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course Phy 201
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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Because the density of gold is too high
13 g/cm^2
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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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V= 4/3 (3.14)(2500^3)
V= 6.5E10
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2500 kg / m^3 is the density of the rock.
If you cube this you get units of kg^3 / m^9. You won't end up with volume units, which would be m^3.
The problem is that 2500 kg / m^3 is a density, not a radius.
You know the radius--you used it in the right place in the calculation below--and you need to use it in calculating the volume.
Then you need to be careful about the units of G, which are N * m^2 / kg^2. Be sure the units of your other quantities are consistent with these units.
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6.67E-11 (6.5E15g)(1000)/(500^2) = 1.73 E^3 N
F= 6.67E-11 (6.5E10)(13gcm^2)/(500^2)
F= 2.25 E-4 N
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What’s the difference in these forces?
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1.73 E3 N
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Could we detect the difference in the lab? If so, how?
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No, bc we do not know the exact density of the sphere below the ground (this is a guess)
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