- #1

Arman777

Gold Member

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- Homework Statement:
- Particle on a hoop - Finding the height that particle falls

- Relevant Equations:
- Lagrangian

There is a particle with mass $m$ sliding from the hoop with radius R. Its asked to find the height of the hoop which the particles falls. Now I did the hard part (I guess) and find the Lagrangian of the system. Which is given as

$$-mR\dot{\theta}^2 + mg\sin\theta = \lambda$$

and

$$\ddot{\theta} = -\frac{g}{R}\cos\theta$$

but I cannot find the height which it falls. I have thought that when it falls from the hoop the constrain force will be ##0## (i.e, ##\lambda = 0##). But nothing seems to be working. Any ideas ?

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