Question: (14%) Problem 6: A ring planet of radius R has a mass M. A space ship with mass m is at point P, a

(14%) Problem 6: A ring planet of radius R has a mass

(14%) Problem 6: A ring planet of radius R has a mass M. A space ship with mass m is at point P, a distance x from the center of the ring along its central axis, as shown in the figure. R x- P A 17% Part (a) What is the magnitude of the force in the y direction? 17% Part (b) Consider a differentially small element of the ring, dM. What is the value of differential force, dF, on the ship due to this element? A 17% Part (c) What is dFx, the x component of dF from part (b)? 17% Part (d) Does the value of dFx depend on where along the ring the element dM is located? 17% Part (e) What is the total force on the ship from the ring (in the x direction)? A 17% Part (f) If a ship at the center of the ring were displaced a small amount from the origin along the x direction, what would be the angular frequency of its oscillations? W = || Grade Summary Deductions 0% Potential 100%

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