## mechanics

• ### A Festive Time: Happy Isaac Newton's Birthday

Alas, Isaac Newton did not actually suddenly understand gravity due to an apple falling on his head. He might have eaten lot of them, though, as he was stuck at home avoiding a pandemic while he was studying it. Sound familiar, anyone?

But, nonetheless, this week is his birthday! So we're sharing a fun resource about Newton's Second Law of Motion, which to give you something to play with at home this week while there's not much else going on... and while you're waiting for classes to start up again so you can see some of our demonstrations of Newton's 2nd!

The PhET Collection at the University of Colorado has a delightful simulation of Newton's second law in action: Forces and Motion.  There are four different simulations within this one site.

The first, Net Force, is shown in the image below. A wagon (which appears to be loaded with candy, potentially a sticky situation) has ropes coming off either end. You can drag pulling humanoids onto the rope on either side; the different sizes are scaled to represent the different force they can apply. Try combining different forces, then press “Go” and watch the wagon start moving. You can add and remove figures from the task to change the force beforehand and while it’s in motion, to see how changing the force changes the acceleration.

The second simulation, Motion, has a skateboard on a level plane; you can load people or objects (a box, a trash can, a refrigerator) onto the skateboard and give it a push; see how changing the force or the mass changes the motion.

The third, Friction, gives us pretty much the same setup – but without the skateboard! See how the force of friction slows the motion compared to moving on the skateboard.

And finally, Acceleration adds a very simple accelerometer to the setup: a bucket of water! See how the angle of the water’s surface changes as different forces are applied. Fortunately, the bucket doesn’t appear to be able to fall off and get everyone wet, always a good thing on a chilly day.

See you in January!

• ### Atwood's Machine: Testing Newton’s Second Law

Figure 1

Atwood’s Machine is a device initially developed by George Atwood in the 18th century as a way of testing Newton’s Laws mechanically. We have a three demonstrations of this device, C4-21: Atwood Machine, C4-22: Horizontal Atwood Machine, and C4-23: Atwood Machine with Heavy Pulleywhich can be used in the classroom to measure the acceleration of masses under gravity.

At its simplest, Atwood’s Machine is a pulley with a string over it, with an object hanging on each end of the string, pulled down by gravity. According to Newton’s Laws, the force on each end of the string is dependent on the mass. In Atwood’s idealized, theoretical mathematical model of the experiment, the pulley and string themselves have no mass, so only the hanging objects’ mass we add affects the force.

So long as the masses are equal, there is the same force pulling down on each object – so there is no net force on the system. So if the two objects start out stationary, they remain stationary, by the principle of inertia. If they start out moving, they continue moving at the same speed (until they run out of string).

If one mass is greater than the other, then there are different forces acting on each end, so there is a net force on the system. This net force will cause the masses to accelerate. But this is where it gets complicated: the force on each end of the string from gravity is proportional to the mass on that end. But because the masses are tied together and transmit force to each other through the tension in the string, the acceleration is proportional to the net force and to the total mass of the system. But since each of the component forces is proportional to that mass, the final acceleration ends up being proportional to the ratio between the difference in masses and the total mass.

You can also use this device another way – by timing how fast the objects accelerate, if you know their masses, then you can measure the force of gravity!

In a real experiment, of course, the string and pulley very much do have mass. Additionally, there is another source of force on the system: the friction in the pulley. This frictional force acts to reduce the speed of the moving masses. Additionally, the force from gravity must move the mass of the rotating pulley as well as the mass of the hanging objects.

For one version of this demonstration (figure 1 above), we carefully chose a pulley with a very low mass, so it behaves very much like the theory predicts.

For the other (figure 2 below), we have a much heavier pulley. It has greater mass, and thus accelerating the hanging objects also means overcoming the pulley’s inertia as well.

Figure 2

This is an important aspect of the difference between theory, simulation, and experiment, and valuable to talk about in class. In a theoretical model, we can propose things that don’t really exist in the real world – massless strings, frictionless pulleys, objects of constant mass but zero size. We use these theoretical experiments to test out theories mathematically, to see if our theories will give results that make sense, and to plan an experiment.

With a real experiment, there are more variables we have to take into account that can affect the results – friction, inertia, heat, objects that stretch and swing and wear down over time. But it’ is these real-world experiments that let us take that final step and ensure that our theories accurately predict the outcome of real-world physics.

A simulation is somewhere in between the two. We can simulate a physics experiment inside a computer, as another way of testing our theories. This has its own limitations, since the computer only knows about the laws of physics we program into it – if our initial assumptions are wrong or if we set them up incorrectly, the simulation may give inaccurate results. But the simulation lets us try out many combinations of factors in succession, making tiny changes each time, in ways we might not be able to in the laboratory. It’s much faster to adjust a measurement in a simulation than it is to build a new device on the workbench.

And, importantly, we can use a simulation to practice an experiment when we can’t get to the laboratory at all!

This simulation, by Andrew Duffy of Boston University, lets us try out the Atwood Machine at home on our computers, or on the screen in the classroom http://physics.bu.edu/~duffy/HTML5/Atwoods_machine.html

We can vary the mass of each of the two hanging objects, from 0.1 kilograms (100 grams, about the mass of a small bar of soap) to 2 kilograms (2,000 grams, close to the mass of a 5-pound bag of flour). You can set the masses and then start the simulation running, and it will measure the forces and acceleration as it runs. Try it out and see if you can replicate our demonstration, then experiment and test its limits!

• ### Demo Highlight: Air Table

We have many demonstrations of the mechanics of collisions in our collection. You can explore them in section C7 of our website.

Among the most valuable for illustrating all kinds of collisions are the air table demonstrations, the large C7-42 and the smaller C7-43, and their portable cousin the hoverpucks, C7-44. All three of these demonstrations use pucks floating on a cushion of air to allow you to show very low friction collisions with various masses. The air tables use an air blower beneath the surface, while the hoverpucks have their own integral fans so they can skitter across the floor of the classroom. All three, of course, require quite a bit of space to use!

So it’s a valuable supplement to them that the PhET Collection at the University of Colorado Boulder has introduced their online simulated Collision Lab, which lets you experiment with collisions of pucks at the comfort of your desk or couch. You can use the air table in the classroom, then try to replicate the experiment at home for further analysis!

• ### Demo Highlight: Free Fall in Vacuum

This week we’re taking a look at an ever-popular demonstration of the laws of motion: Free Fall in Vacuum. You can see it presented in this new video starring Logan Anbinder.

A heavy disc and a lightweight feather are contained in a long glass tube. While the tube is full of air, when you flip it over the disc drops quickly to the bottom, and the feather floats slowly downwards. Once most of the air has been pumped out, however, the two fall together and hit the bottom at the same time.

When no other forces interfere, the two objects experience the same acceleration from gravity. While there is air in the tube, however, air resistance slows both objects, but the feather more so than the disc due to its lighter mass compared to its surface area. This is an excellent example of why, when solving physics problems, we need to identify all of the forces involved in a system and determine their effects.

This demonstration is a classic way of explaining the nature of free fall and gravitational acceleration. Perhaps one of the most dramatic presentations of it came in 1971 when astronaut David Scott carried out this experiment with a hammer and feather on the Moon! Without air, the feather and hammer dropped together to the lunar soil. You can see the video in a NASA archive website here, hosted by Goddard Space Flight Center: https://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_15_feather_drop.html

• ### Demo Highlight: Funnel Cart

Happy New Year, all, and welcome back to the physics demo highlight of the week! This week we’re taking a look at a classic kinematics demonstration, the funnel cart. It’s presented in this new video starring Ruhi Perez.

