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!

I Constrained Falling of three balls

  1. Jan 23, 2017 #1
    Can anyone explain this "mathematically"? i.e. how to calculate the time in each cases?
     
    Last edited: Jan 23, 2017
  2. jcsd
  3. Jan 23, 2017 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    Yes, but not at B level. The math required is called variational calculus. You will need multivariable calculus and differential equations as prerequisites.

    At B level, I would say that it is a combination of maximising the speed and minimising the path length. The upper path is shorter, but the ball accelerates slower in the beginning. The lower path gives a larger mean speed, but is longer.
     
  4. Jan 23, 2017 #3
    Sorry, I did the mistake. It should not be in "B" level. But I've corrected that.
     
  5. Jan 23, 2017 #4

    A.T.

    User Avatar
    Science Advisor
    Gold Member

  6. Jan 23, 2017 #5

    A.T.

    User Avatar
    Science Advisor
    Gold Member

    Here is the full clip BTW:

     
  7. Jan 23, 2017 #6

    jbriggs444

    User Avatar
    Science Advisor

    If one makes the simplifying assumption that the balls roll without slipping then one can model the motion by using an "effective inertial mass" which bundles the effect of the ball's inertial mass together with its moment of inertia. The effect is the same as if the acceleration of gravity was reduced. Unless I am missing something, the Brachistochrone should still be optimal in such a case.
     
  8. Jan 23, 2017 #7

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    I thought about this a bit and I think it is correct as long as the ball radius is small in comparison to the curvature of the track such that the angular velocity of the ball is directly given by the ball's radius and the velocity of the ball.
     
  9. Jan 23, 2017 #8

    jbriggs444

    User Avatar
    Science Advisor

    Good point about the radius. I'd missed that.
     
  10. Jan 29, 2017 #9
    Thanks to all of you (specially @A.T.). Actually I skipped some portions in Classical Mechanics due to (my personal) exam. strategy in completing my Graduation as I am not a good student. That’s why I could not solve this problem. But now, I have found this (The Brachistochrone) in my text book! Wow! It’s very interesting topic.
     
    Last edited: Jan 29, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Constrained Falling of three balls
  1. Items falling in liquids (Replies: 13)

Loading...