Friday Funny!

Today’s Friday Funny is borrowed from the What if? Blog, that answers hypothetical questions with physics!

Glass Half Empty

What if a glass of water was, all of a sudden, literally half empty?

—Vittorio Iacovella

The pessimist is probably more right about how it turns out than the optimist.

When people say “glass half empty”, they usually mean something like a glass containing equal parts water and air:an optimist and pessimist sitting at a table with a half-full - or half-empty glass between them. the optimist's thought bubble reads 'ooh-water! i bet we'll get to drink it!' while the pessimist's thought bubble reads 'drinking fluids postpones detah but doesn't avert it.'Traditionally, the optimist sees the glass as half full while the pessimist sees it as half empty. This has spawned a zillion joke variants—e.g., the engineer sees a glass that’s twice as big as it needs to be, the surrealist sees a giraffe eating a necktie, etc.

But what if the empty half of the glass were actually empty—a vacuum? (Even a vacuum arguably isn’t truly empty, but that’s a question for quantum semantics.)The vacuum would definitely not last long. But exactly what happens depends on a key question that nobody usually bothers to ask: Which half is empty?

For our scenario, we’ll imagine three different half-empty glasses, and follow what happens to them microsecond by microsecond.

three half-empty glasses of waterIn the middle is the traditional air/water glass. On the right is a glass like the traditional one, except the air is replaced by a vacuum. The glass on the left is half full of water and half empty—but it’s the bottom half that’s empty.We’ll imagine the vacuums appear at time t=0.

three half-empty glasses of water at t=0For the first handful of microseconds, nothing happens. On this timescale, even the air molecules are nearly stationary.

three half-empty glasses of water at t=50nsFor the most part, air molecules jiggle around at speeds of a few hundred meters per second. But at any given time, some happen to be moving faster than others. The fastest few are moving at over 1000 meters per second. These are the first to drift into the vacuum in the glass on the right.

The vacuum on the left is surrounded by barriers, so air molecules can’t easily get in. The water, being a liquid, doesn’t expand to fill the vacuum in the same way air does. However, in the vacuum of the glasses, it does start to boil, slowly shedding water vapor into the empty space.

three half-empty glasses at t=150nsWhile the water on the surface in both glasses starts to boil away, in the glass on the right, the air rushing in stops it before it really gets going. The glass on the left continues to fill with a very faint mist of water vapor.

three half-empthy glasses at t=400nsAfter a few hundred microseconds, the air rushing into the glass on the right fills the vacuum completely and rams into the surface of the water, sending a pressure wave through the liquid. The sides of the glass bulge slightly, but they contain the pressure and do not break. A shockwave reverberates through the water and back into the air, joining the turbulence already there.

three half-empty glasses at t=1msThe shockwave from the vacuum collapse takes about a millisecond to spread out through the other two glasses. The glass and water both flex slightly as the wave passes through them. In a few more milliseconds, it reaches the humans’ ears as a loud bang.

three half-empty glasses at t=2msAround this time, the glass on the left starts to visibly lift into the air.

The air pressure is trying to squeeze the glass and water together. This is the force we think of as suction. The vacuum on the right didn’t last long enough for the suction to lift the glass, but since air can’t get into the vacuum on the left, the glass and the water begin to slide toward each other.

three half-empty glasses at t=5msThe boiling water has filled the vacuum with a very small amount of water vapor. As the space gets smaller, the buildup of water vapor slowly increases the pressure on the water’s surface. Eventually, this will slow the boiling, just like higher air pressure would.

three half-empty glasses at t=8msHowever, the glass and water are now moving too fast for the vapor buildup to matter. Less than ten milliseconds after the clock started, they’re flying toward each other at several meters per second. Without a cushion of air between them—only a few wisps of vapor—the water smacks into the bottom of the glass like a hammer.

three half-empty glasses at t=10msWater is very nearly incompressible, so the impact isn’t spread out—it comes as a single sharp shock. The momentary force on the glass is immense, and it breaks.

This “water hammer” effect (which is also responsible for the “clunk” you sometimes hear in old plumbing when you turn off the faucet) can be seen in the well-known party trick (recorded on Mythbusters, analyzed in physics classes, and demonstrated in countless student dorms) of smacking the top of a glass bottle to blow out the bottom.

When the bottle is struck, it’s pushed suddenly downward. The liquid inside doesn’t respond to the suction (air pressure) right away—much like in our scenario—and a gap briefly opens up. It’s a small vacuum—a few fractions of an inch thick—but when it closes, the shock breaks the bottom of the bottle.

In our situation, the forces would be more than enough to destroy even the heaviest drinking glasses.

three half-empty glasses at t=20msThe bottom is carried downward by the water and thunks against the table. The water splashes around it, spraying droplets and glass shards in all directions.