When we push the cart forward, both the ball and the cart are traveling horizontally with the same velocity. When the ball is launched, it has a new motion and velocity in the vertical direction. Even though the ball now has a second, vertical motion, its horizontal motion will not change. Thus, the ball and the cart travel the same horizontal distance in the same amount of time, and the ball lands in the cart! Since the funnel catches the ball, we can clearly see that this demo shows the independence of motion. It is interesting to note that to you and me, it appears that the ball traveled in a parabola or an arch. If you were sitting in the funnel and looking up at the ball, moving with the cart, it would appear that the ball only traveled directly up and then directly back down again! This is an example of examining a physical phenomenon in different reference frames.

For added challenge, consider: What would happen if the track were placed on a slope? Or if the cart had an engine that made it speed up over time? Or if we hung a weight on a string off the end to drag the cart fowards, or to slow it down?

• ### Demo Highlight: Hydraulic Press

Demonstration F1-11: Hydraulic Press is a popular and dramatic way of illustrating Pascal’s Law. See it in action in this new video starring engineering student Sarah Hall:

Pascal’s Law states that, given an incompressible fluid, any change in pressure at one point in the fluid is transmitted throughout that fluid. In a closed container, like this hydraulic cylinder, that pressure exerts a force perpendicular to the walls of the container. The force is dependent on the pressure and on the area. Here, that force is then transmitted up into a wooden board, breaking it.

You can see this illustrated in this EduMedia animation: https://www.edumedia-sciences.com/en/media/442-hydraulic-lift

Experiment with it yourself and see how the force vectors change with area in this simulation by Seng Kwang: https://physicslens.com/hydraulic-press-simulation/

• ### Demo Highlight: Newton's Cradle

A popular demonstration for illustrating elastic collisions and the conservation of energy and momentum in the classroom is C7-11: Collisions of Balls of Equal Masses. Also popularly called Newton’s Cradle, as it helps us illustrate Newton’s laws of motion even if Newton himself may never have had one, you can find these in many places as entertaining desk toys; but they show us some important physics.

You can see the demonstration in action in our new video featuring Dave Buehrle.

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The simplest and most straightforward explanation for the behaviour of this device is just that – that it is an application of basic conservation laws. The collisions between these hard steel spheres are very nearly elastic, so nearly all of the momentum of the incoming spheres is transferred to the outgoing spheres, and nearly all the energy as well so they rise to the same height on the other side. A pendulum swinging back and forth is a classic illustration of the exchange between kinetic energy (from the velocity of the pendulum) and gravitational potential energy (the potential energy the stationary pendulum has as a result of its position when paused at the top of its swing). And this demonstration is, in a sense, just a set of pendula all swinging together, exchanging their energies and momenta, and we can simplify it be treating only the displaced balls as a single pendulum.

Try it out at home and see what happens when you change the number of balls you move and how far you move them.

However, we can also explore more complex analyses. We could also analyze the system as a series of coupled oscillators, transferring energy between them much like a phonon in a crystal lattice – the “wave” of motion does have an observable speed, after all, so we could look at it as a propagation problem. Or we could treat each ball as a mostly elastic but slightly inelastic mass, and calculate its interactions with each of the other balls. This might give us an even more accurate picture of

This is a good example of just how the process of doing physics works. No mathematical model of a physical system is every perfect, and different models can be “right” for different situations. We choose the way of modeling a system that bests helps us understand the system at the level we need to understand it at, whether it’s an atom or a galaxy or a desk-top toy.

• ### Demo Highlight: Pendulum Length Ratio

This week we’re taking a look at a popular demonstration of simple harmonic motion, G1-15. This demonstration consists of a pair of pendula, with one four times the length of the other. You can see them in action in this video with PhD student Subhayan Sahu.

