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!

Homework Help: Complicated Motion Problem

  1. Nov 3, 2011 #1
    A garden roller with external radius a is pulled along a rough horizontal path by force F which acts at a point on its axle and is inclined at an angle alpha with the horizontal.

    Given that resultant force is at a right angle to F, what is the acceleration of the roller? Express in terms of radius a, alpha, and radius of gyration k.

    My set-up (and failure):

    Let H be resultant force, f_s is frictional force

    Forces in x-dir:
    [tex]Hsin( \alpha) = Fcos( \alpha) - f_s[/tex]
    Forces in y-dir:
    [tex]-Hcos( \alpha) = Fsin( \alpha) - mg[/tex]
    Rotational equation of motion:
    [tex]af_s = \frac{mk^2}{a} \ddot{x}[/tex]
    Assume no slipping:
    [tex]\ddot{x} = a \ddot{ \theta}[/tex]
    Solve for x-acceleration:
    [tex]\ddot{x} = \frac{a^2 F - a^2 mgsin( \alpha)}{mk^2 cos( \alpha)}[/tex]
    Correct answer:
    [tex]\ddot{x} = \frac{ga^2 sin( \alpha) cos( \alpha)}{k^2 + a^2 sin^2 (\alpha)}[/tex]

    Where am I going wrong? I don't see why F isn't in the answer...
  2. jcsd
  3. Nov 4, 2011 #2


    User Avatar
    Homework Helper

    I haven't tried to work out the answer myself yet, but you're right that the 'correct answer' looks ridiculous.
    It would predict the same acceleration even when F approaches zero, which is ridiculous.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook