(14%) Problem 1: In the 2012 remake of Total Recall, a plot device centers around an...

   

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(14%) Problem 1: In the 2012 remake of Total Recall, a plot device centers around an elevator that travels through the Earth powered solely by the force of gravity. For simplicity, suppose that the tunnel is straight and travels directly through the center of the Earth. Suppose also that the Earth has a uniform density, and neglect friction and the effects of the Earth's rotation. How many minutes does a one-way trip from one side of the Earth to the other take? Hint: the solution to this problem relies on a remarkable result that 1) the force of gravity vanishes at any point within a spherical shell, and 2) the force of gravity due to a solid sphere can be treated as if it all comes from the center point. The modern proof of this turns out to be simple enough (the original proof took the incomparable genius Newton more than a decade to derive) but relies on math and physics best left until next semester when you get to Gauss's Law. t = || minutes Grade Summary Deductions Potential 0% 100% (14%) Problem 1: In the 2012 remake of Total Recall, a plot device centers around an elevator that travels through the Earth powered solely by the force of gravity. For simplicity, suppose that the tunnel is straight and travels directly through the center of the Earth. Suppose also that the Earth has a uniform density, and neglect friction and the effects of the Earth's rotation. How many minutes does a one-way trip from one side of the Earth to the other take? Hint: the solution to this problem relies on a remarkable result that 1) the force of gravity vanishes at any point within a spherical shell, and 2) the force of gravity due to a solid sphere can be treated as if it all comes from the center point. The modern proof of this turns out to be simple enough (the original proof took the incomparable genius Newton more than a decade to derive) but relies on math and physics best left until next semester when you get to Gauss's Law. t = || minutes Grade Summary Deductions Potential 0% 100%