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Kinematics of Rigid Bodies

  1. May 28, 2008 #1
    Edit: Tried to post three times and forum kept adding the prompts. Removed Prompts.

    1. The problem statement, all variables and given/known data
    Three blocks are initially at rest on a level frictionless surface. At t=0s, a three identical forces are applied to a different point on each block.
    Each block is a rectangle approximately 3x1 oriented with the long sides facing north/south. The center of mass on each block is at (1.5,.5) if the lower left corner of the block is (0,0)

    The force on block 1 is applied at about (1,.5)
    The force on block 2 is applied at the center of mass
    The force on block 3 is applied at about (3,.5)


    a) Draw an arrow on the diagram indicating the direction of acceleration of each blocks center of mass. If the acceleration is zero, state so explicitly.
    b) Rank the center of mass accelerations from largest to smallest and explain. Draw a point FBD for each block

    2. Relevant equations
    Conceptual problem.

    3. The attempt at a solution
    I think that all the accelerations will be equal. Accelerations are equal at the center of mass regardless of where the force is applied. However I'm confused because it seems like some of the force should go to rotating the object, and if that is true, the accelerations of each of these objects centers of mass will be different.
    So either B1=B2=B3 or B2>B1>B3. The FBDs would be different depending on each. If B1=B2=B3, they would be quite simple, just one vector pointing North, but if B2>B1>B3, there would be (I think) the same but with different magnitudes.

    It's a pretty simple problem I think, but I may have overthought it and become confused. Help!
  2. jcsd
  3. May 28, 2008 #2
    I'm going with B3>B1>B2. I'm basing this on the idea that the force has the biggest advantage with B3 because the surface is shouldering half the weight. Regardless of direction, the magnitude would be greater. Maybe?? heh
    Last edited: May 28, 2008
  4. May 29, 2008 #3


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    Welcome to PF!

    Hi KBL-8! Welcome to PF! :smile:

    You're confused because you're thinking that the rotation of a body might decrease (or increase) its acceleration.

    Hint: what is the total acceleration of a body relative to its centre of mass? :smile:
  5. May 29, 2008 #4
    Theres an explanation here:

  6. May 30, 2008 #5


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    Hi KBL-8! :smile:

    Are you sure the book isn't asking for the angular accelerations?

    That would make a lot more sense! :smile:
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