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Problem_of_the_Week_7_Solution

# Problem_of_the_Week_7_Solution - Problem of the Week 7...

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Problem of the Week # 7 - Solution In the rough approximation that the density of the Earth is uniform throughout its interior, the gravitational force on a mass m inside the Earth at a distance r from the center is mgr R , where R is the radius R of the Earth. (Note that at the surface r = R , and the gravitational force is mgR R = mg .) Using this uniform-density approximation, calculate the amount of energy required to move a mass m from the center of the Earth to the surface, through a tiny hole, without changing its speed. Also calculate the additional amount of energy required to move the mass from the surface of the Earth to a great distance away, without changing its speed. In what follows, we will take the mass, m , to be the system , and the Earth and an external agent to be in the surroundings . We first need to calculate the gravitational force on mass m as a function of its (radial) distance r , from the Earth’s center. This force depends only on the mass within the sphere of radius r .

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Problem_of_the_Week_7_Solution - Problem of the Week 7...

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