A typical laboratory centrifuge rotates at 4000rpm. Test tubes have to be placed

Question

A typical laboratory centrifuge rotates at 4000rpm. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations.

1) What is the acceleration at the end of a test tube that is 10

cm from the axis of rotation?

2) For comparison, what is the magnitude of the acceleration a test tube would experience if stopped in a 1.0ms long encounter with a hard floor after falling from a height 1.0m?

A typical laboratory centrifuge rotates at 4000rpm. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations. What is the acceleration at the end of a test tube that is 10 cm from the axis of rotation? For comparison, what is the magnitude of the acceleration a test tube would experience if stopped in a 1.0ms long encounter with a hard floor after falling from a height 1.0m?

Explanation / Answer

A)
4000 rpm
= 4000 / 60 = 66.67 rps
= 66.67 * 2 * pi = 419.1 rad/s

Acceleration in the centrifuge = (rad/s)^2 * radius
= 419.1^2 * 0.1
= 17564.481 m/s^2

B)
Velocity afer falling 1 m
v^2 = u^2 + 2as
v^2 = 0 + 2 * 9.81 * 1
= 19.62

v = 19.62^0.5
= 4.4294 m/s

Acceleration on hitting the floor
v = at
a = 4.4294 / 10^-3
= 4429 m/s^2

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