An algebra problem

A story from the tutoring room, where I encountered a student taking first semester chemistry for science majors who was struggling with a simple density problem.

(Why they teach complicated algebra problems before they teach any chemistry is a mystery to me, but I no longer remember what pedagogy my chemistry classes followed.)

Given that our chemistry class has college algebra as a prerequisite, I think the problem itself is instructive.

After a significant amount of prompting on an easier problem, the student was able to get all of the given data for this problem into the appropriate chem-SI units of g and cm. This left something like the following problem, except written as a fraction:

2.705 = 276/(30.48 * 1219.2 * X)

Solve for X.

The student was,it appeared, utterly helpless when faced with all of those numbers.

My suggestion that he cross multiply the X and 2.705 met the sort of look I would expect if I had said it in Japanese. OK, clear fractions? Still no luck. I don't think he saw this as a fraction. Multiply both sides by X? Ah, progress. Now he could compute the right side and solve 2.705*X = Number. Just to check, I asked him about

5 = 7/(3*X)

No problem there, although slow as molasses doing it.

When I started telling this story to a chemistry colleague, she starting laughing so hard that she almost fell out of her chair before I was halfway through it. She regularly sees this at the start of every semester. Now I know why she says my students aren't like hers. Many (but not all) of the kids who make that kind of mistake are weeded out by pre-calc and trig before they get to me.

When I asked a couple of math colleagues about this problem, I learned that they include problems with "messy" numbers on pre-calc exams, but not in college algebra. They also said they suspect that not all pre-calc classes give messy application problems. So that is why I was not surprised that a student in Becky Hirta's Calculus Circus had trouble with a graph where the answer was not obviously going to come out in simple integer steps.

Footnote:

Two of my physics students messed up a problem essentially as follows:

2.66 = 7.79+3.47*X

2.66/7.79 = 7.79/7.79 + 3.47*X

0.3415 = 3.47*X

To save you the effort, 2.66/7.79 is about 0.3415. Bet you didn't know that 7.79/7.79 was zero!

Yep, that is how at least two of them "canceled" that number that was added on the right. Again, my math colleagues tell me that this sort of error is not uncommon among students entering calculus 1, and that they are more likely to make it with numbers rather than symbols. I have to wonder if they would have subtracted 7.79 if it had been at the end

2.66 = 3.47*X + 7.79

instead of at the beginning....

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Mars has Dirt!

Not to be trite, but some of the headlines and quotes have been amusing. "You might be able to grow asparagus in it." What makes this important is that there was no guarantee that the geology on Mars would produce anything like the mix of ingredients we find on earth. Just look at our Moon, which allegedly comes from the same crustal material we farm here on Earth. As emphasized in the BBC story and one from CNN linked below, the soil is mildly alkaline. Bad for azaleas and citrus, but great for lots of other plants and containing the trace elements useful for simple cellular life forms on earth.

(By the way, if you want a clickable image for a high resolution look at the "clumps of rosy red soil", you should use the ones on the main Phoenix news site. You can also follow Phoenix's exploits on its Twitter page.)

Buried in some stories of this important discovery (but prominent in the MSNBC story, which links to a nice little article on space.com) is the HOW it was done. Wet chemistry on another planet!

Hey, it is hard enough to do wet chemistry in an intro chemistry lab!

I am really impressed with the work of what I assume is a team of analytical chemists (the folks who focus on developing instrumentation) from my limited knowledge through a grad school friend who is an analytical chem PhD working in the medical field.

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Thank You Bill Simpson

That is what Tony Pedregon said in a live interview with ESPN between walking away from the wreck of his car (and some assistance for his second degree burns from the first-response team at Pomona) and getting a hug and kiss on the forehead from (fellow driver) John Force on his way to the ambulance.

If you have not seen the fireball on the news (it has been on everything from NBC Today on Monday through the evening news, a pair of YouTube links are below the fold.

Tony Pedregon repeated that thought in a CNN interview Tuesday morning (80% of the way down), when he said "But I've got to shake the hand of the guy that makes the fire equipment because it did its job." The guy who invented the Nomex firesuit is Bill Simpson.

If you don't know about Bill Simpson and fire safety in auto racing, keep reading. Last year was the 40th anniversary of this innovation.

