Posts Tagged ‘physics’

The barometer

The start of school for many of us inspires me to drag out the famous (to some of us) story of The Barometer.

Miniature barometer next to miniature physics book. Pen for scale.

As the story goes, a physics teacher posed this question on an exam and got surprising results.

Show how it’s possible to determine the height of a tall building with the aid of a barometer.

One student answered this way:

“Take the barometer to the top of the building and attach a long piece of rope to it. Lower the barometer until it hits the sidewalk, then pull it up and measure the length of the rope, which will give you the height of the building.”

What? The teacher expected a different answer, using the standard equation involving the difference in pressure at the top and bottom of the building.

When challenged to come up with “the right answer,” the student gave several more. Among them:

1. Take the barometer out on a sunny day and measure the height of the barometer, the length of its shadow, and the length of the shadow of the building. Using simple proportion, determine the height of the building.

2. Take the barometer and begin to walk up the stairs. As you climb the stairs, you mark off the length of the barometer along the wall. You then count the number of marks, and this will give you the height of the building in barometer units.

And so on.

My favorite remains this one:

“Take the barometer to the basement and knock on the superintendent’s door. When the superintendent answers, say: ‘Mr. Superintendent, if you will tell me the height of this building, I will give you this barometer.’”

How would you grade this student?

** Legend has it that the student was Niels Bohr (1885-1962, Nobel Prize in physics, 1922), but then a legend can say anything and get away with it.

The Physics of Santa

It’s time to drag out the old physics-of-Christmas essays. In case you missed it in my newsletter, here’s my favorite version about how it’s impossible for Santa to get his job done:

There are about 2 billion children in the world and even at one toy each, we have something like 400,000 tons of sleigh, toys, and a hefty old man traveling at 650 miles per second to get around world in one night.

A simple calculation shows that Santa has 1/1000th of a second to

• pull up on a roof

• hop out

• climb down the chimney

• figure out who’s nice

• distribute the presents

• eat a snack

• say Ho, Ho, Ho

• go back up the chimney

• dust off his suit, and move on.

Not just exhausting, but physically impossible.

Or, he could just hail a cab.

Even though there’s not a lot of sleigh traffic up there, it’s not a feasible trip.

But now, I’m about to offer a rebuttal.

All we have to do is call on worm holes, those tricky features of space-time that allow a shortcut through the universe.

Imagine you’re standing in a long line at the post office. You’re at one end of the room and the clerk is at the other, lots of people-mass in between. Now imagine a piece of paper with a stick figure representing you at one corner, and a figure at the diagonally opposite corner to represent the clerk. Fold the paper so that your stick figure is on top of the clerk’s.

See? You’ve just taken a shortcut to the head of the line.

That’s what Santa can do. With a little math and a dash of relativity theory we can show that, in fact, with every stop, Santa can come out of the chimney before he gets in!

No problem making all those stops.

So, yes, Virginia, relatively speaking, Santa can do it!

Now if only I could find the right wormhole to get me through Bay Area freeways.

Oh, the pressure!

Interesting conversation with a young art graduate student the other night: He’s not thrilled with his classes, especially with the exercises his professor assigns. Bottom line—he just wants to be able to go into the classroom/studio and do his own artist-thing. Nothing should be right or wrong in an art class.

Can the same be said for physics classes? The discussion prompted me to resurrect an old physics story. As the legend goes, a physics teacher posed this question on an exam and got surprising results.

Show how it’s possible to determine the height of a tall building with the aid of a barometer.

One student answered this way:

“Take the barometer to the top of the building and attach a long piece of rope to it. Lower the barometer until it hits the sidewalk, then pull it up and measure the length of the rope, which will give you the height of the building.”

What? The teacher expected a different answer, using an equation involving the difference in pressure at the top and bottom of the building.

ΔP/Δh = (-mg/kT)/P

When challenged to come up with “the right answer,” the student gave several. Among them:

1. Take the barometer out on a sunny day and measure the height of the barometer, the length of its shadow, and the length of the shadow of the building. Using simple proportion, determine the height of the building.

2. Take the barometer and begin to walk up the stairs. As you climb the stairs, you mark off the length of the barometer along the wall. You then count the number of marks, and this will give you the height of the building in barometer units.

And so on.

My favorite remains this one:

“Take the barometer to the basement and knock on the superintendent’s door. When the superintendent answers, say: ‘Mr. Superintendent, if you will tell me the height of this building, I will give you this barometer.’”

How would you grade this student?

** Legend has it that the student was Niels Bohr (1885-1962, Nobel Prize in physics, 1922), but then a legend can say anything and get away with it.