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Homework Help: Conservation of energy

  1. Apr 29, 2017 #1
    1. The problem statement, all variables and given/known data
    A block of mass 10kg starts at the top of a frictionless track which forms a quarter circle with radius 10m. It is given an initial downward velocity of 10m/s. What is the velocity at the bottom of the track?

    2. Relevant equations
    KEtranslational, f+ KErotational, f+PEf=KEtranslational, i+KErotational, i+ PEf
    KE, rotational=1/2Iw2
    KE, translational=1/2mv2
    3. The attempt at a solution
    I believe the initial equation would be set up like this.
    1/2mvf2+ 1/2 MR2(V/R)2+mghf=1/2mvi2+1/2 MR2(V/R)2+mghi

    which would then reduce to:

    This does not seem like the likely way to do it because we are not given the height of the mass at the top. Should I be using the rotational and translational KE in the equation? At what point is it rotational and what point translational?
  2. jcsd
  3. Apr 29, 2017 #2
    Look carefully.

    Why would it rotate? When does something rotate?
  4. Apr 29, 2017 #3
    Would the radius be the initial height?

    When it is rolling? I'm not exactly sure.
  5. Apr 29, 2017 #4
    That is correct.

    Try and think intuitively if you don't know the physics behind it.
  6. Apr 29, 2017 #5
    Ok, now I see how to do this. I obtained 17.2 m/s, which is correct. Thank you!

    However, I still don't see how the radius could be equal to the height of the ramp. There is a picture provided that looks like a skateboard ramp, with a strict vertical height and then the inside being curved with a radius. The vertical height does not look equal to the radius, even though I know this is not to scale.
  7. Apr 29, 2017 #6
    Does the picture below look like the picture you have of the skateboard ramp? Is the quarter circle oriented like that? Quarter circle track.jpg
  8. Apr 29, 2017 #7
    yes, it is just like that, except flipped so that the curve is on the right and height on the left.
  9. Apr 29, 2017 #8
    So does it make sense to you that the radius = height?
  10. Apr 29, 2017 #9
    Yes, I do see it now-my picture did not have the radius being pointed horizontally and vertically, just down the middle. Thank you for all your help!
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