Engineers design a cylindrical habitation ring for a spacecraft so that occupants…
PHYSICS · Multi-part · CBSE · Physics · Motion in a Plane · Motion in a Plane
Problem
Engineers design a cylindrical habitation ring for a spacecraft so that occupants will feel an "artificial gravity" equal to 0.40 g directed toward the outer wall. The ring is intended to rotate as a rigid body in deep space.
(a) Derive an algebraic expression for the required period of rotation T in terms of the ring’s radius R and the desired centripetal acceleration expressed as a multiple k of g (here k=0.40).
(b) For a proposed ring radius of 45 m, calculate the exact period (in seconds) and the corresponding rotation rate in revolutions per minute that will achieve the target artificial gravity.
(c) If mission planners later decide to double the ring’s radius while keeping the same artificial gravity level, determine by what factor the period must change. Explain your reasoning clearly.
(d) Discuss one potential advantage and one potential engineering challenge that arise from increasing the radius in order to reduce the rotation rate, drawing on the physical relationships you established.