# Effective Weight of Falling Object

1. Feb 29, 2004

### damon

I'm am trying to determine the effective weight of a branch that falls from a tree to the ground. When I say the "effective weight" I mean the effect of the increased speed of the branch as it falls.

The branch would fall from say 30 metres (say 90 feet) and would initially weigh 1 kilgrams (say 2.2 pounds).

I'd appreciate either the answer or a formula to work it out. BTW, I'm not a student we are just fighting our local Council (in Sydney) to remove a tree!! They think the branches are small but when they hit they hurt!!

Thanks in advance for any assistance.

Damon

2. Feb 29, 2004

The mass of an object never changes.

You might look into the kinetic energy of the branch. The faster it moves, the more energy it has, and the farther it falls, the faster it moves. It's easy to show that the energy of an object falling from height h and mass m has energy

$$E = (9.8\frac{\textrm{m}}{\textrm{s}^2})mh$$

Edit: Just took out some superfluous information that might be a source of confusion.

Last edited: Feb 29, 2004
3. Feb 29, 2004

### eagleone

$$(9.8\frac{\textrm{m}}{\textrm{s}^2})mh = 1/2 mv^2$$
Calculate v - velocity.

Hack, when I started, I’m going to finish it :) :
$$v ={\sqrt{2gh}}$$
$$v= 4.43{\sqrt{h}}$$
When you have h (height of that branch/three) you can calculate its velocity (you can see how it doesn’t depends on mass). But this is theoretical value calculated without air resistance (+ if the branch if alive with leafs, this “friction” factor is greater).

How much it weights? Weight is measure for force so you can calculate it (again theoretically) from:
$$F = m*a$$ you don’t know a, but let’s say that collision lasts t=0.3s, and branch decelerates form v to v=0, than you can say: $$a = v / t^2$$. (you can use “ordinary” weight of branch as m).

Hope I helped,
Greetz

P.S. I have to mention that this is somehow interesting/funny to me, your fighting to cut tree, that as you say, endangers you, and we have an unexploded Tomahawk in our backyard, that we are too trying to get rid off . What a world (NHF – just comparing).