Meanwhile, the detached upper portion of the glass continues to rise.

three half-empty glasses at t=500ms zoomed out to the table with the optimist (thinking 'Coool!') and the pessimist (thinking 'uh oh.')After half a second, the observers, hearing a pop, have begun to flinch. Their heads lift involuntarily to follow the rising movement of the glass.

two half-empty glasses on the table at t=1s, the third glass breaking into fragments The glass has just enough speed to bang against the ceiling, breaking into fragments…

two half-empty glasses on the table at t=1.5s, the third glass now a mass of fragments raining down from the ceiling.… which, their momentum now spent, returns to the table.

The lesson: If the optimist says the glass is half full, and the pessimist says the glass is half empty, the physicist ducks.

Students & Technology

As an online homework tool and education partner, WebAssign is always interested in the latest technology trends, especially in the student learning community.

Technology has quickly become a critical part of student learning, but check out this infographic to see what devices and methods students rely on most for academic success.
Undergraduate Students & Technology

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Using Physics Clicker Questions with WebAssign

Physics education research has shown that an effective way to increase student conceptual understanding is to increase classroom interaction.  In large lectures, many instructors have done this by posing “clicker” questions during class.  These are short, multiple choice conceptual questions, posed to students during class at regular intervals, that allow students to engage with the material as it is being presented.  Typically, after discussing possible answers with their classmates, students vote for their answer using a personal response system, or handheld “clicker” device.  The polling data is received by the instructor, allowing him or her to instantly see how many students voted for each response.  By getting instant feedback on whether or not students understand the concept, the instructor can then adjust the lecture accordingly.

Many instructors have put a great deal of thought and effort into designing well-crafted clicker questions that get to the heart of student understanding of key concepts.  As part of our commitment to providing a vast array of high quality questions to supplement all teaching styles, WebAssign is pleased to provide the Assessing-to-Learn (A2L) Conceptual Clicker Question collection as an additional resource, available to all instructors, at no additional cost to students.

This collection was created by physics education researchers Robert J. Dufresne and William J. Gerace while at the University of Massachusetts.  Consisting of approximately 300 questions, this resource can be used both in-class or outside class as a great way to help students develop conceptual understanding and qualitative reasoning skills in physics.

You can add these clicker questions to your course by selecting Conceptual Clicker Questions – Assessing-to-Learn under Additional Resources when creating a new course.

Once this resource has been added to your course, you can create assignments using these questions as you would with any other textbook questions in WebAssign.  From the Assignment Editor, click Question Browser, then in the Question Browser window, scroll down to My Resources.  Click Conceptual Clicker Questions – Assessing-to-Learn and from here you will be able to browse chapters and select questions for your assignment.

If you’d like to pose these questions to your students in class, note that it is possible to use WebAssign as a clicker system, provided both you and your students have access to WebAssign in class and your students have access to laptops.  For more information read Using WebAssign as a Clicker System in WebAssign’s Instructor Online Help.

We encourage you to take advantage of this excellent collection of research-inspired questions.  As always, if you need more information, or if you need help adopting this resource, don’t hesitate to contact us!

Happy Thanksgiving from WebAssign!

Here’s an early “Friday Funny” to get you in the holiday spirit!

Q: What do mathematicians eat on Thanksgiving?

A: Pumpkin Pi.

Have a better joke? Send it in here to be posted as one of our Friday Funnies!

Content Services Spares an Afternoon From WebAssign

The WebAssign Content Services team recently took the afternoon off to celebrate the completion of another successful project cycle to go bowling!  A total of 59 projects consisting of over 50,000 questions were added to WebAssign for use by instructors and students this past cycle.  All members of Content Services enjoyed a lunch buffet and two hours of bowling fun at Sparians, a local bowling center.  Eleven teams in all participated in a friendly bowling competition to determine who had the honor of receiving bragging rights in the office, gift cards, and of course miniature bowling trophies!

Our Winning Team!

The “Split Happens” team claimed the day with the Highest Team Average over two games.  The aptly named “Zombowlies” team came “back to life” in the second game to win the Most Improved award.  Lastly, “The Bowling Buccaneers” took the honors for the Most Enthusiastic team as they came dressed to compete in their pirate garb!

The Bowling Buccaneers

With the fun and relaxation over, the Content Services team is back to diligently working on the next project cycle to ensure high quality content is available for our users next year!

Friday Funny

Today’s Friday Funny is brought to you by a WebAssign employee!

Q: Why was the  rubber band pistol confiscated from algebra class?

A: Because it was a weapon of math disruption.

Have a better Friday Funny than this one?  Send it in today!

Tips and Tricks: Rescheduling & Unscheduling an Assignment

Our new scheduling functionality uses a class week model that allows you to easily drag and drop assignments to the specific week you want them to be due on.  However, if you change your mind about the assignment settings, or need to push the due date out a couple of days, rescheduling is as easy as dragging and dropping your assignment to another week.  You can also use the Actions menu to accomplish this same task and both options work for unscheduling assignments completely.

For more details on rescheduling and unscheduling assignments check out the tutorial video below that demonstrates this process step by step.  For further help on scheduling or creating courses please visit our online Instructor Support or Video Tutorials page.