1. Limited time only! Sign up for a free 30min personal 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!

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
    PE=mgh
    I=MR2
    w=v/r
    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:
    vf2=vi2+ghinitial

    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!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted