# How much does a falling object weights ?

1. Apr 8, 2009

### quantoshake11

how much does a falling object "weights"?

Hi ev. the other day i was asked by a friend that does "aerial silk" (http://en.wikipedia.org/wiki/Aerial_silk, just found out it was called that :P) how much (still) weight should the beam (to which the silk is tied) hold in order to hold her weight after falling say, h meters.. i started thinking about it, thinking it would be easy, but i'm not sure how to approach it. I mean, i can get the energy that needs to be lost (mgh), but i'm not sure how to "spread it around" in a way that won't make me say 'sure, go ahead' and then end up bringing flowers to the hospital
Is there another way to approach this problem? what do i need to figure out to "spread around" correctly the energy lost? I guess this is more of an engineering question, please move the thread at will..
pd: this is my first post so i should mention. i'm not a native english speaker, i hope that you will learn to forgive the way i get around to say things which can get strange sometimes.. no grammar nazis around?

2. Apr 8, 2009

### Lok

Re: how much does a falling object "weights"?

This is a tough question from an engineering point of view. As it has very little to do with the rope's yield strength ( the amount of force needed to break it) and more to do with toughness ( non English speaker myself so could be wrong on terminology) that is the amount of energy it receives per second ( power) that it can withstand. Some materials have better shock resistence than others.

E.g. Diamond. Very hard material that can hold an huge amount of pressure or tension before breaking, but if you drop it on a hard floor it would break. Machining using diamonds can reach speeds of 900 m/s but it needs a very slow acceleration opposed to other more tougher materials that can enter machining at full speed. Glass too, a small cylinder the size of your fist could hold a car ( 1500kg 3000 pounds pressure) but be broken by a small rock at small speed. Dymneea a very long polymer material will yield (start deforming) at very small loads, but is tougher than kevlar used in bulletproof vests (will replace it soon).

Basically a tough material can be Kevlar, Dymneea, carbon fiber, etc. most materials that are used to make bullet proof vests. So these are best for making safety ropes ( material cost not taken into account).

So the problem is finding the toughness of the rope. No idea where you could look. There is a value for breaking speed for materials but that does not take into account the energy involved.

3. Apr 8, 2009

### ImAnEngineer

Re: how much does a falling object "weights"?

quote: "i can get the energy that needs to be lost (mgh), but i'm not sure how to "spread it around"

Could you explain it a little more specific? I don't really understand the problem.

4. Apr 8, 2009

### quantoshake11

Re: how much does a falling object "weights"?

well, i meant that the kinetic energy gained from the fall would be lost after the stop. well, not lost, but "spread around" the system. Some might go to elongating the silk, some to deform the beam, and some to heating up the enviroment, and some to a place i don't know. My first guess is to forget about the heating up, so i would have to see how much is going to stretch the silk and how much for the beam. What i'm not sure is:
1) is there another kind of energy transfer besides the stretch of the silk and deformation of the beam?
2) how can i make an estimate on how much energy will go to each part of the system?
I thought that if i got the answer to question 2) i could solve the problem.
but.
having read that i realize that i could not test it in the way i planned. and confirmed my suspicions that this is not an easy problem... i'm gonna see if i can find anything about thoughness on wikipedia. thanks for the moment. not that the problem is solved or anything, but it helped :P

oh. the problem is this. you have a silk acrobat falling from a certain height, tied up to the silk that is in turn tied up to a bolt. is the bolt or the silk going to break?. suppose you know anything you can get without breaking the elements (of course you could device some way to test whether or not it will hold, in wich case if it breaks it doesn't matter since it would've break in the real test and the beam was useless anyways. And of course you could just get a rock and throw it to see if anything breaks, but the point is to do it in some neater way...)

5. Apr 8, 2009

### quantoshake11

Re: how much does a falling object "weights"?

oh. i found it on wikipedia. it is called toughness. and yeah... well.. i'm just not going to think much about the problem now. it's really an engineering thing, and the tests are all destructive ones :S... if you do have some tables of thoughnesses of common alloys used for beams, a link is highly appreciated. I guess that if she keeps nagging me i'm just going to suggest the "throw the rock and see if it breaks" option.
thanks again Lok :)
http://en.wikipedia.org/wiki/Toughness
http://en.wikipedia.org/wiki/Izod_impact_strength_test
http://en.wikipedia.org/wiki/Charpy_impact_test#Definition

6. Apr 9, 2009

### Lok

Re: how much does a falling object "weights"?

The peak force can be computed by measuring the amount of elastic deformation during the fall. All materials have elasticity, and it's value is important for computing the breaking velocity.
For example a high elasticity means a mild shock wave, while low elasticity means a very powerfull shock. If the shock wave travells faster than the velocity with which the molecules of the thread can reorient or respond to the external force it will deform or break.

Sorry but i don't know of any table for toughness. It would be interesting to have one.

7. Apr 9, 2009

### Lok

Re: how much does a falling object "weights"?

Btw silk was a bulletproofing material before modern plastics appeared so it is very tough. 5-8 layers of silk would be enough to catch a bullet. Don't know if it is used today for the aerial silk.

And yes the throw the rock is a very good option. See how thick a rope has to be ( unthread a rope and use only a few threads ) to absorb all the energy of a 50 kg rock and break. The rock should have very little energy (speed for measure) after the rope breaks. And then do the engineering choice when you just cant or it's to complicated. Use a safety factor. When human life at stake it's 12 ( so use 12*the amount of threads found to be sufficient), if it's industry it's 4, aeronautics 1-1.5 (just for weight purposes) if you hate life in general use 0.7