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Dynamics friction problem

  1. Oct 25, 2012 #1
    1. The problem statement, all variables and given/known data

    The static friction coefficient between the grippers and the ball is 0.5, and the grippers
    hold the ball such that they touch the middle of the ball on opposite sides.

    Find the clamping force required to keep the ball from slipping out, if the ball weighs 10 lb.

    us= 0.5
    Mass of ball = 10 lb
    gravity = 9.81 m/s^2

    Angular velocity (wd) = 5 rad/s = Angular velocity of robot arm as they are attached.

    2. Relevant equations
    rc=4cos45 + 2sin45 = 4.243 ft
    Motion of point C
    Vc = (wr)(rc)
    ar=[itex]\alpha[/itex]rc
    an= wr^2 (rc)
    ac= sqrt(ar^2 + an^2)

    3. The attempt at a solution

    Using the above equations and the givens I found the rc which I used along with wr to solve for Vc.

    Vc = ( 5.0 rad/s) ( 4.243 ft) = 21.2 ft/s

    Then solved for both components of acceleration where :

    at= [itex]\alpha[/itex] rc = 0
    an= wr^2 x rc = 25 x 4.243ft = 106.07 ft/s^2

    Then solved for magnitude which just equalled the normal acceleration

    ac= 106.07 rad/s^2

    Currently stuck on what to do for the second part of the question. I understand that I need to do a force FBD as I am given us and the mass of the ball. Noting that the pincers touch the middle of the ball on both sides, wouldn't that mean the contact forces oppose each other ( equal and opposite direction ) ?
     

    Attached Files:

  2. jcsd
  3. Oct 26, 2012 #2
    Yes.

    The sum of the forces acting on that ball must produce that acceleration, otherwise the ball isn't going to follow the circular path as you've assumed. The grip will be equal, opposite and perpendicular to that acceleration so that alone cannot produce that acceleration. But then there's the friction...
     
    Last edited: Oct 26, 2012
  4. Oct 29, 2012 #3
    I realized that movement was only constrained in the j direction, therefore there was a k and i direction force of friction. I then gathered components in those directions and solved the system giving me the answer ! Thanks for the guidance !
     
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