1dekha!
first wala sahi karne ke baad bhi nai ban raha
What is constraint equation..??
First a few examples of constraint equation
a) If there is a stone tied to a rope that you are whirling around your head.. there is a constraint equation.
b) If there is a body kept on the floor..
c) the points on a solid body
d) If a pulley system is there, then every single thread on it will give a constraint equation.
The equation is nothing but the mathematical manifestation of the constraint involved..
Lets see it by examples by example...
What are your first guesses for the above?
-
UP 0 DOWN 0 1 31
31 Answers
62Yes John
So here our system is both the pulley and the room or the wall..
And only MG is the external force.. so we have not considered it :)
1thanx a lot !
1 final thing we just have to consider internal forces naa!!!
62It should be done for every single moving poitnt
see here in the string the net force is zero.. up and down
so F=0 at all points
On the two pulleys the net force is agian zero (2T-T-T)
So we have effectively taken all points.. I should have mentioned thta..
11http://targetiit.com/iit_jee_forum/posts/pulley_system_3889.html
LOOK AT THIS QUESTION AND SEE HOW ASISH HAS APPLIED THE CONSTRAINT EQUATION
1But the that should nto be done for every single product...
wat shud not be done?
and for what?(single product)din get wat u mean!
plz clarify
622nd one it wont be easy to use..
But the that should nto be done for every single product...
1do we consider only points at the ends of the thread.
thanx!
plz also show how to use it in second one!
62Here see the work done by internal forces
They will be f.ds
Now a lot of points are static.. there will be no work at those points..
Like the points touching the wall.. ds=0 so work is zero
At the points where F and ds are both non zero are the two blocks
T.s1+2T.s2=0
hence
s1+2s2=0
Hence after differentiating we get
a1+2a2=0
1yeh to figure dekhte hi samajh gaya tha becoz sum of distances will be constant=2a,surely ellipse
but how to use it to solve the ques.
62constraint is exactly what it means in english
Like if you tie a cow with a rope then it cant move outside the circle
Just like that things are tied to each other so that the motion of one is affected by the motion of other..
That is a constraint..
Like if you tie two men with a rope.. (like in krishna serial :P)
Then the constraint is that their distance cant be greater than the length of the rope
11Sir,
Pls tell me wat exactly is constraint?
Pls sir
I know i am a bit dumb
62hmm.. see nahi banna is ok.. this is a single question of its type..
What is the constraint here?
Hint: answer is ellipse! Think it over the night :)
1a.distance of stone remains constant from our hand.
b.net force is zero
c.are nearly fixed
d.length remains constant
62ok john...
Here try to find the constraint equation...
The two dark rods are fixed... The pulley can rotate.
Assume anylength that is not given and angle..
1sob!bhaiya this was easy but in tough ones i really mess up-dunno why?????????
plz post any very complex one!then u will come to know where i am stuck
62yup .. my wrong.. I had c in mind.. :)
And I drew the wrong lines.. let me fix them :P
So you knwo constraint relations already :)
1i think it shud be b+b-a+d=constant.
2b+d-a=constant
2b+d=constant
2v(right)-v(left)=0
2a(right)=a(left)
isn't it
62in the above post, see that the toal length of the rope going over the pulleys is given by b+(b-a)+(d-a)
and c-b = constant
hence the total length of the rope is given by 2b-a+d-a = 2b+d-2a
now see this length does not change .. so the constaint equation becomes
2b+d-2a = constatn
but a is itself a constant. so 2c+d = constant...
To complete it for you..
d and c are lengths .. so what you have to do is to find it in terms of acceleration..
See that dd/dt will give the velocity in the downward direction.
while dc/dt will give the velocity of the 2nd mass in the downward direction
same with second derivatives.. they will give the accelerations...
Hence the constraint equation will be found by differentiating the relation 2c+d = constant... two times
which gives
2\frac{c^2b}{dt^2}+\frac{d^2(d)}{dt^2}=0
1i just guessed(as it was taking a lot of time u din reply)u lready know i don't know how to write constraint equation for questions
62how??
John this is where constraint comes into picture..
I am trying to explain..
