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Degree of freedom of a block of wood sliding on a horizontal plane

  1. Oct 20, 2014 #1
    1. The problem statement, all variables and given/known data
    Find out the degrees of freedom of a block of wood sliding on a horizontal plane.

    2. Relevant equations
    DoF=Nn-k
    N=no. of dimensions. n=no. of particles.k= no. of constraints.

    3. The attempt at a solution
    I am considering the block of wood as a rigid body made of n no. of particles.
    But it will move with respect to a center of mass.
    I will need 3 points on the body to define the CM.
    As the body is constrained to move on a plane each of these 3 points can be denoted with 2 coordinate points.
    Each of these 3 points has fixed distance from each other so there will be 3 constraints if these points are non collinear.
    So i think the answer should be 3×2-3=3.
    Are my deductions correct??
     
  2. jcsd
  3. Oct 21, 2014 #2

    BvU

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    So you have 2 dimensions. One particle with no constraints would have two degrees of freedom ? Not 4 (x, y, vx, vy) ?

    I also don't quite follow how you need 3 points to define the CM. Wouldn't e.g. two corners be enough ? Could you explain ? (It may be correct, I just wonder)
     
  4. Oct 21, 2014 #3
    Please BvU clarify one thing, should i consider the block of wood a rigid 3d body or a point particle??
     
  5. Oct 21, 2014 #4

    BvU

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    It's a block of wood. To me that sounds closer to a rigid body than to a point particle.
    You said you need three points to pinpoint the block. Why three ?

    What is the basis for your relevant equation ? Does a particle on a plane with no further constraints have 2 degrees of freedom in your book ?
     
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