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A semi truck weighing exactly 10,000 pounds gets onto a bridge that is 100 miles long. The bridge's actual weight limit (not the posted limit) is exactly 10,000 pounds; any more will break the bridge. After going about 80 miles down the bridge a small bird lands on the truck. What happens?

(I.E., what happens to the truck and the bridge? I don't care what happens to the small bird or the driver

Here's the version with math that gives away the trick a bit but has less loopholes:

A diesel semi-truck operating at the remarkable fuel economy of 10mpg begins to cross a bridge. At the moment immediately prior to the wheels contacting the bridge surface proper, the total weight of the truck and all its contents is exactly 10,000 pounds. The bridge can hold a maximum of exactly 10,003 pounds without collapsing. After traveling 80 miles along the 100 mile long bridge - all the while with 0 vertical motion whatsoever - an exceptionally large, full-grown male kori bustard lands on the top of the truck. Does the bridge collapse?

Clarifications: (Yes, it's an easy puzzle that's already answered so this isn't required. I'm an engineer, though, and I demand that such things be rigorous. Holes pointed out by you internet people must be mended!)

  1. The given weight of the truck includes the truck itself as well as all things being carried by the truck such as the cargo, the driver, the driver's breakfast inside their stomach, the fuel, the cardboard box stuck in the axle, all the magical snails that live on the left front axle, etc. It is the weight that would be shown by a scale if the truck was sitting stationary on one at that moment.
  2. The bridge weight limit given is the actual bridge's limit and not the posted limit.
  3. For all you people from sane countries in which the metric system feels more natural, feel free to change the units without conversion. For all practical purposes, the question could have a truck of WEIGHT going over a bridge of GREAT LENGTH that has a weight limit of the same WEIGHT and it's traveled 80% of GREAT LENGTH when the bird lands.
  4. The driver is not consuming or excreting anything besides the air within the cabin which is open to the atmosphere outside the cabin. It is irrelevant if it is open based on open windows or the air conditioning.
  5. The truck has a diesel engine without any electrical source powerful enough to provide or significantly support locomotion.
  6. The bridge can be treated as a perfectly rigid object with all stress equally distributed. The total weight it can handle is as posted in the original question.
  7. During the truck's voyage across the bridge, there are no loads applied to the bridge besides the truck and the eventual landing of the bird. Yes, this means the bridge is the most sanitary outdoor construction of all time as no living things exist upon it's structure.
  8. The truck weight is taken as the driver has just inhaled a full breath of air. Note that the bird weighs more than the weight of such a breath.
  9. The bridge is perfectly smooth. The truck experiences no bumps or vibrations of any kind. There is no vertical movement of the truck at any point while traveling the bridge. Magic.
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    $\begingroup$ I posted this in honor of it being question 10,000 on puzzling.stackexchange.com (per the URL). As Vikram pointed out, this is not the same as having 10,000 questions on ??. My original phrasing was poor in this regard. $\endgroup$
    – Engineer Toast
    Commented Mar 9, 2015 at 14:45
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    $\begingroup$ It has probably crossed the weakest spot on the bridge already, so I think nothing would happen. $\endgroup$
    – kasperd
    Commented Mar 9, 2015 at 17:41
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    $\begingroup$ Since the air in the lungs is not significantly compressed, it does not really add to the driver's weight (though it does add to his mass). He probably loses more weight in a breath from moisture added to his breath than he'd gain from the very limited compression of air in the lungs. $\endgroup$
    – Johnny
    Commented Mar 9, 2015 at 17:42
  • $\begingroup$ The bridge needs to be perfectly flat too or the vertical displacement caused by bounces could create dynamic loading above the 10 kips. A bump as the driver enters the bridge would cause it to collapse immediately. Additionally, the force distribution changes if the driver accelerates forward or backward, so hopefully the bridge can handle that as well! $\endgroup$
    – do-the-thing-please
    Commented Mar 9, 2015 at 19:35
  • $\begingroup$ If you are over the posted limit, assume the bridge will collapse. Besides, who knows when earthquakes happen? $\endgroup$
    – bjb568
    Commented Mar 9, 2015 at 21:55

5 Answers 5

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By the time the truck has gone 80 miles, it has consumed a significant amount of fuel. At that point, the weight of the bird is not sufficient to bring the weight of the truck back up to 10,000 lbs.

