IIT JEE , AIEEE Forum - Physics , Mechanics

avneesh

can anyone tell me what the hell are pulley constraints and how do you use them

thanks

biki

pulley constraints means using the given arrangement to our benefit.
In problems, there are some restrictions in the arrangement given..e,g, - say when the system moves , a part pf the system remains always a right angled triangle. So u can use the pythagoras theorem and diffrentiate it w.r.t time twice to get relation between the accl^ns of different constituents of the arrangement..

gimme a sum ... and i will explain... u'll understand better

elastiboysai

Hi
Here are some examples:

Q. Find the Constraint relation between a₁, a₂, and a₃.

Fig (8)

Solution:

Points 1, 2, 3, 4 are movable let their displacements from a fixed line be x₁, x₂, x₃, and x₄.

We have x₁+x₄ = l₁ (length of first string) ---------------- (1)

And (x₂ ? x₄) + (x₃ ? x₄) = l₂ (length of second string)

Or x₂ + x₃ ? 2x₄ = l₂ ----------------- (2)

Or double differentiating with respect to time we get

a₁ + a₄ = 0 ------------------- (3)

a₂ + a₃ ? 2a₄ = 0 ------------------ (4)

But since a₄ = -a₁ from equation (3)

We have a₂ + a₃ + 2a₁ = 0

This is the required constant relation between a₁, a₂, and a₃.

( http://www.goiit.com/chapters/tutorial/physics/newtons-law-com-2.htm )

elastiboysai

Q. Using Constraint equations find the relation between a₁ and a₂?

Fig (32)

Solution:

Points 1, 2, 3, 4 are movable. Let their displacements from a fixed line be x₁, x₂, x₃ and x₄.

On double differentiating w.r.t time we get,

Solving (1), (2) and (3) we get,

Desired relation between a₁ and a₂.

biki

consider the figure

the upper and lower parts are almost equal...

So 2l + x + d = constant

=> 2dl/dt + dx/dt + dd/dt = 0

=> 2d²l/dt² + d²x/dt² + 0 = 0

So 2x(mag. accln of M) = mag. of accl^n of m

avneesh

thanks a lot guys

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