1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    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 with Rotation

  1. Dec 4, 2013 #1
    1. The problem statement, all variables and given/known data

    A small circular object with mass m and radius r has a moment of inertia given by I = cmr^2. The
    object rolls without slipping along the track shown in the figure. The track ends with a ramp of height R = 2.5 m that launches the object vertically. The object starts from a height H = 6.0 m. To what maximum height will it rise after leaving the ramp if c = 0.40?

    3. The attempt at a solution

    My solution to this problem is 4.7 m.
    So I'm pretty sure my answer is right but the textbook indicates the answer is 5.0 m which confuses me.

    I applied conservation of energy from the starting point, mgH to the launch point (when it leave the ramp), mgR + 1/mv^2 + 1/2I[itex]\omega[/itex]^2 , and then solved for v obtaining 6.55m/s.
    Then, I used the equation v^2 = 2g(h-R), where h is the maximum height reached (note I'm
    pretty sure once the object leaves the ramp, it loses its rotational motion and maintains only
    linear motion after-though correct me if I'm wrong). Rearranging and substituting I obtain
  2. jcsd
  3. Dec 4, 2013 #2
    The textbook is correct here. The magnitude of velocity at the end of ramp is not 6.55 m/s.

    That said, I suggest that you do not plug in the numbers until you solve everything symbolically. You will see that many things cancel each other out.
  4. Dec 4, 2013 #3
    Rather silly mistake on my part. I rearranged my equations and everything, but for some reason wrote c= 0.60 at the top of my page and kept referencing that value ....
  5. Dec 4, 2013 #4
    Which, I assume, means you got the correct result?
  6. Dec 4, 2013 #5
    oh yeah I did. Thanks.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted