One of the most popular and visually stunning illustrations of buoyancy and relationship between temperature and pressure is the hot air balloon. Some of you may have had a chance to see one recently at our Maryland STEM Festival event, FLIGHT!

 A hot air balloon rises in the air as a result of its buoyancy. As the air is heated, the increased average kinetic energy of the particles in the gas mean its average density is less, and so it rises through the air. In the outdoors, a modern hot air balloon carries its heat source with it, and can keep the air at a constant higher temperature, so the balloon will rise until it reaches equilibrium at an elevation where the density of the outer atmosphere is no longer sufficiently higher than that of the air in the balloon.

 Our demonstration balloon, however, more closely resembles the earliest experimental crewed hot air balloons, which heated the air with a heat source located on the ground (a bonfire then, an electric heat gun for us). So these balloons rise only until they have gone too far from the fixed heat source and the air begins to cool down again, reducing buoyancy until they settle back to the ground – or return to the heat source!

 The earliest records of the development of uncrewed hot air balloons, like ours, go back over 1,000 years in China, and are recorded some other parts of East and Southeast Asia as well. The were used for entertainment purposes and for signaling between distant points. The earliest known crewed hot air balloon experiments currently known date to the eighteenth century in Europe, though others may have occurred earlier elsewhere.

 Simple hot air balloons are easy to make, and are a fun home experiment. Larger demonstration models can be valuable in class to spur discussion of buoyancy and the behaviour of gases, and studying the history of both the technology and the theoretical understanding of their thermodyanmics can be a useful and interesting student project.

This is a simple demonstration, that students can easily try at home. It can also be valuable in class, and is recommended for introductory mechanics lectures. It is perhaps most suited to the second day of discussing center of mass and balance, after students have been introduced to the absic concept of what center of mass is and how it affects the equilibrium position of an object under gravity.

An empty soda can can sit upright on its bottom, or can be laid on its side, but cannot be at rest at any angle between these. However, this can be changed by adding a liquid to the system.

Pour approximately 150ml of water into the can, and then try carefully balancing the can at an angle, as seen in the photo above. (This may require experimenting to find the exact right amount of water for any given can; we recommend doing this in front of the class so they can see the process.)

Ask your students why this should happen? The mass has increased, but why does that change how it balances? The water moves when the can tilts, causing the center of mass to shift – with just the right amount of water, the new center of mass will be above the edge of the can, and so it will balance.

Some cans will tend towards a particular orientation and will roll along the edge to that point; invite students to hypothesize why this is. They may see that the location of the hole and tab in the top of the can affects the equilibrium position – consider how this can be used in class to relate to the concept of symmetry. The can’s behaviour as it reaches equilibrium is a damped harmonic oscillation, and is a good introduction to how fluid action can cause damping from within a system, as well as from an external source.

As you plan for your next class, check it out on our website at B1-18: Center of Mass - Soda Can and Water.

Happy Labor Day to all in the US!

(and belated greetings to readers elsewhere for whom Labor Day was in May.)

This holiday celebrates all kinds of work, but in physics Work is a more specific and mathematically defined quantity Today we’re taking a look at a couple of recent articles in The Physics Teacher that related to the concept of work in the classroom.

In physics, work is the energy transferred to or from a body via the application of force over a distance. Positive work is work done in the direction of motion, negative work is done in the opposing direction (or has components in those directions, in a 3-dimensional system). We sometimes, conversely, refer to energy as the ability to do work.

A recent paper in The Physics Teacher by G. Planinšič & E. Etkina, “Boiling water by doing work” (https://doi.org/10.1119/5.0049411), shows some of this relationship between work and energy. As work is done on a system, moving a rope, some of the energy in the system is dispersed as heat. This heat is then seen to boil water. In their videos (linked in the article), you can see the relationship between work done on the system and temperature, and calculate for yourself the efficiency of energy conversion.

