1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Frequency of Centrifuge

Tags:
  1. Apr 9, 2016 #1
    1. The problem statement, all variables and given/known data
    A research apparatus called a centrifuge undergoes a centripetal acceleration with a magnitude of 3.3x10^6m/s^2. The centrifuge has a radius of 8.4cm. Calculate the frequency of the centrifuge in hertz and in revolutions per minute.

    Ac=3.3x10^6,/s^2 r=0.084m

    2. Relevant equations
    ac=4pi^2rf^2


    3. The attempt at a solution
    I tried solving this by isolating for f and plugging in all of my given values, but the answer I got was 683963.585Hz while the correct answer is 10 000Hz. Also, how do you convert Hz to revolutions per minute- do you just divide by 60?
     
  2. jcsd
  3. Apr 9, 2016 #2
    Acceleration = v^2/r. Tangential velocity is the square root of (acceleration X radius), the tangential velocity is 1,665 m / s. The frequency is the tangential velocity divided by the circumference of rotation, or (1,665 m / s) / (5.27 m), or 315.46 cycles per second (Hertz). That gives a frequency of 18,927 cycles per minute.

    Let's assume that the correct answer is 10,000 Hz. Then the tangential velocity is 52,779 m / s. The acceleration would be 3.3 *10^9 m / s^2.

    ac=4pi^2rf^2 should be ac=4pi^2r/f^2. And by the way, the f is not frequency but time for a single rotation. Check the dimensional analysis.
     
    Last edited: Apr 9, 2016
  4. Apr 9, 2016 #3
    check your calculation;

    to find out rev. per minute from rev per sec one should not divide by 60
     
  5. Apr 10, 2016 #4
    Speaking of checking calculations (picture me with a red face), the tangential velocity using a = (v^2 / r) is 1,587.5 m/s. This gives a rate of 300.8 Hz or 18,046.5 RPM.

    Using a = (4 * pi^2 * r / t^2) results in a time of 0.00332 seconds per revolution. This agrees at 300.8 Hz, and the tangential velocity agrees at 1,587.5 m/s.
     
  6. Apr 10, 2016 #5
    well i am getting about 1000 Hz and if converted to per minute it will be 60 thousand rev per minute but where did i do wrong?
     
  7. Apr 10, 2016 #6
    You may be right, who knows? In any case, here are my numbers and equations.
    ac=4pi^2rf^2, above is not correct, should be ac = 4*pi^2*r/f^2. Note that f is not the frequency but the time to complete one revolution. See concurrent dimensional analysis below.
    f = [(4*pi^2*r)/ac]^0.5, [(4*9.8696*0.84)/(3*10^6)]^0.5 (meters)/(meters/seconds squared) = (seconds squared)
    f=(1.1054*10^-5)^0.5 (seconds squared)^0.5
    f=3.325*10^-3 seconds
    The frequency is the inverse of that number, or 300.7746 (revolutions (dimensionless) / second).
    The tangential velocity is 300.7746 (revolutions per second * meters per revolution), or
    (300.7746 * 2 * pi * 0.84) = 1,587.45 (meters/second)

    Now let's use ac = v^2/r
    v=(ac*r)^0.5, (3*10^6*0.84)^0.5 [(meters/seconds squared)*(meters)]^0.5=(meters squared/seconds squared)^0.5=(meters/second)
    v= 1,587.45 (meters/second)

    Show your numbers and equations and let's see where the problems lie.
     
  8. Apr 10, 2016 #7
    i did it more simply -therefore i might have made errors-
    acceleration = w^2 . R where w is angular velocity as w= 2.pi/T where T is time taken to complete one revolution,
    in one second no. of rev. n=1 /T so,

    w
    = 2.pi.n where n is the no. of revolution per sec

    acceleration(a) = 4. Pi^2.n^2 . R therefore n= Sqrt ( a / 4.pi^2 .R) ; n= sqrt [ 3.3 . 10^6) /( 4.(3.14)^2 . 0.084) ]
    putting in numbers its approx n =1000 this is equivalent to frequency in Hz ,
    so in 1 minute i.e. 60 seconds =1000.60 = 60,000 rev. per minute.

    however these numbers are very high
     
    Last edited: Apr 10, 2016
  9. Apr 11, 2016 #8
    I cannot see what the problem is other than the insistence that n=1,000. Look at your own equation. When I calculate the value of that equation I get 300.7746 Hz, or 18,046.47 RPM. Using any of the other available equations for these numbers the result is the same.

    That's all I've got.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Frequency of Centrifuge
  1. Centrifugal Forces (Replies: 3)

  2. Centrifugal Force (Replies: 4)

  3. Centrifugal force (Replies: 3)

Loading...