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

[sudipmaity]

Homework Statement

Find out the degrees of freedom of a block of wood sliding on a horizontal plane.

Homework Equations

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

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??
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[BvU]

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

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)

 

[sudipmaity]

Please BvU clarify one thing, should i consider the block of wood a rigid 3d body or a point particle??

 

[BvU]

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 ?

 

[paranormal]

Your deductions are correct. The degree of freedom for a block of wood sliding on a horizontal plane is 3. This means that it can move in three independent directions on the plane. The three constraints, as you mentioned, are the fixed distance between the three points on the block, which restricts its movement to the plane. This is a common example in mechanics to demonstrate the concept of degrees of freedom.