A paper in The Physics Teacher last year by P. Gash looks at potential energy and work in a more familiar mechanical system: a Slinky. In “A Slinky’s Elastic Potential Energy” (https://doi.org/10.1119/1.5145416), we can see a detailed breakdown of the forces acting on the coils of a Slinky. You can check out the experimental data for yourself and calculate the work done by gravity on the spring. It’s a handy reminder that work in the physics sense doesn’t always mean human labor!

We have many demonstrations in our collection relating to physical work. Section C8 of our demonstration index is all about the mechanics of energy, power, and work; all are useful in the classroom, and many can be tried at home as well with materials you have on hand! There are many other demonstrations that explore energy and work as well, from thermodynamics experiments like the one in the paper above, to the newly repaired J4-31: Energy Stored in a Capacitor, which shows a capacitor that holds enough energy to let a motor do the work of lifting the capacitor itself against gravity. Now that’s a nice bit of work!

This week we’re introducing a new feature of the blog: STEM News Tips. Every week we’ll be bringing you short introductions to recent publications and current events in physics, physics education, and adjacent fields.

 This week, we’re checking out a new paper from Timo Reuter and Miriam Leuchter in the Journal of Research in Science Teaching. (https://doi.org/10.1002/tea.21647). In Children's concepts of gears and their promotion through play, Reuter &Leuchter surveyed how young people came to understand a simple machine through hands-on interaction. Interactive and experiential learning is a vital part of modern STEM education, and something we try to promote through our demonstrations and programs.

 The relationship between turning direction, turning speed, and the arrangement and size of interacting gears is a basic concept in introductory mechanics. Before students can truly comprehend the mathematics of force and torque, they need to have an intuitive familiarity with how such objects interact in the real world. It’s valuable to take a look at how young children begin to grasp these concepts years before they come to high school and university physics classrooms.

 Check out the article here! https://onlinelibrary.wiley.com/doi/full/10.1002/tea.21647

A question that came in via Twitter recently is one that comes up a lot this time of year, as we tend to want to spend more and more time curled up with a warm beverage. How does my little round teapot fill up so many cups? And why is the tea in the pot still warm when the tea in my cup has gone cold? The answer comes down to geometry!

Here’s a pretty ordinary sized teapot from the cabinet, and an official UMD Physics mug. We’ve tested it twice today and confirmed: This teapot can fill this mug six times. Sure, the pot is bigger than the mug, but it doesn’t look that much bigger, right?

The teapot can even fill this bigger UMD Physics travel mug four times! How?

The answer is related to what biologists call the Square-Cube Law. As an object grows in size, its volume increases faster than its surface area. If you take a cubical container and double its length, width, and height, multiplying by 2 in each direction, then its surface area is multiplied by 4, the square of 2. But its volume is multiplied by 8, the cube of 2. The exact numbers will change, though, depending on the shape of the container. Every shape has its own relationship among liner size, area, and volume. As it turns out, the most efficient shape, with the highest ratio of volume to surface, is a sphere.

This sounds like just abstruse math, but it actually explains a lot about things we deal with every day, from teapots and fuel tanks to giraffes and polar bears. (OK, maybe not all of us deal with polar bears every day, but it’s good to know about them anyway.)

Here’s an example from the demonstration collection. This round flask and this tall cylinder each hold the same volume of water, 500 milliliters. The cylinder is much longer and narrower than the sphere, so it looks bigger, but it has the same volume!

One thing that makes this interesting is that, having a larger surface area, the cylinder is also heavier. It takes more glass to make a 500mL cylinder than to make a 500mL sphere. That might not matter much for our purposes, when we just want one container to sit on the table, but it can make a big difference in large storage containers, or in places where weight is important, like spacecraft.

This is also why fluids in free fall, like raindrops, form into spheres. The surface tension of the liquid is pulling inwards, compressing the surface to the smallest area for that volume of water: a sphere. On a larger scale, this even happens to big accumulations of rock, pulled in by gravity over a long period of time. We call them planets – and luck for us, they do tend to end up round!

That’s all interesting, but isn’t my tea getting cold after all this?

