Centrifuge Acceleration Calculations

[kser]

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

 

[rock.freak667]

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"

 

[kser]

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?

 

[rock.freak667]

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 a_mercury=N²r

 

[kser]

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...

 

[kser]

nevermind! got it. thanks so much!