Question

This is a dynamics problem from an ENGR 2350 class. Hope you can help.

A medical centrifuge has an acceleration of α = A − Bω2, where constants A and B
are design parameters. Select A and B such that the samples to a maximum horizontalacceleration of 12,000 g’s and will reach 90% of its maximum operating speed in 2 min. The centrifuge has a radius of 300mm.

Answer 1

"Acceleration, a = A - Bw^2 = A - B(v/r)^2 w = v/r = A - Bv^2/r^2 eq 1) At maximum acceleration, we have da/dv = 0 = A - B/r^2 2v 2 Bv/r^2 = A B = Ar^2/2v eq ii) Therefore From 1) we get,