Physics Help: Proving Elevator Problem Not Our Fault

[jackrules]

So the school is trying to blame, and make us pay for the alleged breaking of an elevator on me and my two friends and we are trying to prove it is not possible. I need some physics help cause my last physics course was in high school. There were 3 of us, weighing 190lbs, 169lbs and 159lbs, respectively, for a total of 518lbs or 234.96 kilograms. They claimed we were jumping so I want to see how high we would have to have jumped in order to go over the weight limit (2,500lbs or 1,133.98 kilograms) and show them it’s not possible for us to have broken the elevator and that it was in bad shape already.

I figured we could measure the height of the jumps at the following:
.25ft (.0762m)
.5ft (.1524m)
.75ft (.2286m)
1ft (.3048m)

I believe those are all the measurements we need, I will be willing to provide any others. Any help appreciated, these repairs may be expensive and we are poor college students.. Faculty just trying to get more money out of us! Thanks all.

 

[bcrelling]

Put very simply, consdering the total weight limit is alomst 5 times greater than your combined weight, whilst jumping you'd have to push down with a force 4 times greater than your body weight to reach it.

Try squating 4 times your body weight!

 

[Danger]

If the school thinks that it can get away with that BS, you should tell them that you'll sue them for having unsafe equipment. There's no way in the world that you could have broken a certified elevator, so if you did break it, it was already severely defective. They're hooped; go have a celebratory beer (but take the stairs).

 

[Lsos]

I can't do the math right now, but indeed if the weight limit of the elevator was 2,500 lbs and there were only 3 of you totaling 518 lbs, I fail to see how you could exceed this limit by jumping. You would not only have to jump high enough to land/ jump with a force of 5 gs, but you would all have to do it simultaneously with a high degree of motivation.

On top of that, there's usually ridiculous safety factors built into elevators, so that even if you managed to exceed the load it still shouldn't break.

 

[Crazymechanic]

Normal modern day elevators , actually I believe they have this feature for a quite a long time have a built in sensor which detects overweight so normally if there would be even a little more weight in the elevator as it's maximum load written on the wall then the elevator should not do anything at all.
Normally they have a beep sound or something like that when you put too much weight in them they just stop and do nothing.

Ofcourse jumping in an elevator puts additional stresses on the mechanical parts of the elevator but let's be honest if elevators would break that easy then highrise structures would be literally impossible but they do not break that easily unless ofcourse they are used as hell and not seen a maintenance in many many years.

 

[russ_watters]

So you were jumping when it broke, right?

 

[jbriggs444]

Probably you were jumping in rhythm attuned to the elevator's resonant frequency. That means that it's not just you bouncing up and down putting strain on the cables. It's the elevator itself. Estimates of how much force you can put on the floor are not directly relevant -- that's just how hard you're driving the oscillation. It's the force of the oscillation on the cables that's relevant.

 

[A.T.]

Did it actually break, or was some security lock enabled, that has to be disabled by a technician?

 

[Danger]

Any certified elevator (in North America) has 4 or 5 support cables, any one of which is sufficient to support the rated load. There are also flywheel governors and rail clamps that will instantly halt a fall. If the label says that the limit is 2,500 lbs., you would have to have imparted an impact loading of at least 10,000 lbs. in order to cause any damage to the cables. I don't know what the overage for the structure of the car is, but it is most assuredly a lot more than the rated limit. You'd need a lot more friends, and maybe a pet hippo, to break anything.

 

[jackrules]

yeah, with my calculations we would need 2 more people and we would all need to jump at least 6 inches all at the same time to be over the limit. and mind you, 6 inches is a pretty healthy jump

and after telling us it would take another week to fix blah blah blah, they fixed it yesterday

 

[russ_watters]

So it broke while you were jumping on it. Your fault, whether it should have broken or not. In any case, resonance is a possible explanation, as jbriggs said. When people feel something bouncing, they have a tendency to purposely bounce with it. And if you did that, you could have easily exceeded the load limit.

 

[sophiecentaur]

Let's face it chaps. You were messing about in the lift and trying to wreck it. You deserve to get your butts kicked. They should suspend you or leave you in the lift for an unspecified time till you grow up. Don't come to PF for sympathy.

 

[246ohms]

The resonant behaviour is interesting as it may be the three of you could get get the lift into resonance and exceed the 2500lb limit, it has happened many times in bridges where synchronous excitation of people transversing it cause resonant problems. Take the Albert Bridge which actually has a sign stating that troops must break step whilst crossing the bridge. They closed the Millenium Bridge for similar reasons.

Maybe a key point here is "was there a sign in the lift saying - NO jumping". Never seen one myself but if there is - busted.

