# Physics Assignment Help With Constraint Relations

## How to determine Constraint Relation

**1. ** Assume the direction of acceleration of each block, e.g. *a*1 (*downward*) and *a*2 (*upward*) in this case.

**2. ** Locate the position of each block from a fixed point (depending on convenience), e.g. *centre of the pulley *in this case.

**3. ** *Identify the constraint *and write down the equation of constraint in terms of the distance assumed.

For example, in the chosen problem, *the length of string remains constant *is the constraint or restriction.

Thus,*x*1 + *x*2 = constant

Differentiating both the sides w.r.t. time, we get

Each term on the left side represents velocity of the block.

Since we have to find a relation between accelerations, therefore, we differentiate it once again w.r.t. time.

Thus

Since the block *m1 *is assumed to be moving downward (*x1 *is increasing with time)

, *a*1 > 0

and block *m*2 is assumed to be moving upward (*x*2 is decreasing with time)

, *a*2 > 0

Thus *a*1 - *a*2 = 0

or *a*1 = *a*2 = *a*

*Alternatively, *one can also assume the distance of each block from the ground as shown in the figure.

One can easily see that an expression for length of the string can not be written unless we locate the centre of the pulley w.r.t. ground.

If *y*0 be the distance of the ground from the centre of the pulley then the length of string is

(*y*0 -*y*1) + (*y*0 - *y*2) = constant

2*y*0 - *y*1 - *y*2 = constant

Differentiating twice w.r.t. time, we get

0 -

Now, and

Thus *a*1 - *a*2 = 0

*a*1 = *a*2 = *a*

Substituting *a*1 = *a*2 = *a *in equations (i) and (ii) and after solving them, we get

*a* =

also *T* =

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