We can see that as the pendulum oscillates, its period is proportional to the square root of its length. The fact that a simple pendulum’s period is dependent only on its length and on the force of gravity is very handy for other purposes, too! Mechanical clocks are built around a pendulum for this reason, and if you have no clock at all you can make a simple time-measuring device by just making a pendulum and counting its oscillations. Very sensitive measurements of the motion of a pendulum have even been used to measure minute differences in the force of gravity, letting us map Earth’s gravitational field.

You can also experiment with this at home, with any heavy object and some string. (But advice: ask before using somebody else’s shoelaces for this, they might need them!) If you’re short on string, or if you want to try adjusting different variables at the same time to see how the pendulum’s motion changes, you can also check out this simulation at The Physics Aviary: https://www.thephysicsaviary.com/Physics/Programs/Labs/PendulumLab/

• ### Demo Highlight: Racing Balls 2

Earlier this summer, we introduced these demonstration highlight of the week articles with the Racing Balls demo. It’s been one of our most popular ever! This week we’re returning to it to check out some new resources.

Thanks to a UMD Teaching Innovation Grant, we’ve created new videos of many demonstrations, including this one, where Eliot Hammer presents the Racing Balls demo!

And Don Lynch has created a new animation of the demonstration as well, seen here:

This lets us see the balls in motion and compare their positions to an energy graph, showing the transition between kinetic and potential energy and how it affects the motion of the balls in the tracks. The balls each begin and end with the same potential and kinetic energy and the same velocity. But for a distance in the middle, the ball on the lowered track exchanges some of its potential energy for more kinetic energy, and a greater velocity. When the track returns to the original height, the ball is back to having the same potential and kinetic energy, and the same velocity it started with. But in the meantime, it has moved farther ahead in space during the time it had greater velocity, and so reaches the end of the track first.

This is a valuable way of showing the relationship between energy and velocity, and between velocity, position, and time. It’s also a good example of how the combination of real-world demonstrations and simulations can enhance our physics teaching.

Check out additional videos, animations, and simulations in the Tools & Resources menu above!

• ### Demo Highlight: Rolling vs. Sliding

This week we’re taking a look at a deceptively simple demonstration, D1-61: Rolling versus Sliding. An aluminum cylinder rolls down an inclined plane. An identical aluminum cylinder has tiny bearings on one end, so that when stood upright on that end it effectively slides almost without friction down the incline. You might invite your students to make a prediction: If the two cylinders are started from the top at the same time, will the rolling cylinder or the sliding cylinder reach the bottom of the incline first?

The two cylinders start at the same height with the same potential energy. As they slide or roll down the ramp, that potential energy is converted into kinetic energy. Linear kinetic energy is proportional to the mass of the cylinder and the square of its velocity. However, the rolling one also has rotational kinetic energy, which is proportional to the moment of inertia of the cylinder and the square of its angular velocity. So for the rolling cylinder, some of the potential energy is converted into rotational kinetic energy as it rolls, and only some of the potential energy is converted into linear potential energy, giving it a lower velocity as it goes down the ramp.

So the sliding cylinder reaches the bottom first!

It can be helpful to illustrate this exchange of energies with graphs. Andrew Duffy at Boston University has created simulations with animated energy graphs, one here for a mass sliding down a ramp, and another here for a mass rolling down a ramp. Try them out for yourself! You can see that the potential and kinetic components always sum to the same total energy, showing that energy is conserved.

• ### Demo Highlight: Suspended Slinky

This week, we’re taking a look At the ever-popular demonstration G3-28: Suspended Slinky®. This handy device lets us demonstrate both transverse and longitudinal waves in the classroom. You can see it in action in this new video with physics student Jeffrey Wack.

As Jeffrey shows us, there are two directions that matter when characterizing a wave: the direction of propagation, where the wave as a whole is going; and the direction of displacement, the motion of the individual elements that make up a wave. In a longitudinal wave, these are parallel – the individual particles of air in a sound wave move back and forth in the direction of travel of the sound, or the individual loops of wire in a spring move back and forth along the length of the spring. In a transverse wave, by contrast, they are perpendicular – the electric and magnetic fields in a radio wave oscillating perpendicular to the direction of propagation, or the loops of a spring swinging side to side as a transverse wave moves down the length of the spring.