In the old days, when I was a kid, people died or were horribly scarred for life after an incident like this one. The only fire protection was from cotton clothing that had been soaked with fire retardant chemicals.

In one of those strange coincidences, Nomex, a fire resistant fabric invented by DuPont, and Bill Simpson, inventor of the drag chute used to reduce the need for braking when you may only have a quarter mile or two to slow down from 200 or 300 mph, came together through the US space program. You can read about it in his Wikipedia biography linked above. He learned about Nomex and figured out how to use it to make a fire suit.

One of his more legendary marketing ploys was to make a movie where he tested it himself by soaking it in gasoline and lighting it. The famous (infamous) video of Bill testing a fire suit can be found on his new company's web site.

A key thing to remember is that safety is not a static thing. Just this year, NHRA increased the level of protection required in nitro cars. As performance improves and speeds increase, the intensity of a fire will increase. Surviving a fireball of gallons of nitromethane mixed with oil fed by oxygen flowing in at 270 mph does not happen by accident.

Video of the Explosion:

The video embedded here consists of the replays of the event shown by ESPN to sort out what happened.



There is also a YouTube video (ESPN copyright violation) called "Tony Pedregon on Fire" that shows the live-to-tape broadcast of the incident as it happened. You can see, around the 1:06 mark, Tony shaking his burned right hand after he gets out of the car as well as the burned knees of his fire suit.

[Still incomplete ???]

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More of Middle America

Success! Got a good shot of the sort of highway sign I noticed on the first leg of the trip.

Now I just have to get some info from highway department and turn it into a physics problem. The approximately 2 foot wide base makes it ideal for a torque problem, and treating the two trusses and the sign as if each was a uniform object is probably not a bad approximation.

The shortage of "W" stickers continues, with a new twist. I saw the first example of a "coverup" - an oval sticker in the style of the "W'04" ones, except this says "GOP". Looks like the perfect way for a disgruntled Republican to show they line up with Hagel (and now Lugar) rather than Cheney and Bush. Still rare, however.

I also saw a regular "W" sticker and, more interestingly, one that read "May God Bless W" printed in a flag pattern. The latter was in a car with Florida plates driven by white haired folks who, apparently, think that their God would bless someone who ships people off to be tortured after even less of a trial than Pontius Pilate gave His Son. The United States is, truly, a land for everyone.

Puzzling over the mindset of the half of the Republican Party that still thinks things are going as planned in Iraq kept me awake for another hundred miles, but I prefer roadside delights like that pictured below to break up the monotony.

The sculpture is huge, by the way, and would not come cheap.

Then there are the things you don't want to see. Stopped traffic:

For an hour, parked on the freeway.

It did, however, turn out to be an interesting break from the road that contained an interesting lesson in chemistry and physics. Got a chance to talk to a wide variety of people who were on the highway, a truly interstate group. Among them was the driver of the truck you see in front of me. He filled us in on what he had heard over the radio about the wreck. Later I asked him about his load, since his tanker truck had an amusing warning sign suggesting a corrosive liquid.

He said the truck was carrying Maleic Anhydride, used in everything from making epoxy type resins to food products. (Google, in addition to confirming my memory of how to spell the name, confirms that it is used to make artificial sweeteners as well as epoxy hardeners and oil additives.) It was being transported in the liquid state at 150 deg F. It is solid at room temperature, so he needed to keep his truck running to avoid a very nasty problem. Although it reacts to become Maleic Acid when it encounters water, a spill is more likely to result in a white solid when it cools and hits the ground. One web link gives the MSDS info on it, and shows the "corrosive" symbol I saw on the truck. I'm glad I don't have an iPhone, where I would have known that info while parked behind it!

Bet you never guessed that a pretty truck like that would be carrying a hot chemical.

Anyway, the accident had occurred hours earlier. Reportedly the driver had either fallen asleep or had a heart attack, although there was also another vehicle involved. In any case, a truck hauling a double trailer (like the one in the parade picture) had run off the road, dumping his load in the ditch. You can't see any of that in the picture below, but you can see part of the response team.

Traffic had to wait while the back hoe was used to right the truck, because it had to swing across the only lane available for traffic. At the same time, a "bobcat" was being used to clean up the load from the ditch.

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