Calculate new RPM after change in g-force in a centrifuge

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Homework Help Overview

The discussion revolves around calculating the new RPM of a centrifuge after a change in g-force when transitioning from Earth to Mercury. The problem involves understanding the relationship between RPM, acceleration, and gravitational force in different environments.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the relevant equations for calculating centripetal acceleration and question the definitions of variables such as g. There are discussions about the implications of using different values of g in the context of centrifuge operation.

Discussion Status

Some participants have provided insights into the equations and the nature of acceleration produced by a centrifuge. There is an ongoing exploration of the assumptions made in the problem statement, particularly regarding the use of the term g and its implications for the calculations. Clarifications are being sought, and attempts to articulate the reasoning behind the calculations are being made.

Contextual Notes

The problem involves a centrifuge operating under different gravitational conditions, which raises questions about how acceleration is defined and calculated in those contexts. There are concerns about the clarity of the problem statement and the potential for confusion regarding the variables involved.

EFB
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Homework Statement
A laboratory centrifuge on earth makes n rpm (rev/min) and produces an acceleration of 6.50 g at its outer end.

This centrifuge is now used in a space capsule on the planet Mercury, where g is 0.378 what it is on earth. How many rpm (in terms of n ) should it make to produce 4 g at its outer end?
Relevant Equations
Maybe: A=RPM∗pi∗2/60∗r
where A = "acceleration from RPM", r = "radius"
Supposed answer = 0.482n
 
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Welcome to PF. :smile:

EFB said:
Relevant Equations:: RCF = (RPM)^2 * 1,1118*10^(-5)*r
What is RCF? And where did you get this formula? And what are the units of each quantity in that formula?

EDIT -- It appears the OP has edited his post to change his Relevant Equation. Whatever.

@EFB -- Instead of editing your original post (OP) after it has been replied to, please just add a new reply that updates what you were wanting to post. That can eliminate confusion by your first responding users. Thanks.
 
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EFB said:
Relevant Equations:: Maybe: A=RPM∗pi∗2/60∗r
Certainly RPM∗pi∗2/60 is the rotation rate converted to radians per second, which is useful. But multiplying that by a distance, r, gives something with the dimension length/time. That is not an acceleration.
What sort of acceleration does a centrifuge produce (the clue is in the name)?
What is the formula for that sort of acceleration?
What direction does it act in?
 
And why does the local value of g matter for centrifuge operation? :wink:
 
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Is that the exact statement of the problem? The term g is used to represent two different things. Good grief.
 
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hutchphd said:
Is that the exact statement of the problem? The term g is used to represent two different things. Good grief.
Good point. So which one is meant in "How many rpm … should it make to produce 4 g at its outer end?"?
 
berkeman said:
And why does the local value of g matter for centrifuge operation? :wink:
A centrifuge rotating at 0 RPM on earth produces a g force of 1 gee.

A centrifuge producing a resultant of 6.5 gee on earth must be generating some lesser amount of centripetal acceleration.
 
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EFB said:
Homework Statement:: A laboratory centrifuge on earth makes n rpm (rev/min) and produces an acceleration of 6.50 g at its outer end.

This centrifuge is now used in a space capsule on the planet Mercury, where g is 0.378 what it is on earth. How many rpm (in terms of n ) should it make to produce 4 g at its outer end?
Relevant Equations:: Maybe: A=RPM∗pi∗2/60∗r
where A = "acceleration from RPM", r = "radius"

Supposed answer = 0.482n
Edit: gMercury = 0.378 * gEarth
Question: How many rpm(in terms of n) should it make to produce 4 gMercury at its outer end?
 
EFB said:
Edit: gMercury = 0.378 * gEarth
Question: How many rpm(in terms of n) should it make to produce 4 gMercury at its outer end?
That's clearer. So please post an attempt. You could start by trying to answer my questions in post #3.
 
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haruspex said:
Certainly RPM∗pi∗2/60 is the rotation rate converted to radians per second, which is useful. But multiplying that by a distance, r, gives something with the dimension length/time. That is not an acceleration.
What sort of acceleration does a centrifuge produce (the clue is in the name)?
What is the formula for that sort of acceleration?
What direction does it act in?
acentrifugal = v2/r
The direction of acentrifugal is straight outwards from the edge of the circular motion.
 
  • #11
haruspex said:
That's clearer. So please post an attempt. You could start by trying to answer my questions in post #3.
Since ac = v2 and r is constant, ac changes according with v.
v is represented by n rpm.
n rpm => ac,Earth/0.378 gMercury
Wanted: k, where k is constant such that k * n => ac = 4 gMercury:
k * n => 4/(ac,Earth/0.378)
Since k * n rpm is the velocity and a is altered according with v:
k = √(4/(ac,Earth/0.378))
Ans: 0.482*n rpm
I get the right answer, but do not fully understand what I have done. I have tried to write down the solution as I best understand it.
 
  • #12
EFB said:
Since ac = v2 and r is constant, ac changes according with v.
v is represented by n rpm.
n rpm => ac,Earth/0.378 gMercury
Wanted: k, where k is constant such that k * n => ac = 4 gMercury:
k * n => 4/(ac,Earth/0.378)
Since k * n rpm is the velocity and a is altered according with v:
k = √(4/(ac,Earth/0.378))
Ans: 0.482*n rpm
I get the right answer, but do not fully understand what I have done. I have tried to write down the solution as I best understand it.
Your working is very hard to follow. Mistakes like leaving out an "r" and omitting a power of 2 in:
"Since ac = v2/r and r is constant, ac changes according with v2"
don't help. And you keep using"=>" in ways that are not mathematically defined. Not sure how to read them.
If you can write it out in a way that others can follow, you'll probably understand it better yourself.
 

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