Doing the maths it would seem with a 5g jump you would hit the roof and counter much of the implied downward force with an upward impact and hurt your head.

But one must also question why one would want to synchronously excite a lift, damage it and maybe even fall down the lift shaft - so many questions unanswered.

 

[Crazymechanic]

I think if we take the resonance problem here into account we would have to know how high the elevator itself is , not even precisely but approximately how many floors or levels it covers.
Because if the elevator is kinda "small" like the ones used in a three to four storey buildings then the corresponding cables are also pretty short and the jumping would have a pretty small if any effect.

The resonance problems usually come into play on long or high structures like long bridges , elevators or structures were long supporting columns and or cables are used.

But for the height of the elevator I guess the OP is the most competent person around here ...


P.S. sophiecentaur reading your comment I do get the feeling that you have dealt with such a case at some point in your life.
Nevertheless I agree that too liberal of a system and attitude from authorities of any kind is sometimes even a more devastating thing than a totalitarian authority or government...
Although this is a suit yourself argument.

 

[A.T.]

Now I'm not a fancy big city lawyer, but...

So it broke while you were jumping on it.

They were performing physics experiments.

Your fault, whether it should have broken or not.

Was there a sign in the lift explicitly prohibiting jumping around? Jumping around is part of normal behavior of kids. An elevator in a school should be jump proof.

 

[sophiecentaur]

@AT
So how much do we have to spend on cotton wool, to protect kids from the consequences of daft behaviour? Why should there be a list of dos and donts on every piece of equipment? If a school trampoline broke when they were jumping on it, would they have been told off?
The OP is just trying a 'technical' defence when it was just a matter of a stupid act. I tried the same thing when I was caught for a bit of silly vandalism at the age of 12. The Head gave me four whacks on my backside and rightly so. Less harm in the long run than some liberal response. I haven't been moved to vandalism since.

 

[sophiecentaur]

@AT
So how much do we have to spend on cotton wool, to protect kids from the consequences of daft behaviour? Why should there be a list of dos and donts on every piece of equipment? If a school trampoline broke when they were jumping on it, would they have been told off? no. Someone would have been in the wrong for a bad maintenance regime.
The OP is just trying a 'technical' defence when it was just a matter of a stupid act. I tried the same thing when I was caught for a bit of silly vandalism at the age of 12. The Head gave me four whacks on my backside and rightly so. Less harm in the long run than some liberal response. I haven't been moved to vandalism since.
I must say, that all reads as a bit more Redneck than I meant it to but I'll go with it.

 

[A.T.]

Why should there be a list of dos and donts on every piece of equipment?

Silly hyperbole, an elevator floor is something you are allowed to walk on. If it was an old wooden staircase that broke down, would you also blame the kids for running on it, instead of walking slowly and cautiously.

If the elevator cannot stand jumping, don't allow kids to use it. This will solve the obesity problem too.

 

[Crazymechanic]

Well quite honestly both sides are guilty , the kids for jumping where normally one should just stand to wait when the door opens and then they can walk out and go wherever they desire to, and the elevator for that it broke down.
It sounds silly but things can break down at the most unimaginable ways even when used normally , it's a matter of many many factors that we cannot even keep trace of so we have insurance companies for cases like these where no real physical proof of ones bad intentions can be found to be the real cause of the accident , although very likely it was.

 

[Lsos]

People will jump on elevators. That's what people do. Hell, the elevator in my very building got stuck and I had to call help because a guy I know, an adult male at that, was jumping in it. An overweight adult male. An overweight adult male who's a professor at the Eindhoven University of Technology.

Yeah, maybe he had a bit to drink, but an an elevator should be designed to cope with that. If we can put a man on the moon, we should be able to build an elevator to handle some kids jumping.

There are no stupid people, just stupid designs.

 

[sophiecentaur]

I suspect that the lift just went into shutdown mode as a result of the jumping. The school had to pay for a man to come and re-set it. It's not unreasonable to suggest that the eejits who made it happen should pay in some way for the man's time. There was probably no danger involved - just tiresome inconvenience for the rest of the school. I have been in a small hotel lift that would refuse to operate if too many people got in it.
I can't understand why anyone should be endorsing the sort of behaviour that the OP describes. "Kids do it" is no way to think. (Would a parent say that?) Kids will do more and more if they aren't given any direction. Haven't you heard of the essential rôle of negative feedback in a control loop?

 

[vivesdn]

The fall of a 30cm jump will get you falling at 2.5m/s. This speed will go to 0 being the elevator cables to provide the force. I do not expect steel cables to be elastical so I'll suppose 3mm of elongation. Under these conditions, in less than 0.01 seconds you'll come to rest, which means more than 300m/s2 of acceleration. Maybe 70000N of load for all of you. Of course, your legs will provide a partial dampening, but just to understand that forces involved are far greater than your wheighs combined.

