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The word "payload" was not used in our textbook and
I am not sure what it means in this cotext.
Students are not physics majors and ths problem was
chosen to drill them in the use of the formula explained
in the text. Some problems may indeed be "open-ended"
but drill-and-practice problems are also useful sometimes.
I am not addressing the issue of how many problems of
each kind produce the best result.
A SAMPLE OF BLOOD IS PLACED IN A CENTRIFUGE
OF RADIUS 15 CM. THE MASS OF A RED CORPUSCULE
IS 3E-16 KG AND THE MAGNITUDE OF THE FORCE
REQUIRED TO MAKE IT SETTLE OUT OF THE PLASMA
IS 4E-11 N. AT HOW MANY REVOLUTIONS PER
SECOND SHOULD THE CENTRIFUGE BE OPERATED?
!50 rev/sec was calculated with r=R and it seems to me that
this is not sufficient.
Problem #21 from College Physics of Serway& Faughn
(5th edition, page 211) asks students to calculate v when
m, R and F=(m*v^2)/R are given. The answer one gets
(150 rev/s) is the same as that shown in the book. Note
that R is "the radius of the centrifuge".
The problem defines F as "the force required to make
it [particle of mass m] settle out of the plasma". Most
blood particles are initially at r<R.