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!

Showing acceleration is constant

  1. Jan 30, 2009 #1
    I hope I posted in the right place. Sorry in advanced.

    1. The problem statement, all variables and given/known data
    A buzzing fly moves in a helical path given by the equation
    r(t) = ib sin [tex]\omega[/tex]t + jb cos [tex]\omega[/tex]t + kct[tex]^{2}[/tex]
    Show that the magnitude of the acceleration of the fly is constant, provided b, [tex]\omega[/tex], and c are constant.

    3. The attempt at a solution
    x = b sin [tex]\omega[/tex]t
    y = b cos [tex]\omega[/tex]t
    z = ct[tex]^{2}[/tex]

    In class we did a similar problem, but in that problem we had to find the trajectory in space. I'm a little slow, but it's just not helping me with this one. Same with the textbook. I'll go to my teacher if I have to.

    I'm not asking someone to do the problem, just get me started. Once that happens, I'll try to go over it here in case I have more questions. Thank you!
  2. jcsd
  3. Jan 30, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    The acceleration is the second derivative of r(t) with respect to t. What is that?
  4. Jan 31, 2009 #3
    The first derivative:
    ib[tex]\omega[/tex] cos [tex]\omega[/tex]t - jb[tex]\omega[/tex] sin [tex]\omega[/tex]t + 2kct

    Second derivative:
    -ib[tex]\omega[/tex][tex]^{2}[/tex] sin [tex]\omega[/tex]t - jb[tex]\omega[/tex][tex]^{2}[/tex] cos [tex]\omega[/tex]t + 2kc

    Is that right?
  5. Jan 31, 2009 #4


    User Avatar
    Science Advisor

    Now find the magnitude...
  6. Jan 31, 2009 #5


    User Avatar
    Homework Helper
    Gold Member

    Sure; that;s correct :approve:....But very ugly!:yuck::wink: Try writing the entire equation inside the [ tex] or [ itex] tags instead:

    [tex]\mathbf{a}(t)=-b\omega^2\sin(\omega t)\mathbf{i}-b\omega^2\cos(\omega t)\mathbf{j}+2c\mathbf{k}[/tex]

    (You can click on the above equation to see the code that generated it)

    Now, as Nabeshin said, calculate the magnitude :smile:
  7. Feb 2, 2009 #6
    Thank you guys :)

    Now what is the first step in calculating the magnitude? I am used to plugging in numbers to do that.
  8. Feb 2, 2009 #7


    User Avatar
    Homework Helper
    Gold Member

    You know what the x,y, and z-components of a are, so square them, add the squares, and take the square root as per usual.

  9. Feb 2, 2009 #8
    So I take [tex]\mathbf{a}[/tex] (the second derivative above), and factor in x for the first part. So it would look like this:

    [tex]\mathbf{a_x}(t)=[-b\omega^2\sin(\omega t)\mathbf{i}-b\omega^2\cos(\omega t)\mathbf{j}+2c\mathbf{k}*\mathbf{b}sin(\omega t)]^2[/tex], where [tex]\mathbf{b}sin(\omega t)[/tex] is x.

    Then do the same thing for y and z, add the terms up, and take the square root. Am I on the right track? Then I simplify as much as possible?
  10. Feb 2, 2009 #9


    User Avatar
    Homework Helper
    Gold Member


    No! [itex]a_x[/itex] is the x-component of a....that's just [itex]-b\omega^2\sin(\omega t)[/itex]....what are
    [itex]a_y[/itex] and [itex]a_z[/itex]?
  11. Feb 2, 2009 #10
    Thank you. I always over complicate things. I believe I know how to do it now.

    To answer your question, y is [tex]-b\omega^2\cos(\omega t)[/tex] and z is [tex]2c[/tex]
    Now I square them, add them up, and take the square root of that sum (this:[tex]||\mathbf{a}||=\sqrt{a_x^2+a_y^2+a_y^2}[/tex]). Correct?
  12. Feb 2, 2009 #11

    D H

    Staff: Mentor

    Correct. So what is the result?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Showing acceleration is constant
  1. Constant Acceleration (Replies: 1)

  2. Constant Acceleration (Replies: 3)