This is why rock climbing is done with dynamic (elastical) ropes and not steel ones, just to allow elongation to reduce acceleration and peak load.
Jumping inside an elevator is not a good idea, even when maximum load is not achieved.

 

[jbriggs444]

The fall of a 30cm jump will get you falling at 2.5m/s. This speed will go to 0 being the elevator cables to provide the force. I do not expect steel cables to be elastical so I'll suppose 3mm of elongation. Under these conditions, in less than 0.01 seconds you'll come to rest, which means more than 300m/s2 of acceleration. Maybe 70000N of load for all of you. Of course, your legs will provide a partial dampening, but just to understand that forces involved are far greater than your wheighs combined.

If you came to a stop in 3 mm after a 30 cm drop then you would experience at least 30cm/3mm = 100 g's (9800 m/s²) of peak acceleration.

But if you experienced 100 g's of acceleration, your feet, ankles, knees, hips and spine would not bring you to a stop within 3 mm. So the initial assumption of a 3mm stop is unjustified and any conclusions drawn from that assumption (such as a force of 70000 Newtons or a duration of 10 ms) are invalidated. [Those numbers are suspect -- my calculations differ greatly]

Further, if you decide to try to account for high force by postulating high rigidity you have the problem of jump synchronization. The higher you make the rigidity, the briefer the impact period becomes. If your rigidity figure says "3 mm" then your have to postulate students jumping with a synchronization tolerance of 2.5 ms (by my figures). Otherwise their force contributions don't add.

Offhand, I don't know how many g's you can pull in a feet flat, knees-locked, spine-straight,
arms-at-your-sides, muscles-tense landing from a maximum height vertical jump. I do know that it's not very fun.

 

[Crazymechanic]

Also I think that the reason why mountain climbers don't use metal ropes or cables is not because of their properties rather their weight , I mean the job is very hard to do and bringing a ton of equipment with you surely will make it impossible.

 

[sophiecentaur]

Also I think that the reason why mountain climbers don't use metal ropes or cables is not because of their properties rather their weight , I mean the job is very hard to do and bringing a ton of equipment with you surely will make it impossible.

There is a very good reason why rock climbers use nylon yet sailors use polyester for halyards. Some jobs need a low modulus and others need a high modulus. Both ropes are light weight c/w piano wire equivalent.

 

[Travis_King]

I see it this way:

My university wood shop had one of those retracting table saw blades (SawStop) that would retract virtually the instant it touched a finger (or a hot dog, or any fleshy, conductive material). It is a terrific device as far as safety goes, but they are somewhat expensive and have to be replaced if they go off (as they destroy the blade, and the mechanism itself).

If a student ripping a piece of lumber and his finger accidentally touched the blade--causing the blade to retract; saving his finger but ultimately costing the school money for the replacement--the school would gladly pay for the replacement. The student did nothing on purpose, and the device served its purpose.

However, if the student tried to run a hot dog through the saw to test the device (which then, obviously retracted the blade and required a whole new setup), we would hold this student responsible for all damages and costs. And rightly so.

If you're in an elevator and something goes wrong, generally no one will give you any problem as its recognized that if a safety feature engages while you are using something properly, then all that really happened is the device (which needs to be fixed/replaced/whatever) saved them from the liability if you had been injured had it not done its thing.

If you misuse something, like an elevator, and cause some safety device to engage (which then has to be fixed/replaced/whatever) then you created unecessary costs for the school.

With that said, it stinks to have to pay damages for things like this. If you're going to try to defend yourself, it might be a good idea to find out what exactly happened with the elevator, and also maybe contact the manufacturer, to see if you can go with the "the safety shouldn't have engaged with just three people jumping pretty asynchronously". Trying to use basic physics on a problem like this is almost laughable though. You're best bet (i'd think) is, if they already know that you were jumping in there, to explain that you were curious about the feelings of varying g-forces in elevators and that you knew that the three of you couldn't produce enough force to reach the rated weight limit so you figured it would be ok (ignorance is your savior here, not physics). You want them to know that you weren't jumping just to horse around (unless you were, then you deserve to pay for the damages) and that you really didn't expect anything to happen, given the load rating as stated on the sign.

Rudimentary physics will not get you off this one. You'll just look like a jerk and wind up paying anyway. If it's a lot of money that they're looking for and you have no other recourse, maybe find an engineer willing to work for cheap who can help you make your case. If they want you to pay, showing them a piece of paper with three lines of math and "seeee, told you!" won't thwart them.

