1. The problem statement, all variables and given/known data 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? 2. Relevant equations a = v^{2}/R 3. 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
since we are given rpm or 'ω', let's use a=ω^{2}r instead. So you know that at the outer end a= 3.40g=ω^{2}r. Our ω in this case is n so n^{2}r=3.40g Now halfway to the end is r/2 and ω is the same so we get now: a_{1}=n^{2}(r/2) → (n^{2}r)/2=a_{1} try dividing the two equations in red and get a_{1}/3.40g = "something"
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}=N^{2}r
yup. i'm sorry i just dont 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....