No, and here’s why: The total amount of heat in the container is proportional to its volume. But the radiation of heat away from the container is proportional to its surface area. So my nearly spherical teapot loses heat a lot more slowly than that tall cylinder does. Plus, because there’s less surface area for the same volume, we can make the walls thicker for the same weight, giving it better insulation.

And that’s where the polar bears come in. (Not literally, polar bears should not drink tea.) Ever wonder why so many animals in warm climates evolved long, lanky builds, while arctic animals tend to be rounder? A lot of it comes down to heat. A round polar bear loses heat a lot more slowly, so they can burn fewer calories to stay warm. That can be important in the long winters when there’s not much to eat. In a hot climate where the bigger problem is staying cool, many animals tend to be thinner. Others find other ways to increase their surface area, like the big ears on an elephant, to radiate heat away faster. There are lots of other factors at play in evolution as well, of course, but heat is always an important one.

This relates to why animals only come in certain sizes, too. If you scale up an ant 100 times in each direction, its mass increases by one million - but the surface area of its legs doesn't, so it can't stand up!

So sit back, make a pot of tea, and curl up with a good book about somewhere warmer. And spring will be here before you know it!

(Note: No tea was harmed in the creation of this blog post. But quite a lot of it was consumed.)

‘Tis the spooky season, and what could be more seasonal than bats? This week we’re exploring a different kind of bats than the usual, though. So let’s take a swing at the physics of baseball and softball bats!

A baseball or softball bat is an irregularly shaped object that is swung as a lever and then experiences a large impact. This impact sets up vibrations in the bat; you can see several vibrational modes modeled on this webpage created by Dan Russell of Penn State University: https://www.acs.psu.edu/drussell/Demos/batvibes.html He illustrates here that wooden bats are solid, and bend lengthwise, like a tuning bar; aluminum and composite bats, however, are frequently hollow, and can flex across their diameters as well, like a hoop or bell.

One of the most widely recognized specialists in the field of baseball physics is Alan Nathan of the University of Illinois; you can check out his homepage here: http://baseball.physics.illinois.edu/ where he discusses many aspects of the physics of the sport, current and historical. Particularly interesting is his collection of slow-motion images of ball and bat collisions and their analysis: http://baseball.physics.illinois.edu/ball-bat.html .

 You can experiment with this physics yourself with our demonstration D2-21 Center of Percussion: Bat and Mallet. 

 Many articles have been published over the years exploring the physics of bats, particularly with a view to classroom discussion. We’ve collected for you some highlights from the American Journal of Physics and The Physics Teacher, presented chronologically so you can explore the development of this topic over time.

H. Brody. “The sweet spot of a baseball bat”

American Journal of Physics 54, 640 (1986); https://doi.org/10.1119/1.14854

Explores the idea of a bat’s “sweet spot,” the point of impact at which maximum energy is imparted to the ball.

G. Watts & S. Baroni. “Baseball–bat collisions and the resulting trajectories of spinning balls”

American Journal of Physics 57, 40 (1989); https://doi.org/10.1119/1.15864

Examines collisions between bat and ball as rigid bodies.

H. Brody. “Models of baseball bats”

American Journal of Physics 58, 756 (1990); https://doi.org/10.1119/1.16378

Examines collisions between bat and ball and the bat’s vibrations, treating it as a free object in space.

L. L. Van Zandt. “The dynamical theory of the baseball bat”

American Journal of Physics 60, 172 (1992); https://doi.org/10.1119/1.16939

Models the bat as a vibrating elastic mass with a normal mode.

R. Cross. “The sweet spot of a baseball bat”

American Journal of Physics 66, 772 (1998); https://doi.org/10.1119/1.19030

Compares the calculation of a bat’s “sweet spot” as the center of percussion or as a vibrational node.

A. Nathan. “Dynamics of the baseball–bat collision”

American Journal of Physics 68, 979 (2000); https://doi.org/10.1119/1.1286119

Presents a way to model the physics of the collision between a bat and a ball.