 

[Danger]

Everyone still seems to be overlooking the fact that although they could have exceeded the posted limit, they could not possibly have exceeded the design limit. That is almost (or more than, depending upon the machinery) half an order of magnitude over the posted one. (If one of the 4 or 5 cables drops to 60% of its posted limit, the machine shuts down automatically.)
Sophie beat me to mentioning the next factor that I was going to bring up, in his post #21. (edit: actually A.T. beat us both on that, but somehow I overlooked his very brief first post that suggested it.) If they did manage to exceed the posted limit, the weight sensor should have instantly shut down the motor. If that caused further failure, the brakes would have engaged.
If all that happened was an equipment shut-down, then I can see that they might be held accountable for the expense of having the elevator inspector show up, reset the machine, and certify it as operational. It would be very difficult to assess damages due to the time that it spent in the mandatory "dormant" mode before the inspector arrived. If the elevator was not put into dormant mode (including wiring off the doors, pulling the fuses and padlocking the operation switch in the "off" position) or it was and then was reactivated by anyone other than a licensed elevator inspector, the school is clearly liable from a legal standpoint.
There are hundred of pages of regulations regarding these things. I've read them, but I'm sure not going to waste any more time on this. I mean, really... they even specify the fraction of a millimetre of slippage allowed per metre of travel on the drive sheaves...

 

[A.T.]

However, if the student tried to run a hot dog through the saw to test the device (which then, obviously retracted the blade and required a whole new setup), we would hold this student responsible for all damages and costs. And rightly so.

Before you let students use a saw, you give them plenty of safety instructions. What not to do, and what the costs of the killing the blade are.

So, if the all the students were explicitly advised not to jump in the elevator, or if there was a sign in the elevator strictly forbidding jumping, or if it was the second time this guys did it - then you can claim intended vandalism.

 

[sophiecentaur]

The acid test would be to ask.whether they would have done the same thing if a teacher had been present. That would establish their motives ank knowledge about right and wrong. I suspect there's a hint of post hoc rationalisation in the story.
I'm not sure what you are trying to defend here.

 

[Danger]

I'm not sure what you are trying to defend here.

I am trying to defend the laws of physics, by which they could not possibly have caused any damage, other than a triggered shut-down, unless the thing was a rattletrap to start with.
Try to look at this from a more pedestrian aspect. Let's say that you are going to your hotel room, and there are 6 other people in the elevator. You don't even think about it, even though that might bring the load within a few kilos of the posted limit. Now, just as you're about to depart, a morbidly obese fellow (maybe 150 kilos) steps in. Do you expect to fall into the sub-basement as soon as he boards?

 

[sophiecentaur]

I am trying to defend the laws of physics,

The laws of physics are not in question. The lift design is almost certainly quite adequate to deal with some very high stresses and I don't think anyone is suggesting that these young miscreants were in any danger at all or that significant material damage was done.
My issue is with the 'laws of' behaviour and the assumption that these lads couldn't be expected to restrain themselves without specific training or notices (or a nearby figure of authority). One of the purposes of a school is to regulate behaviour (it seems that many parents do not assume that responsibility any more) and the sort of negative feedback that the school dished out was quite in order. There is no telling what inconvenience they caused by taking the lift out of action. Should no one have taken any punitive action? Is it ok to accept that "kids do that sort of thing"?

 

[Danger]

Is it ok to accept that "kids do that sort of thing"?

Well to start with, I never saw a mention of their ages anywhere. I assumed them to be university students rather than "kids". (Alright, we're both older than dirt so they're kids to us, but not in the eyes of society.)
Given that, have you considered that these "kids" knew that their behaviour wouldn't have any effect upon a certified elevator and thus had no malice in mind?

 

[A.T.]

Should no one have taken any punitive action?

Hyperbole-man strikes again. The issue was financial responsibility, not "any punitive action". I don't see grounds for financial responsibility, if they were first-time offenders and not explicitly informed about the elevators sensibilities.

 

[Danger]

The issue was financial responsibility, not "any punitive action".

Thanks for that. I was about to edit my last post to add that fact, but it's nice that you got in ahead of me.

 

[vivesdn]

If you came to a stop in 3 mm after a 30 cm drop then you would experience at least 30cm/3mm = 100 g's (9800 m/s²) of peak acceleration.

I think that space does not relate with time lineally. So 3mm would not be 100g's but 30g's. Said that, 3mm was only an assumption to note that tension on a steel cable can be much higer that just body weight. And of course, the guys did not behave as solid rods as you point out. But note that you do not need 30g's to be out of the maximum load, but less that 5g's.

As for rock climbing: a 10m fall (quite normal by the way) on a steel line and you would prefer to be free falling.