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I Forge Iron

Math problem


Steve Sells

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A backhoe weighing 22 tons is on top of a lowboy trailer and heading east on Interstate 70 near Hays, Kansas . The extended shovel arm is made of hardened refined steel and the approaching overpass is made of commercial-grade concrete, reinforced with 1 inch steel rebar spaced at 6 inch intervals in a criss-cross pattern layered at 1 foot vertical spacing.

Solve:

When the shovel arm hits the overpass, how fast do you have to be going to slice the bridge in half ? (Assume no effect for headwind and no braking by the driver.)

Extra Credit: Solve for the time and distance Required for the entire rig to come to a complete stop after hitting the overpass at the speed calculated above. Yes, you can also neglect friction coefficients.

I wonder if he will he stop using his cell phone while driving in the future?

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The driver was going half fast enough to cut the overpass completely, but if he was at the precise speed required, the rig would have stopped at the moment the cut was completed. Hence, no extra time or distance involved for the rig to stop. B)

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ok, no need to take into effect headwinds or braking, the speed is 164.3 mph at impact.

the extra credit is a little tricky as you did not mention if the truck driver then used the brakes or was it a coasting stop. so without braking on a flat road, no winds ect. 3.76 miles, that also covers the removal of any and all acceleration methods.

hope that helps

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the real question is did the driver know he lost his trailer? I would suspect that the king pin broke he heard a big bang but never looked back got to his job site and then was suprised to find out he had no trailer.

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Well faster than he was going for sure! I was surprised at how cheap the estimated cost of repair was. I've wondered about sacrificial max height indicators located before the last exit before such an underpass; but that one didn't look like it was a "low" one---just a very high load!

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What has me a bit perplexed is that somehow the arm got up through the middle of the bridge but didn't break completely through the side that it was coming from!

The top front of the cab appears to have been riped up, so this indicates to me that when the back hoe struck the bridge it tilted back and started to slide under the bridge with the arm going more horizontal. Then this lifted up the cab enough to strike the underside of the bridge which produced a see-saw action which shot the arm up through the center of the bridge.

Something like that must have happened since the upper part of the bridge on both sides are intact, but the arm is sticking up through the bridge higher then them, very odd.

As to the calculation, frankly I don't think that the back hoe is capable of completely cutting through the bridge, the arm acting as a lever would pivot the cab up regardless of how fast it was traveling and what happened is what would happen. I hardly see a mark on the bottom of the walkway on the side that it entered from.

Cool stuff, thanks for bringing it up.

Caleb Ramsby

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Max height signs don't always mean much either. Buddy had just put his nice stereo and complete cassette collection into the timberjack buncher he was running. Was to be bedded out past Castlegar someplace. They lost the top 4" of the cab going under the underpass at Castlegar. Think they measured 3-4 times to make sure they were not over max height. tuens out they were good but Highways had put a 5" lift on the road through there and used the old signage. think buddy found 2 out of a lot of tapes...everthing mounted and stored up top. Faller buncher was a rightoff. And from what I gather they were only doing 80km/h though that stretch of road.

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