A. Nathan. “Characterizing the performance of baseball bats”

American Journal of Physics 71, 134 (2003); https://doi.org/10.1119/1.1522699

Introduces ways of measuring and modeling baseball bats in the physics lab.

R. Cross. “A double pendulum swing experiment: In search of a better bat”

American Journal of Physics 73, 330 (2005); https://doi.org/10.1119/1.1842729

Looks at the motion of a double pendulum and how it can model the swing of a bat or racquet.

R. Cross & A. Nathan. “Scattering of a baseball by a bat”

American Journal of Physics 74, 896 (2006); https://doi.org/10.1119/1.2209246

Examines the relationship between distance, speed, and spin of a ball hit by a bat.

R. Cross & A. Nathan. “Experimental study of the gear effect in ball collisions”

American Journal of Physics 75, 658 (2007); https://doi.org/10.1119/1.2713788

Looks at the possibility of whether slippage between surfaces in a baseball impact can be modeled like meshing gears.

R. Cross. “Mechanics of swinging a bat”

American Journal of Physics 77, 36 (2009); https://doi.org/10.1119/1.2983146

Models the force pairs at work in swinging a bat.

D. Russell. “Swing Weights of Baseball and Softball Bats”

The Physics Teacher 48, 471 (2010); https://doi.org/10.1119/1.3488193

Explores the moment of inertia of bats, commonly called the “swing weight” in sports writing.

A. Nathan, L. Smith, & D. Russel. “Corked bats, juiced balls, and humidors: The physics of cheating in baseball”

American Journal of Physics 79, 575 (2011); https://doi.org/10.1119/1.3554642

Examines the physics underlying several baseball controversies.

D. Kagan. “The vibrations in a rubber baseball bat”

The Physics Teacher 49, 588 (2011); https://doi.org/10.1119/1.3661118

Discusses some experiments with a rubber bat.

I. Aguilar & D. Kagan. “Breaking Bat”

The Physics Teacher 51, 80 (2013); https://doi.org/10.1119/1.4775523

Describes experiments with the breaking points of different wooden bats.

J. Kensrud, A. Nathan, & L. Smith. “Oblique collisions of baseballs and softballs with a bat”

American Journal of Physics 85, 503 (2017); https://doi.org/10.1119/1.4982793

Examines ball and bat collisions with a high speed camera.

K. Wagoner & D. Flanagan. “Baseball Physics: A New Mechanics Lab”

The Physics Teacher 56, 290 (2018); https://doi.org/10.1119/1.5033871

Describes a series of student lab activities to explore the mechanics of baseball.

And one final note, on balls rather than bats: new work in materials science is studying how softer materials inside solid projectiles can affect how they launch. Read all about it in this new post at the American Physical Society website:

Springy Material Boosts Projectile Performance https://physics.aps.org/articles/v13/160

 Update: And for those who read all the way to the end but are still upset about the lack of cute fuzzy bats: "What Bats Can Teach Humans About Coronavirus Immunity" at JSTOR Daily

We’ve all seen this classic stage magic trick: You arrange a nice table setting, with plate and cup and silverware and maybe a nice vase of flowers, on a pretty silk tablecloth. Then you yank the tablecloth out from underneath, but the dishes all stay on the table! We even have a video clip of it here.

 Newton’s First Law of Motion states that an object’s velocity is constant unless there is a net force acting on it. What this means is that if an object is not moving (at rest), it will not start moving until there is a force pushing or pulling on it. If an object is moving at a constant speed and direction, it will keep going with that same speed and direction unless a force pushes or pulls on it to change that. An object’s inertia is its resistance to changing its velocity, e.g. how difficult it is to start it moving from rest.

So that’s what’s going on here. We are applying a force to the tablecloth, pulling it away. But so long as we have a smooth, unwrinkled tablecloth, we’re not applying any force to the dishes, just the cloth. So the cloth moves away quickly, but the dishes stay where they were. This is a very popular way of demonstrating inertia, and you can find it on our website.

