Planet Earth as a Spring. Assume that the Earth is perfect sphere of mass M=5.98x10^24kg, radius 6,370km, and uniform density. Imagine a long, straight tunnel through the center of the Earth, connecting the North and South poles . A capsule of mass m is dropped into this tunnel. It falls through the center of the Earth, stops when it reaches the opposite pole, and then returns. This is an example of simple harmonic motion. A.Calculate the force constant for simple harmonic motion of this capsule.(Hint:Show that F=-kr, and find k) B.Find the time it takes for the capsule, dropped into the tunnel at the North pole, to return to the North pole C. Explain in 2-3 sentences what would happen if we instead drilled a tunnel through the center of the Earth from the equator, and dropped the capsule down there. Would the resulting motion be different from the pole-to-pole case? PLEASE SHOW ALL ANSWERS AND UNITS. AND HOW YOU CAME UP WITH THE EQUATION FOR THE ANSWERS

Question

Planet Earth as a Spring. Assume that the Earth is perfect sphere of mass M=5.98x10^24kg, radius 6,370km, and uniform density. Imagine a long, straight tunnel through the center of the Earth, connecting the North and South poles . A capsule of mass m is dropped into this tunnel. It falls through the center of the Earth, stops when it reaches the opposite pole, and then returns. This is an example of simple harmonic motion. A.Calculate the force constant for simple harmonic motion of this capsule.(Hint:Show that F=-kr, and find k) B.Find the time it takes for the capsule, dropped into the tunnel at the North pole, to return to the North pole C. Explain in 2-3 sentences what would happen if we instead drilled a tunnel through the center of the Earth from the equator, and dropped the capsule down there. Would the resulting motion be different from the pole-to-pole case? PLEASE SHOW ALL ANSWERS AND UNITS. AND HOW YOU CAME UP WITH THE EQUATION FOR THE ANSWERS>
Physics