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Constraint Relations

The motion of a body is influenced by the forces acting on it as well as by the geometrical constraints imposed on it. For example, a block of mass mass is acted upon by a force force as shown in fig. The horizontal component of force horizontal component of force tends to move the block in the horizontal direction; and the vertical component of the force vertical component of the forcetends to move the block in the vertical direction. As the block cannot penetrate the floor, therefore, the block cannot move vertically downward and hence, it moves horizontally only.

Hence motion of the block is governed by the geometrical constraints.
Another type of geometrical constraint is the inextensible string. For example, two blocks blocks m1 and m2 connected together by an inextensible string and blocks m1 and m2 connected together by an inextensible string are connected together by an inextensible string, as shown in fig. When the block m1 is pulled by a horizontal force is pulled by a horizontal force, it cannot accelerate alone because it is attached to block m2 string with a string. Since the string is inextensible, therefore, the rightwards displacements of blocks displacements of blocks m1 and displacements of blocks m2 are equal. Hence, both the blocks accelerates equally in the same direction.

blocks m1 and m2 accelerates  equally in the same direction

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