The dishes do have a force pulling straight down on them, of course – the force of gravity. They aren’t actually moving downwards because they can’t go through the table. Technically, the table and tablecloth exert an upward force on the dishes, which is formally called the normal force (“Normal” here is using an archaic definition that means “perpendicular to the plane,” not what we usually mean by normal). The normal force here is equal and opposite to the force of gravity, counterbalancing it and canceling it out, so the dishes don’t move. When the tablecloth goes away, the dishes are for a moment not touching anything, so gravity does pull them down a very short distance, the thickness of the tablecloth, and they hit the table with a clatter. But the point is that they don’t follow the tablecloth off the table.

But there can be some more complex issues at work here. Why does it matter that the tablecloth is smooth and unwrinkled? Why do you have to pull quickly on the tablecloth, and not slowly? Why do we sometimes see this trick fail, and end up with the dishes all breaking on the floor? (Please don’t do that.) Perhaps the physics is more subtle than it first appears.

One issue to consider is that force and acceleration are vector quantities; they have a magnitude and a direction. Remember the note above that the “normal” force from the table is called that because it’s perpendicular? That matters here. Newton’s law says that the object is at rest stays at rest until acted upon by a force. That force will then give the object an acceleration in a particular direction. The force we’re putting on the tablecloth is a contact force – we pull on the tablecloth, and it experiences a force in the direction we pull. The tablecloth and table are pushing straight up with a normal force so long as the dishes are touching them. Gravity is different – gravity acts at a distance, and pulls down on things regardless of whether or not they’re touching something.

So gravity is pulling the dishes straight down, the table is pushing the dishes straight up. We pull sideways on the tablecloth. Nothing is pushing sideways on the dishes, though, so they only feel forces going up and down. But! If the tablecloth is wrinkled, then when that wrinkle is pulled against the side of the dishes, it’s now transferring that sideways force we put on the tablecloth into the side of the dishes, and pushes them along… which could mean they follow the tablecloth off the table and onto the floor. So the tablecloth needs to be flat, so that we’re only applying sideways forces to the tablecloth, and no sideways force vectors get a chance to interact with the dishes.

But there’s something else in play here, that makes this complicated: Friction. Specifically, contact friction. This is a force that acts between two object that are touching each other. As we’re pulling the tablecloth past the plate, there is a frictional force between the bottom surface of the plate and the top surface of the tablecloth. How large this force is is partially dependent on the properties of the surfaces and how they interact, what we call the coefficient of friction. This is essentially a way of measuring how rough or smooth the junction between two things is. So using a smooth silk or rayon tablecloth will give a very low coefficient of friction, while a rough wool or linen tablecloth might result a higher one, and thus exert more sideways frictional force on the dishes. If this frictional force is too high, it might be enough to overcome the inertia of the dishes, and drag them along.

Let’s look at a simpler demonstration in our collection, with fewer variables to worry about. Demonstration C3-01 is quite simple: A small steel sphere rests on a stiff piece of plastic, which is resting on a steel stand. Attached to the stand is a spring that you can pull back and release so that it hits the plastic. When it does, the plastic flies out from underneath the sphere, and the sphere drops down and rests on the stand, right below where it was before.

 This demonstration can be valuable in the classroom if you want something a little easier to use than the tablecloth. And it’s also a bit more portable. And, crucially, you can try this at home with materials you probably ready have!

Put a cup or glass on the table, with a playing card on top of it. The card can be from a regular deck of cards, or Yi-gi-oh or Pokemon, or a baseball card or a card from a boardgame, or whatever else is handy; it just needs to be a nice stiff card. Now, get a coin and put it on top of the card, so that the card is holding it above the mouth of the cup.

Now, flick the edge of the card with your finger, quickly and firmly, as seen in this video. You may need to practice this a few times, but once you get the hang of it, the card should fly straight out from under the coin and flutter to the table or the floor. And the coin drops straight down into the cup, just like the steel sphere, and just like the dishes on the table!

 Inertia wins again.

Watch for more secrets of the physics behind these demonstrations in Part 2 of this series, coming soon!