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neelakash
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Homework Statement
A smooth ring of mass m can slide on a fixed horizontal rod.A string tied to the ring passes over a fixed pulley and carries a mass M(<m).At an instant the angle between the rod and the string is θ.Show that if the ring slides with a speed v,the block descends with a speed v cosθ.With what acceleration will the ring start to move if the system is released from rest at θ=30*?
I have attached the figure in a pdf file so that you may see it
Homework Equations
The Attempt at a Solution
I take z axis downwards,x axis rightwards.
The force equations:T cosθ=m D²x
Mg-T=M D²z
Now,we are to find the constraint equation.
I got this:(using the length conservation)
√[x²+c²]+z=L...c is a const
Differentiating twice w.r.t. t we get: Dz=-Dx (cosθ)
What is annoying me is the (-)ve sign before the ansswer.
Somehow this is not correct.Because,in the next part we require this result:
D²z=-D²x cosθ+0(initially Dx=0)
This gives an error in the final answer.
Can anyone please help?