51. In Larry Niven's science-fiction novel Ringworld, a rigid ring of material rotates about a star (Fig. P13.51). The tangential speed of the ring is 1.25×10® m/s, and its radius is 1.53×10" m. (a) Show that the centripetal acceleration of the inhabitants is 10.2 m/s². (b) The inhabitants of this ring world live on the starlit inner surface of the ring. Each person experiences a normal contact force ñ. Acting alone, this normal force would produce an inward acceleration of 9.90 m/s². Additionally, the star at the center of the ring exerts a gravitational force on the ring and its inhabitants. The difference between the total acceleration and the acceleration provided by the normal force is due to the gravitational attraction of the central star. Show that the mass of the star is approximately 1032 kg.

51. In Larry Niven's science-fiction novel Ringworld, a rigid ring of material rotates about a star (Fig. P13.51). The tangential speed of the ring is 1.25×10® m/s, and its radius is 1.53×10" m. (a) Show that the centripetal acceleration of the inhabitants is 10.2 m/s². (b) The inhabitants of this ring world live on the starlit inner surface of the ring. Each person experiences a normal contact force ñ. Acting alone, this normal force would produce an inward acceleration of 9.90 m/s². Additionally, the star at the center of the ring exerts a gravitational force on the ring and its inhabitants. The difference between the total acceleration and the acceleration provided by the normal force is due to the gravitational attraction of the central star. Show that the mass of the star is approximately 1032 kg.