Airbrake of a Centrifuge

An important part of astronaut training is force resistance training. It is done in a large centrifuge, with radius \(r = {{params.r}} \ \rm{m}\) and total mass \(m = {{params.mass}} \ \rm{kg}\). The centrifuge cabin is accelerated to a speed \(\lvert v \rvert = {{params.v}} \ \rm{m/s}\). When it is time to slow down the centrifuge, it is slowed down due to a constant resistive moment \(M = {{params.M}} \ \rm{N.m}\) at the axle and the deployment of an airbrake that creates more air resistance such that the force is described by this equation \(F = {{params.C}}t^{{{params.N}}} \ \rm{N}\).

What is the speed of the cabin \({{params.t}}\) seconds later?

Part 1

What is \(\lvert v \rvert\)?

Answer Section

Please enter in a numeric value in \( m{m/s}\).

Attribution

Problem is licensed under the CC-BY-NC-SA 4.0 license.