1. Not finding help here? Sign up for a free 30min 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!

A cylinder and sphere rolling without slipping

  1. Apr 6, 2006 #1
    A hollow, thin-walled cylinder and a solid sphere start from rest and roll without slipping down an inclined plane of length 5 m. The cylinder arrives at the bottom of the plane 2.9 s after the sphere. Determine the angle between the inclined plane and the horizontal.

    Ok, I think I'm close, but I'm getting really nasty equations at the end so I'm not very confident.

    The acceleration of the sphere is 5*g*sin(x)/7
    The acceleration of the cylinder is g*sin(x)/2

    I'm pretty confident these are correct.

    With the accelerations I should be able to use regular kinematics.

    [tex]\Delta x=\frac{1}{2}at^2[/tex]
    Where [tex]\Delta x=5[/tex] and a=the acceleration of either the sphere or cylinder.

    For the cylinder I get [tex]5=\frac{1}{2}(\frac{gsin\Theta}{2})(t+2.9)^2[/tex]
    For the sphere I get [tex]5=\frac{1}{2}(\frac{5gsin\Theta}{7})t^2[/tex]

    But when I solve for [tex]sin\Theta[/tex] or t, and plug it into the opposite equation, I get nasty looking things like:
    [​IMG]

    Am I doing this right?
     
    Last edited: Apr 6, 2006
  2. jcsd
  3. Apr 6, 2006 #2

    NateTG

    User Avatar
    Science Advisor
    Homework Helper

    Since they roll (rather than sliding) you need to account for the energy that goes into making them spin.
     
  4. Apr 6, 2006 #3

    Doc Al

    User Avatar

    Staff: Mentor

    The equations already take that into consideration.

    To scavok:

    First solve for t by setting [itex]a_1 t^2 = a_2 (t + 2.9)^2[/itex] (the [itex]g \sin\theta[/itex] will drop out).

    Then use t to solve for [itex]\sin\theta[/itex].
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: A cylinder and sphere rolling without slipping
Loading...