SOLVING CONSTRAINT MOTION BY AN EASY WAY : APPLICATION OF WORK ENERGY THEOREM

bladeX -rise of a new sun

SOLVING CONSTRAINT MOTION USING WORK ENERGY THEOREM

- DIPENDRA MISRA

See the diagram given below :

The diagram shows some pulley and rope :

let us divide the case into 2 parts :

PULLEY ARE MASSLESS :

Fig : shows a simple constraint motion

Now the system is massless so

using work-energy theorem (which is a special case of 1^st law of thermodynamics).

KE = ∑work of all forces…….1)

Now KE of a massless system is 0 so

∑work of all forces = 0…………2)

Now in the above system :

the tension in the ropes joint to ceiling will do no work as there is no displacement.

So assuming that all masses accelerate in downward direction.

And calling the displacement of the masses as x1 , x2 and x3.

Now we use the equation no.2 .

Tdx1 + 2Tdx2 + Tdx3 = 0……….3)

dx1 + 2dx2 +dx3=0……….4)

dividing by dt and again differentiating we get :

A1 + 2A2 + A3 = 0………..5)

This is the constraint relation and my respected physics’ teacher Mr. Sanjay Bhisht introduced this method to me for which I am grateful to him. We solved most of the qs using the above method.

CASE 2 : WHEN PULLEY HAVE MASS

Now we know that the constraint relation is same irrespective of the pulley being massless or not so for using above method we can assume that pulley to be massless and use case 1.

SUMMARY

1 : make a system comprising of pulleys and rope. But don’t put bodies having mass except if they are pulley in the system.

2 : then use the work energy theorem

3 : divide by dt and again differentiate and you will get the equation.

: Blade – X

dated : // 5^th july,2009

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