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course Phy 241
Ignore that first submission. hit enter too quickly1/9 9:30
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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19.3 g/cm 3 is the density of gold according to google.
if F=ma, first find the mass of the gold ball.
if diameter is 1000 meters, 1,000m = 100,000cm.
19.3 g / cm^3 * (100,000cm)^3 = 1.93*10^16 grams. acceleration of gravity is 9.81 m/s^2. on the 1kg ball it has a force of 9.81 N. the big ball exerts a force of
9.81 m/s^2 * 1.93*10^13kg = 1.89*10^14N
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That would be the force exerted by Earth's gravity on the ball.
However that isn't the question. The question is about the gravitational effect of the ball on objects in the lab.
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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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If the ball is just below the ground, and the 1kg mass is in the lab, I'm not sure it exerts a force. unless it abstructs the force of gravity barely because of the immense mass. if so, then 2.5kg / m^3 * 1,000m^3 is 2.5*10^12 kg. * 9.81 m/s^2 =
2.45*10^13N. this is a difference of
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To answer this you need to use Newton's Law of Universal Gravitation, applied to the gold ball and the 1 kg mass.
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What’s the difference in these forces?
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-2.4*10^14 Newtons
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Could we detect the difference in the lab? If so, how?
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we could, barely. If we had a bunch of pendulums, we could count the number of periods in one minute, and get a very very accurate swing, with no other forces acting on these. So we can eliminate all other forces except gravity.
We take this data at different points all around the county, ( away from the gold ball ), so we have an exact number of periods / minute. then do the same exact experement directly above the gold ball. If there is a significant change in the number
of periods/ minute, we know there is something absolutely huge underneath the ground. ( huge as in massive ).
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