(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that there is a negligibly thin tree in the forest of infinite length that begun tipping over. Negating frictional effects from the pivoting, does the tree ever hit the ground?

2. Relevant equations

My approach was to solve the problem for a tree of length [itex]l[/itex] and see what happens in the limit as [itex]l \rightarrow \infty[/itex]

[itex]

\tau = I\alpha

[/itex]

[itex]

\tau = Mg\cos{\theta}(l/2)\

[/itex]

[itex]

I = \frac{1}{3} Ml^2\

[/itex]

3. The attempt at a solution

[itex]

I\alpha = Mg\cos{\theta} (l/2)

[/itex]

[itex]

\alpha = \frac{3gl}{2} \cos{\theta}

[/itex]

Now, I know how to approach and get a function for [itex]\omega[/itex] by using energy conservation; however, out of curiosity, would I be able to solve this DE purely mathematically?

In any case, [itex]\omega = \sqrt{\frac{3g(1-\sin{\theta})}{l}} [/itex]

I interpret this to mean that if I take the limit as the length goes to infinity, the tree simply has no angular speed and thus cannot fall over at all. However, this seems unsatisfactory as an answer - is it possible to actually derive an explicit function for [itex]\theta(t)[/itex]?

Thank you all for any help, and I apologize if I have made any sort of oversight or foolish mistake.

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# Homework Help: Infinitely tall tree falling in a forest

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