With what speed does the tip of a 25 meter high tree hit the ground?

  • Thread starter spsch
  • Start date
  • #1
111
21
Homework Statement:
With what speed does the tip of a 25-meter high tree hit the ground?
Assume the tree has a moment of inertia of a long thin rod.
Relevant Equations:
## mg* \frac {l}{2} = \frac {1}{6} *m*l^2 * (\frac {v^2} {l^2}) ##
Hi, I am still working on the same exams problems, the second last one is giving me a bit of a headache after I found this https://physics.stackexchange.com/q...r-an-upright-rigid-body-to-fall-to-the-ground which contradicts my solution.
Can I assume that when the tree hit's the ground all of it's potential energy is converted to rotational energy?
I was thinking this is why they mention the moment of inertia being that of a long thin rod.

So I went with:
## mg* \frac {l}{2} = \frac {1}{6} *m*l^2 * (\frac {v^2} {l^2}) ##

and got: v= ## \sqrt {3*g*l} ##
 

Answers and Replies

  • #2
PeroK
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
18,681
10,318
Problem Statement: With what speed does the tip of a 25-meter high tree hit the ground?
Assume the tree has a moment of inertia of a long thin rod.
Relevant Equations: ## mg* \frac {l}{2} = \frac {1}{6} *m*l^2 * (\frac {v^2} {l^2}) ##

Hi, I am still working on the same exams problems, the second last one is giving me a bit of a headache after I found this https://physics.stackexchange.com/q...r-an-upright-rigid-body-to-fall-to-the-ground which contradicts my solution.
Can I assume that when the tree hit's the ground all of it's potential energy is converted to rotational energy?
I was thinking this is why they mention the moment of inertia being that of a long thin rod.

So I went with:
## mg* \frac {l}{2} = \frac {1}{6} *m*l^2 * (\frac {v^2} {l^2}) ##

and got: v= ## \sqrt {3*g*l} ##

That looks correct. I'm not sure where the contradition is.
 
  • #3
111
21
That looks correct. I'm not sure where the contradition is.
Hi, Thanks. I used the formula from that link and got a different speed. Around 19, whereas my solution gets about 27 meters per second.
I probably made a mistake in plugging in the numbers.

Thank you so much for checking!
 

Related Threads on With what speed does the tip of a 25 meter high tree hit the ground?

Replies
2
Views
4K
Replies
11
Views
5K
Replies
2
Views
1K
Replies
6
Views
4K
Replies
8
Views
5K
Replies
4
Views
2K
Replies
1
Views
1K
Replies
1
Views
5K
Top