Please show all of your work A proposed space elevator is configured as in the d

Question

Please show all of your work

A proposed space elevator is configured as in the diagram. First suggested in 1895, it would provide a means to lift cargo into orbit without the need for rockets. A counterweight (mass mc) is attached to a point on the Earth's equator by means of a massless tether. An ascent module (mass ma including cargo) travels upward at a constant speed va. In answering the following questions, ignore all drag forces and any vertical acceleration of the ascent module. Write an expression for the upward force that must be applied to the ascent module as it rises in order To maintain a constant velocity. Express this as a function of the module's distance A from the Earth's center. For what value of A R does the applied force equal zero? Express your answer in terms of the Earth radius R. As the ascent module rises a Coriolis force will act on it. In order to counter this force a thruster must be attached to the module. What force (magnitude and direction ) must this thruster supply?

Explanation / Answer

1 a) FORCE ACTING ON THE ACENT MODULE AT A DISTANCE A FROM EARTHS CENTRE

DUE TO EARTH = G*Me*Ma / A^2 , WHERE Me = MASS OF EARTH

FORCE ACTING ON THE ACENT MODULE AT A DISTANCE A FROM EARTHS CENTRE DUE TO MASS Mc = G*Mc*Ma / (C-A)^2

net force = (G*Me*Ma / A^2) - (G*Mc*Ma / A^2)

So this much amount of FOrce must applied to maintain constant velocity( net force = 0)

so force applied = (G*Me*Ma / A^2) - (G*Mc*Ma /(C-A)^2)

1 b) this force will be zero when G*Me*Ma / A^2 - G*Mc*Ma /(C-A)^2 =0

or G*Me*Ma / A^2 = G*Mc*Ma /(C-A)^2

=> Me/A^2 = Mc/ (C-A)^2

solve this to get A

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