Centrifuge Acceleration Calculations

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In summary, on Earth, a centrifuge makes n rpm and produces an acceleration of 3.40 g at its outer end. This centrifuge is now used in a space capsule on the planet Mercury, where gMercury is 0.378 what it is on earth. To produce 4 gMercury at its outer end, this centrifuge would need to make n rpm.
  • #1
kser
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Homework Statement


A laboratory centrifuge on Earth makes n rpm (rev/min) and produces an acceleration of 3.40 g at its outer end.

Part A: What is the acceleration (in g's) at a point halfway out to the end?

Part B: This centrifuge is now used in a space capsule on the planet Mercury, where gMercury is 0.378 what it is on earth. How many rpm (in terms of n) should it make to produce 4 gMercury at its outer end?

Homework Equations



a = v2/R

The Attempt at a Solution



Well using the equation for centripetal acceleration, I figure if the Radius is half then the acceleration in g's would be double for part A. Is that right? or would it be half?

For part B I'm not exactly sure what to use or do. What kind of equation could I use?

Any help would be great! Thanks so much, really thank you
 
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  • #2
kser said:

Homework Equations



a = v2/R

since we are given rpm or 'ω', let's use a=ω2r instead.


So you know that at the outer end a= 3.40g=ω2r. Our ω in this case is n

so n2r=3.40g


Now halfway to the end is r/2 and ω is the same so we get now:

a1=n2(r/2) → (n2r)/2=a1

try dividing the two equations in red and get a1/3.40g = "something"
 
  • #3
what do you mean by "dividing the two equations"? combine them? so a/3.40g = ((n^2r)/2))/n^2r ? I'm sorry, am i just looking into this way too much? I don't get what you're saying. because the way i see it. n is constant so when you half the radius, that also halves the acceleration right?
 
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  • #4
kser said:
what do you mean by "dividing the two equations"? combine them? so a/3.40g = ((n^2r)/2))/n^2r ? I'm sorry, am i just looking into this way too much? I don't get what you're saying. because the way i see it. n is constant so when you half the radius, that also halves the acceleration right?

yes that is what I meant by divide.

For the second part, the 'r' is the same at the outer end. So in terms of 'n' find the r using what happens on Earth. The use amercury=N2r
 
  • #5
yup. I'm sorry i just don't get it. ugh. this whole mercury part it just not makin sense.

so i find r in terms of n and get: r = 3.4/n^2 <--- is that even right? can't be because then I don't see how that would give me what I'm looking for. i am just not good at this stuf...
 
  • #6
nevermind! got it. thanks so much!
 

1. What is a centrifuge?

A centrifuge is a laboratory instrument that uses centrifugal force to separate components of a mixture based on their density. It is commonly used in chemistry, biology, and medical laboratories.

2. How does a centrifuge work?

A centrifuge works by spinning the mixture at high speeds, causing the denser components to move towards the outer edge of the container and the less dense components to remain in the center. This process is known as centrifugation.

3. What is the purpose of a centrifuge?

The purpose of a centrifuge is to separate components of a mixture based on their density. This is useful in various scientific fields, such as isolating cells or proteins in biology, purifying chemicals in chemistry, and separating blood components in medical procedures.

4. How fast does a centrifuge spin?

The speed at which a centrifuge spins can vary depending on the type and model. Generally, they can range from a few hundred revolutions per minute (RPM) to tens of thousands of RPM.

5. Are there different types of centrifuges?

Yes, there are different types of centrifuges, each designed for specific purposes. Some common types include microcentrifuges, ultracentrifuges, and refrigerated centrifuges. They can also vary in terms of size, capacity, and speed.

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