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Slider energy on rod

  1. Feb 19, 2007 #1
    1. The problem statement, all variables and given/known data
    Collar B has a mass of 4 kg and is attached to a spring of constant 1500 N/m and of undeformed length 0.4 m. The system is set in motion with r = 0.2 m, v_theta = 6 m/s, and v_r = 0. Neglecting the mass of the rod and the effect of friction, determine the radial and transverse components of the velocity of the collar when r = 0.5 m.

    2. Relevant theories

    Conservation of energy - kinetic and potential energy

    3. The attempt at a solution

    I used conservation of energy :

    V_spring_initial = V_spring_final + T_slider_final

    x_initial_spring = abs(0.2-0.4)
    x_final_spring = abs(0.5-0.4)

    I solved for v_r and got 3.35 m/s, which is NOT the right answer.

    If I figure out how to solve for v_r, I'm still in the situation where I don't really know how to solve for v_theta. I'm thinking I can determine the force due to the spring and set that equal to m*a_normal, solve for v_theta there (because v^2 = (v_tangential)^2 = (v_theta)^2).

    Can I get some help? Thanks a bunch!

    Attached Files:

  2. jcsd
  3. Feb 19, 2007 #2
    Use conservation of angular momentum to find the velocity in the tangential direction as a function of the radius.

    Use a net force equation to find the velocity in the radial direction as a function of the radius. (You can consider it as an "inertial" frame with a fictional force, if you want.)
  4. Feb 19, 2007 #3
    We haven't done angular momentum in class yet. While I do know it, he wants us to try and stick to the concepts we know.
  5. Feb 20, 2007 #4
    Is there any more thoughts on this one or no??
  6. Feb 20, 2007 #5


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    Homework Helper

    If one looks at just the SHM motion of the slider its energy stays constant throughout the motion:


    which enables one to calculate the radial velocity at any position.

    Looking at the bigger picture the total mechanical energy (which will stay
    constant since the slider is subject to a conservative force) of the slider should also include its rotational kinetic energy:

    [tex]\frac{1}{2}I\omega ^2[/tex]

    , where its rotational velocity is determined by the tangential velocity.
    Last edited: Feb 20, 2007
  7. Feb 20, 2007 #6
    But the concept of moment of inertia hasn't been formally introduced in our class yet, so we can't really use that equation.
  8. Feb 20, 2007 #7
    How did you get the answer for Vr? What principle did you use? I was going to suggest you use the work-energy principle.
  9. Feb 21, 2007 #8


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    Homework Helper

    Ok. You can then still use the fact that T + V will stay constant. The speed that you get will be the real speed of the slider, that is the tangential and radial speed combined or just v.
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