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Question on finding maximum magnitude of acceleration

  1. May 8, 2016 #1
    1. The problem statement, all variables and given/known data
    An object is moving in the xy-plane according to the equations x(t) = 3sin(3t) and y(t) = 4cos(3t). What is the maximum magnitude of the particle's acceleration?

    1. 1) 5 m/s2

    2. 2) 15 m/s2

    3. 3) 30 m/s2

    4. 4) 36 m/s2 [the accepted answer]

    5. 5) 45 m/s2

    2. Relevant equations
    x(t) = Asin(wt + phase constant)

    3. The attempt at a solution
    So, I know that for each dimension if I take the second derivative of the two position equations I get acceleration, and the maximum acceleration for each of those two is simply A*omega^2.

    So that's what I did.

    For acceleration in the x-dimension, I get: 3*3^2.
    For acceleration in the y-dimension, I get 4*3^2.

    Taking the squares of the two acceleration components and then summing them and taking the square root of the sum gives 45, which is what I got. Why do the authors then believe 36 m/sec^2 is the right answer?

    Thanks in advance for the input!
     
  2. jcsd
  3. May 8, 2016 #2

    TSny

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    Does ax, max occur at the same instant that ay, max occurs?
     
  4. May 8, 2016 #3
    no, of course not. how would I fix for that, then?
     
  5. May 8, 2016 #4
    But how would I be able to tell if the aymax and axmax occur simultaneously?
     
  6. May 8, 2016 #5

    TSny

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    Can you find an expression for the magnitude of the (total) acceleration as a function of time?
     
  7. May 8, 2016 #6
    Yes, take the squares of the two equations, sum and square root.

    I am too lazy to write it out here, unless it is really needed. ;-)
     
  8. May 8, 2016 #7

    TSny

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    Find expressions for ax and ay as functions of time. By inspection you will see that their max values do not occur at the same time.
     
  9. May 8, 2016 #8
    are your accelerations correctly written-
    i think there are cosine /sine terms also in the accelerations.
    check.
    or you can find r the radius vector and find out the acceleration and find out the maximum.
     
  10. May 8, 2016 #9
    Aha, OK. thanks.
     
  11. May 8, 2016 #10
    I was just doing manipulations of maximum and minimum values [just the amplitudes of the two equations..... if you know what I mean]
     
  12. May 8, 2016 #11

    TSny

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    That's pretty lazy. :oldeyes:
    I wouldn't have suggested it unless I thought it was worth the trouble. :oldsmile:
     
  13. May 8, 2016 #12
    sqrt( 3sin(3t)^2 + 4cos(3t)^2 )

    Here you go, sir!
     
  14. May 8, 2016 #13

    TSny

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    No, that's not the sum of the squares of the acceleration components.
    ##a = \sqrt{a_x^2+a_y^2}##
     
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