Physics question

[audiobliss]

A friend asked me this question, and now it's got me to thinking.

If you're given two ropes of the exact same material, thickness, and quality, but one is longer, which one is stronger?

The way I'm looking at it, the longer one would be stronger. Imagine this: If you're suspending weights in the air with these ropes, when you add some weight, the rope will stretch. It seems to me that the longer rope will be able to stretch more. Say you have a 10' rope that will stretch a foot and a 40' rope that will stretch three feet. You can add how much ever weight to the 10' rope that will make it stretch one foot before you reach the point where the rope has reached its limit. With the 40' rope, you can add how much ever weight it takes to make it stretch three feet before it gets to that point. It just makes sense to me that the longer rope will be able to hold more weight.

Now, that's not to say it's stronger. When you ask me if something is stronger, I would want to factor out such things as length, and it just doesn't make sense to me that two exact same ropes, but of different lengths, won't be of the same strength. But I still think one will be able to bear more weight.

Another question is that, if indeed one is stronger than the other, how great does the difference in lengths have to be before it's a significant difference?

Any thoughts?

[MacLeod]

I would say the length doesnt matter (seems like Im telling chicks that all the time) they would still both be of the same strength.

If youre on a train moving at the speed of light and you walk from the front to the back, are you moving faster than the speed of light?

[audiobliss]

I heard it posed "If you're on a train at the speed of light and you throw a possum out the window...what happens?" My answer was that everything goes black and the words "Game Over...You Win" appear in the sky.

:p

[whitetruk]

i dunno what weighs more a pound of water or a pound of beer.
i don`t think the length matters rope can only handle so much weight. but i dunno

[ND13]

I believe that the shorter rope would be the stronger of the two.

[audiobliss]

Ok...I want reasons with these answers, too, lol. WHY do you think that, Noel?

[McLoki]

I believe that the shorter rope would be the stronger of the two.
I agree - I think the shorter rope would be stronger because if the rope breaks it will be due to some deficiency or imperfection somewhere in the rope. (that weakest link thing)

You already said the ropes were the same so the shorter rope has no point in it that is weaker than the long rope. The long rope has the additional length that could have a weaker point.

More a logic answer than physics, but there you go...

Michael

[ND13]

Ok...I want reasons with these answers, too, lol. WHY do you think that, Noel?


I ain't gots the time for these games!!!!! :D

I haven't taken physics in 20 years, I just know. Kind of like I know that, in a vacuum, everything falls at 9.8m/second. It's there in the memory banks, just having hard drive issues in bringing up all the relevant info. I can't remember the exact reason, just that the shorter length of the same exact type of rope will be stronger. I'm sure that there's at least one physicist in our ranks.

[audiobliss]

You already said the ropes were the same so the shorter rope has no point in it that is weaker than the long rope.

But by the same token the longer rope has no point that is weaker than the weakest point in the shorter rope.

For the sake of argumentation, let's assume that the two ropes are perfect in their construction and use of material. Thus, there are no weak spots. This means that they truly are identical except for their lengths.

ND - Get to working on that HD!! :p

[nadams]

Noel- sounds like you might have some bad sectors. Who knows, a defrag might help just as well :)

[TheReaper]

I would say the length doesnt matter (seems like Im telling chicks that all the time) they would still both be of the same strength.
I agree with MacLeod (ouch!). When you suspend a 10lb weight at the end of a rope. Each point along the rope experiences 10lbs of force. If the weakeast point on each rope (ropes being equal quality), breaks at 10lbs of force. Both ropes will break at the same time.

Edit:

I take that back, the longer rope will break first. Because you will have the additional weight of the extra length of rope. (now I don't agree with MacLeod :) )

[Vr3MxStyler2k3]

NVMmmmm

[exalted512]

length most certainly does matter. If i had my physics notes from last year I could give you the equation, but its at my g/f's house. But I do believe it takes more force to break a shorter rope than a longer rope.
-Cody

[audiobliss]

I agree with MacLeod (ouch!). When you suspend a 10lb weight at the end of a rope. Each point along the rope experiences 10lbs of force.

I challenge that. I would think that the rope distributes the weight equally along its length. And thus, the longer the rope, the less stress being exerted along a given length of that rope.

[McLoki]

I challenge that. I would think that the rope distributes the weight equally along its length. And thus, the longer the rope, the less stress being exerted along a given length of that rope.
That would mean given a long enough rope, it would never break. I am sticking with my shorter rope idea and not giving you a reason for it. (cuz there really isn't one - I just think the longer rope would break first.)

Michael

[Vr3MxStyler2k3]

shorter one....

because I rule. :D

[audiobliss]

That would mean given a long enough rope, it would never break.

Just because you can carry it to such a conlcusion doesn't mean it's not true. (Assuming that's true) just because a long enough rope could never be broken, doesn't mean that you can actually make one that's long enough. ;)

I can't remember the correct terminology to adequately express what I'm fixing to attempt to say, but I'll try to explain it anyways....

Remember that the force, in this example, is being applied with the rope's length, not against it.

Tomorrow I'm going to ask an instructor at school if I can find him. Also, my friend was going to ask his physics instructor. So, we'll then have at least two more ideas to throw out there.