There are many kinds of waves in the world, some transverse and some longitudinal, and some that combine characteristics of both! These animations by Dan Russell of Penn State illustrate some examples of this, such as waves in water where the individual water molecules are actually moving in a circle as the wave propagates through.

You can experiment with comparing longitudinal and transverse waves at home with this simulator from Tom Walsh at oPhysics. Try setting different amplitudes and frequencies, and see what changes in each wave as you do so.

• ### Demo Highlight: The Racing Balls in Slow Motion

Ready for a fun kinematics experiment you can experience and learn about from the comfort of home?

Demonstration C2-11: The Racing Balls is one of our most popular kinematics demonstrations, as it presents an interesting conundrum.

We have two long tracks, on which a pair of equal-mass billiard balls can roll with very little friction. At one end is a spring-loaded launcher that can send the balls rolling down the tracks with the same initial speed. One of the tracks remains straight and level all the way to the end. The other slopes down to a lower height, runs level at that height for a short distance, then slopes back up to the original level again.

The challenge for you all is to predict what will happen when the balls reach the end of the track: will the ball on the straight track reach the end first, will the ball on the dipped track reach the end first, or will the get there at the same time?

Here’s what happens:When we release the spring, the balls start forward with the same speed. The ball on the rear track, which is straight, travels with this same speed the entire length of the track, until it reaches the end.

But when the ball on the bending track reaches the downward slope, it increases in speed as it goes downhill, as we see in this short video.

While that ball rolls along the flat lower section of track, it does so with this greater speed. So it covers this distance in less time than the ball on the higher track does. When the ball on the bent track rolls back uphill, it slows down to its original speed. Now this ball has undergone two periods of acceleration: a positive acceleration as it gained speed, and a negative acceleration as it lost that speed again. Let’s see that in slow motion in this video clip

So the two balls both have the same speed again when they reach the end of the track. But they don’t get there at the same time; the ball from the bent track gets there first!

The ball on the bent track had a higher speed for a short time, while it was on the lowered section of track. This means that when you take the entire trip into account, that ball had a higher average speed, even though its initial and final speeds were the same.

For further discussion, consider other ways you could analyze this problem. Can you separate out the force vectors acting on each ball? Can you calculate the energy of the system? Will this help predict the result, or not? This is an important question to look at when studying any problem – deciding which variables matter and need to be measured in order to predict the outcome.

• ### Demo Highlight: The Ripple Tank and a Ripple Tank Simulator

.Welcome back! This week, we’re looking at one of our particularly popular and versatile demonstrations, the Ripple Tank.

The Physics Demonstration Facility has two versions of this demo, so we can reach as many audiences as possible. We have a table top version for outreach events and local classrooms, and a portable version to reach out-of-building locations. These ripple tank demonstrations can both be used to highlight a variety of wave phenomena.

A properly set up ripple tank with its various accessories, can illustrate many different aspects of the physics of waves – single and double point source circular waves, plane waves, interference, diffraction through openings and around obstacles. With a movable mount and careful planning, it can even show the Doppler effect!

Some of this is hard to do at home, but fortunately, there are options. Simulators exist that can carry out at least some of the experiments you might usually use the ripple tank for. You can take screenshots of them to illustrate lectures, or send the link to students to experiment with at home.

There are several different ripple tank simulators, such as this versatile one from Paul Falstad: http://www.falstad.com/ripple/

• When first opened, the simulator defaults to emulating a tank of water with a single oscillating source in it. It is tinted a cerulean color for easy viewing, but can be switched to several different color schemes via a drop-down menu. If you prefer the traditional view, #4 on that menu is a greyscale view that closely approximates the familiar shadow projection of the tabletop ripple tank.

