The Asteroid Mining Tether · AI Generator #GEN-E58F8B99

Physics · mechanics

Problem

A space mining operation uses a rotating tether system to extract material from an asteroid. The system consists of a central station of mass M=2000  kgM = 2000\;\text{kg} connected by a strong cable to a mining pod of mass m=500  kgm = 500\;\text{kg}. The cable has length L=100  mL = 100\;\text{m} and negligible mass. Initially, the system rotates in free space with angular velocity ω0=0.20  rad/s\omega_0 = 0.20\;\text{rad/s} about their center of mass. The mining pod then uses its thrusters to reel in the cable, shortening it to length L/2=50  mL/2 = 50\;\text{m} while maintaining circular motion. (a) Find the angular velocity ωf\omega_f of the system after the cable is shortened. (b) Calculate the work done by the thrusters during this process. (c) If instead the cable were cut instantaneously when the mining pod reaches the shortened radius, what would be the speed of the pod relative to the center of mass at that instant?

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