meters, just under the ground below the physics lab?
Look up the density of gold, then figure out how much gravitational force that ball would exert on a 1 kg mass in the lab.
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gold density = 19.32g/cm^3 or 19320kg/m^3
v=(4/3)pi(500)^3=523598775.6 m^3
m=19321 kg/m^3*523598775.6 m^3= 1.0*10^13kg
Fgrav=G (Mm/r^2)
=(6*10^-11(Nm^2/kg^2))*(1.0*10^13kg(1kg))/(500m)^2=0.0024N
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Assuming that the density of the 1000-meter diameter sphere just below the ground is 2500 kg / m^3 (which is what it would be if the ball is typical earth-crust material), how much force does it exert on that 1-kg mass in the lab?
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m=2500kg/m^3*523598775.6m^3=1.3*10^12kg
Fgrav=(6*10^-11Nm^2/kg)*((1.3*10^12kg)(1kg))/(500m)^2=3.12*10^-4N
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What’s the difference in these forces?
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0.0024N-(3.12*10^-4)=0.002088N
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Could we detect the difference in the lab? If so, how?
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I don't think we would dectect the difference
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Very good.
If we could accurately time a 25-cm-long pendulum, I believe that this difference in force would result in about one extra cycle every 15 minutes.
Comparing this pendulum with an idential pendulum at least a kilometer away would clearly reveal the difference after just a few minutes.
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