Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Ball rolling down a ramp

  1. Jul 8, 2014 #1
    suppose you had a ball rolling down a ramp, without slipping and compare it to a ball that starts with a velocity u that is horizontally to the side. how would the time taken be different to reach the bottom?
     
  2. jcsd
  3. Jul 8, 2014 #2

    A.T.

    User Avatar
    Science Advisor
    Gold Member

    Starting with zero speed?

    Thrown horizontally from same height as the first ball?

    Consider the vertical accelerations in both cases.
     
  4. Jul 8, 2014 #3

    1. yes starting with 0 speed.
    2. it's rolling down a ramp but yes at same height.
    3. vertical acceleration is just gsin(theta) am I right?
     
  5. Jul 8, 2014 #4

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    Perhaps look at it from an energy perspective. Both start with PE but one is rolling and the other not. Apply conservation of energy. They can't both have the same linear KE at the bottom. The one that's just falling/sliding will have converted all of the initial PE to linear KE. The one that's rolling will have converted some to rotational KE leaving less for linear KE.
     
  6. Jul 8, 2014 #5

    so in other words the one that rotates more will go down the ramp slower?

    it would be mgh = 0.5mv^2 + 0.5Iw^2 right?
     
  7. Jul 8, 2014 #6

    A.T.

    User Avatar
    Science Advisor
    Gold Member

    For sliding. Rotational inertia makes it even slower.
     
  8. Jul 8, 2014 #7

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    Correct.

    Whereas for a block or ball sliding down a frictionless inclined surface it's just mgh = 0.5mv^2.

    So the final velocity must be different.

    Aside: In both cases we're ignoring energy losses to friction but there must be some friction in the case of the ball that's rolling or it wouldn't start rotating.
     
  9. Jul 8, 2014 #8
    In the case of the rolling (without sliding) ball, friction doesnt do work and there arent energy loses. The pseudo-work of friction (equal to Friction X length of ramp) equals the final rotational kinetic energy of the ball.
     
  10. Jul 8, 2014 #9

    jbriggs444

    User Avatar
    Science Advisor

    That component of friction is accounted for. Hence the 0.5 I ω2 term. Rolling resistance, if any, is not accounted for.
     
  11. Jul 8, 2014 #10

    CWatters

    User Avatar
    Science Advisor
    Homework Helper

    Yes sorry. It was the rolling resistance I meant was being ignored.
     
  12. Jul 8, 2014 #11

    olivermsun

    User Avatar
    Science Advisor

    I think the OP is asking whether an additional component of motion in the plane of the ramp (at right angles to both "downslope" and "normal") would change the time it takes for the ball to reach the bottom.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Ball rolling down a ramp
  1. Rolling down a ramp (Replies: 2)

Loading...