[keith allen]

My dog ate that page...sorry :rolleyes:

[audiobliss]

And just to make it clear....for the sake of argumentation, there is NO outside interference. That means no wind, no birds to peck holes in the rope, not jagged edges to saw the ropes in two, etc. That also means that actually physically connecting the ropes to the weights/anchor has to be factored out of the equaion. The only variable that we're debating here is the effect the length of the ropes has on their strength.

[Vr3MxStyler2k3]

To bad punk...

I cut that rope dead center...

Short rope wins!

[beardog03]

the shorter one would have the downward force more evenly distributed throughout the whole rope , thus giving it more strenghth...



a longer rope would have the energy somewhere in the middle...


that`s my story and I`m stickin to it ..~

[bobman1235]

Just reading through these things, I'd like to point out two quickies because I'm anal-retentive -

1. The speed of light thing. Obviously it's a joke, but technically nothing can travel at teh speed of light, only approach it, so it's a moot point :-D Plus, the speed of light is 300,000,000 m/s or so, so you running or walking or whatever adds, what, 1? 2? Kind of insignificant, and it's not like there's a wall at the speed of light saying "nothing can move faster than this." It's a theory. OK, I'm done.

2. Things in a vacuum don't fall at 9.8m/s, they accelerate at 9.8 m/s/s. So after a second they're falling considerably faster than 9.8 m/s.

[beardog03]

ya , but what about the rope..?!!

[TheReaper]

If youre on a train moving at the speed of light and you walk from the front to the back, are you moving faster than the speed of light?
Assuming the train is moving forwards, slower (front to back <- ).

[audiobliss]

ROFL I didn't even catch that!! That's hilarious!!! That's even better than building a box out of 4 sides!!!!!

:D:D:D:D

[organ]

I think the longer rope would break first.

Let's see... When I used to smoke up, I rolled long and short joints. While smoking, the longer joint would sometimes loose it's stiffness and bend towards the ground a little. Never had this problem with short ones. And I'm talking same rolling paper/same weed here.

[audiobliss]

:rolleyes:

*sigh*

[beardog03]

he said physic`s, not phsycic`s


now I know I didn`t spell any of that right..!!

[ND13]

Just reading through these things, I'd like to point out two quickies because I'm anal-retentive -
2. Things in a vacuum don't fall at 9.8m/s, they accelerate at 9.8 m/s/s. So after a second they're falling considerably faster than 9.8 m/s.

You knew what I meant, geez :rolleyes:

http://www.exploratorium.edu/xref/phenomena/accelerated_motion_-_gravi.html

http://www.newton.dep.anl.gov/askasci/phy00/phy00800.htm

[spwuinmk67]

Having never taken physics before, I'm gonna go with the shorter rope will be stronger. My logic is though, that lets say youve got two pieces of metal rod, one 2' in length, the other 2", which one is easier to bend? Or take a piece of rope and try to pull something with it, when the rope breaks, and you try to now pull it with the shorter piece, the shorter piece doesn't break on you.

[jdhdiggs]

Both ropes will be exactly the same strength, however, the shorter one will be able to hold more load. How much more, how about the difference in weight between the two. Of course this is only valid for vertically hung loads.

You are right that the longer one can stretch further, the problem is that it will stretch more for each similar load resulting in no additional carrying capacity.

Now if you are using said ropes in a rope bridge configuration, the shorter one has signifcant advantages in that the tension to maintain an acceptable shape is far less.

spwuinmk67- you are removing modes of failure in your example as well as reducing the weight of the rope.

[petrym]

I'm withholding my answer until this one gets settled: Chemistry/math problem quick help :D (http://www.polkaudio.com/forums/showthread.php?t=31669)

:p

[Ricardo]

No difference; both ropes will have the same strength and break with the same load.

Because I know. :)

[beardog03]

so what did teach say..?

[HBombToo]

The shorter rope would support more weight than the longer because the longer rope would actually be heavier than the shorter thus decreasing the total.

Sounds like me and ND's physics lessons from 20 years ago stuck... must be due to the increased length of beer drinking time :>)

[Sami]

Let's see... When I used to smoke up, I rolled long and short joints. While smoking, the longer joint would sometimes loose it's stiffness and bend towards the ground a little. Never had this problem with short ones. And I'm talking same rolling paper/same weed here.
That thing you rolled would be of horizontal length while the rope would be vertical, different things. :)

[unc2701]

With a perfect rope in a vertical orientation the only difference is the weight of the longer rope- thus the shorter rope can hold more weight.

In the real world, you have additional factors:
1)Statistically the probably of failure is greater on the longer rope, because it has a greater number of failure points. let's say the average breakage level at a point is 10 pounds- however, some are 12 lbs, some are 8lbs... and some are 6lbs- you're more likely to see that six pound one in a longer rope.

2)you never have a perfect vertical load and the longer the rope, the more leverage can be exerted to cause a failure.

[Tex]

I say they are the same. I think rope strength is determined by material and circumference, not length. But what do I know, I'm new to this forum and I still have a lot to learn :)

[audiobliss]

The physics teacher said that there is no difference in their 'weight-holding-capablities'. They exactly the same.

So,......I was wrong.....*sigh* :(
:p

[Polkersince85]

Good explanation of tensile strenght.
http://en.wikipedia.org/wiki/Tensile_strength