You should have found that the gravitational force is a linear restoring force. Consequently, in the absence of air resistance, objects in the tunnel will oscillate with SHM. Suppose an intrepid astronaut exploring a 200-km-diameter, 3.5 x 10¹8 kg asteroid discovers a tunnel through the center. If she jumps into the hole, how long will it take her to fall all the way through the asteroid and emerge on the other side? Express your answer in minutes.

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Chapter1: Units, Trigonometry. And Vectors
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Suppose a large spherical object, such as a planet, with radius R and mass M has a narrow
tunnel passing diametrically through it. A particle of mass m is inside the tunnel at a distance
x < R from the center. It can be shown that the net gravitational force on the particle is due
entirely to the sphere of mass with radius r<z; there is no net gravitational force from the
mass in the spherical shell with r > I.
Transcribed Image Text:Suppose a large spherical object, such as a planet, with radius R and mass M has a narrow tunnel passing diametrically through it. A particle of mass m is inside the tunnel at a distance x < R from the center. It can be shown that the net gravitational force on the particle is due entirely to the sphere of mass with radius r<z; there is no net gravitational force from the mass in the spherical shell with r > I.
You should have found that the gravitational force is a linear restoring force. Consequently, in the absence of air resistance, objects in the tunnel will oscillate with SHM. Suppose an intrepid astronaut exploring a 200-km-diameter,
3.5 x 10¹8 kg asteroid discovers a tunnel through the center. If she jumps into the hole, how long will it take her to fall all the way through the asteroid and emerge on the other side?
Express your answer in minutes.
Transcribed Image Text:You should have found that the gravitational force is a linear restoring force. Consequently, in the absence of air resistance, objects in the tunnel will oscillate with SHM. Suppose an intrepid astronaut exploring a 200-km-diameter, 3.5 x 10¹8 kg asteroid discovers a tunnel through the center. If she jumps into the hole, how long will it take her to fall all the way through the asteroid and emerge on the other side? Express your answer in minutes.
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