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  • $\begingroup$ It's not exactly the most difficult puzzle. Consider it an exposition puzzle. Well done on the quick draw, though. $\endgroup$
    – Engineer Toast
    Commented Mar 9, 2015 at 14:58
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    $\begingroup$ After 80 miles, I'd also imagine that the trucker has smoked at least enough cigarettes to match the weight of the bird as well. $\endgroup$
    – blakeoft
    Commented Mar 9, 2015 at 15:37
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    $\begingroup$ @EngineerToast if the cabin is sealed, asphyxiation is a bigger problem than weight, puzzle aside :) $\endgroup$
    – Sparr
    Commented Mar 9, 2015 at 21:15
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    $\begingroup$ @EngineerToast if it's sealed, releasing the pressurized oxygen into the cab is going to cause pressure problems, too. $\endgroup$
    – Sparr
    Commented Mar 10, 2015 at 22:18
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    $\begingroup$ And what if it is an ostrich? $\endgroup$
    – vero
    Commented Mar 11, 2015 at 6:11
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Sadly the truck was an electrical one, and it fell... ah... had it been a gas guzzling earth killing one, it would have been saved... a sad sad story :-)

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    $\begingroup$ It would still be fine as the bird is small enough that it weighs less than the electrons ejected from the truck's exhaust. That's how electricity works, right? $\endgroup$
    – Engineer Toast
    Commented Mar 9, 2015 at 15:31
  • $\begingroup$ The weight of the bird is almost 0. The truck won't he weighting 10.000 pounds (whatever that is). Usually, a bird can weight 5-10g. The smaller ones. The bigger ones can go up to 2-3kg. Nothing important. You are inside the truck and you drove for 80 miles! If 5-10g make a difference, you can't eat breakfast before getting in the bridge. $\endgroup$
    – Ismael Miguel
    Commented Mar 9, 2015 at 15:32
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    $\begingroup$ @EngineerToast I'm quite sure the truck will emit, from the exhaust pipe, a rainbow, and that weight will save the truck $\endgroup$
    – xanatos
    Commented Mar 9, 2015 at 16:19
  • $\begingroup$ @IsmaelMiguel What if it's a robot truck that drives itself or, more realistically, the beginning weight of the truck includes the driver? $\endgroup$
    – Engineer Toast
    Commented Mar 9, 2015 at 16:23
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    $\begingroup$ @IsmaelMiguel Fixed per clarification 8. I believe we are somewhat past the question's intent at this point. $\endgroup$
    – Engineer Toast
    Commented Mar 9, 2015 at 17:39
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If the truck weighs exactly 10,000 units when stationary and the ultimate limit of the bridge is 10,000 units, then the truck will probably break the bridge at the beginning. Downforce from the air moving over the truck would probably increase the truck's force enough to break the bridge.

Or is this the classic "model the truck as a sphere moving through a frictionless vacuum"? Vacuums are no fun... they suck. There must still be friction at the axles and/or wheels, or the truck could coast across without using any fuel, and then the bird would do it in.

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  • $\begingroup$ If the truck was weighed to be exactly 10,000 while it was in motion, any lift or downforce due to airflow was already taken into account. $\endgroup$
    – Johnny
    Commented Mar 9, 2015 at 21:51
  • $\begingroup$ @Johnny the truck was weighed stationary in point 1 of the question. $\endgroup$
    – Nattgew
    Commented Mar 9, 2015 at 21:53
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    $\begingroup$ I'd like to +1 just for "vacuums are no fun... they suck" $\endgroup$
    – Rand al'Thor
    Commented Mar 10, 2015 at 0:35
  • $\begingroup$ xkcd.com/669 $\endgroup$
    – Paul Rowe
    Commented Mar 31, 2015 at 20:40
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Assuming the truck still weighs exactly 10,000 pounds at the time of the bird's approach, then it's not the landing of the bird you have to worry about - it's the flapping of its wings to stay aloft above the truck, which exerts that same amount of force on the air which is in turn exerted on the truck. The bridge will surely break before the bird has even landed on it!

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  • $\begingroup$ The downwash force on the truck from the bird will not be equal to the weight of the bird. Nonetheless a valid point. $\endgroup$
    – Nattgew
    Commented Mar 9, 2015 at 21:52
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    $\begingroup$ @Nattgew Well, okay, obviously if the bird is landing it'll be lower, but still not zero. $\endgroup$
    – fluffy
    Commented Mar 11, 2015 at 4:03
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The bridge can be treated as a perfectly rigid object with all stress equally distributed. The total weight it can handle is as posted in the original question.

This seems to have changed the meaning of the question. I result in the simplest possible bridge which has the interesting artifact of the minimum breaking force is applied to the middle of the bridge. Thus the bridge does not collapse ignoring fuel because the truck has passed the middle already.

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