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Centripetal Acceleration of amusement ride

  1. Sep 23, 2013 #1
    1. The problem statement, all variables and given/known data

    An amusement ride with a radius of 4.8m allows riders to experience 4.3g's of centripetal acceleration. What is the frequency of the ride?

    2. Relevant equations

    a[itex]_{c}[/itex]= 4∏[itex]^{2}[/itex]r∫[itex]^{2}[/itex]


    3. The attempt at a solution

    a[itex]_{c}[/itex]=4.3
    r=4.8m
    ∫=?


    I keep getting a weird answer when I rearrange that equation to solve for ∫, and sub the values in. It might be my algebra
     
  2. jcsd
  3. Sep 23, 2013 #2

    ehild

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    What acceleration does 4.3 g mean in m/s2 units?

    ehild
     
  4. Sep 23, 2013 #3
    I think it's 1g=9.8m/s[itex]^{2}[/itex]
    therefore 4.3g= 42.14m/s[itex]^{2}[/itex]
     
  5. Sep 23, 2013 #4

    ehild

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    What do you get for the frequency?

    ehild
     
  6. Sep 23, 2013 #5
    I'm getting 0.1465 for the frequency
     
  7. Sep 23, 2013 #6

    ehild

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    It is not correct. How did you get it? Show your work.


    ehild
     
  8. Sep 24, 2013 #7
    a[itex]_{c}[/itex]=4∏[itex]^{2}[/itex]r∫[itex]^{2}[/itex]
    ∫[itex]^{2}[/itex]=a[itex]_{c}[/itex]/4∏[itex]^{2}[/itex]r
    ∫=±√(a[itex]_{c}[/itex]/4∏[itex]^{2}[/itex]r)
    ∫=±0.47157


    *calculator mixup on the previous answer*
     
  9. Sep 24, 2013 #8

    ehild

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    You need to use parentheses. ac/4∏2r means ac/4 * ∏2 * r.
    The numerical value is all right, but what is the unit? And give the final result with two significant digits.

    ehild
     
  10. Sep 24, 2013 #9
    I think the unit would be hertz?

    a[itex]_{c}[/itex]=4∏[itex]^{2}[/itex]r∫[itex]^{2}[/itex]
    ∫[itex]^{2}[/itex]=a[itex]_{c}[/itex]/(4∏[itex]^{2}[/itex]r∫[itex]^{2}[/itex])
    ∫=±√(a[itex]_{c}[/itex]/(4∏[itex]^{2}[/itex]r∫[itex]^{2}[/itex]))
    ∫=±0.47hz

    So it would be 0.47hz?
     
  11. Sep 24, 2013 #10

    ehild

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    fg
    ∫[itex]^{2}[/itex]=a[itex]_{c}[/itex]/(4∏[itex]^{2}[/itex]r∫[itex]^{2}[/itex])
    You kept f2 on the right hand side...[tex]f^2=\frac{a_c}{4\pi^2 r}[/tex]


    Yes, it is Hz or 1/s.

    ehild
     
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