• A checkbox below this allows the simulation to be frozen and restarted; another lets you shift to an angled three-dimensional view that can be more difficult to see on small screens, but can be helpful in clarifying complex wave behaviour.

• Sliders adjacent to this let you vary the frequency of the oscillation, and turn on damping.

• Other sliders let you adjust aspects of the simulation process, changing the speed, brightness, and resolution of the simulation box; these are best left alone unless you are struggling with making it work on a slower computer or are having difficulty clarifying complex wave behaviour at an interface.

• In addition to the preprogrammed oscillators, you can excite the simulated ripple tank manually by clicking on it, just like dipping your finger into the water of a real ripple tank.

• A variety of oscillation sources and tank configurations can be selected from the Example dropdown menu. Some likely to be useful for our purposes include:

1. Single Source and Double Source for circular waves from point sources

2. Plane Wave (which does show edge effects at the sides of the “tank”)

3. Single Slit and Double Slit which show diffraction via a plane wave striking a barrier with one or two holes and producing the expected circular waves and interference pattern

4. Obstacle (with a single source circular wave and a small rectangular barrier)

5. Doppler Effect 1 (with a moving source of circular waves).

• For more complex uses, you can also modify the simulation. By right-clicking in the simulation box, you can place additional sources, barriers, and refracting elements. You can also right-click on existing elements and delete them, allowing you to clear the screen and produce an empty “tank” to create your own experiment in.

• You can also place “probes” that will display the wave pattern at that point in a movable oscilloscope-style box. This can be valuable as a challenge for students, to predict the pattern that a probe would read at a given point, or to construct a simulation to produce a particular result.

• ### Demo Highlight: Vector Addition

A vector is a mathematical construct that has two traits: a magnitude and a direction. Many common quantities in physics, like velocity and force, are vectors. Adding together two vectors is not as simple as just adding the magnitudes together; because a vector is pointing in a particular direction, you have to add together the components of the vectors in any given direction to find out the final vector’s total magnitude and final direction. For example, if you tell someone to walk three meters east and then four meters north, they are not actually seven meters away from where they started!

In physics, we often need to add vector quantities, and we have developed several demonstrations to help model this.

Demonstrations A2-22: Magnetic Vectors and A2-24: Vector Algebra are a popular way to provide visible, manipulable vector models in the classroom. Magnetic vectors of several lengths can be attached to the lecture hall chalkboards, and a projected grid can both serve as length measurement and provide axes. If we rotate the grid, we see that the vectors themselves, and their sum, stay the same even if we’re measuring them on different axes.

Demonstration C2-41 presents a physical example of adding vectors together. Two hammers are mounted 90 degrees apart above a ball. If we drop one hammer, it hits the ball and sends it in one direction. If we drop the other hammer, it hits them ball and sends the ball in a direction 90 degrees off from the first. If both hammers strike the ball at the same time and with the same force, the ball moves off faster, and at an angle 45 degrees between the two. One force vector produces an acceleration in the same direction as the force; adding two force vectors gives an acceleration in the direction of the sum of the two forces.

You can try this out at home, if you happen to have some balls and mallets and a lot of patience. But if you don’t, or if your family gets upset when you break things, you can try out vector addition with a simulator instead.

This simulator (linked here), developed by Dr. Andrew Duffy of the Boston University physics department, allows you to add vectors together at home without the risk of breaking any windows. The simulator is set up to add direction vectors together, but as we have seen with the model vectors in the classroom, the addition is the same no matter what the units are.

Two sliders let you adjust the length, or magnitude, of each vector. Two more let you adjust the angle each vector makes with the horizontal axis. If you want to add two vectors at right angles, like our demonstration with the hammers does, set one to 0 degrees and one to 90 degrees, then set the two magnitudes equal. You should see a new sum vector that connects the two. On this graph, the vectors are added up tip-to-tail, rather than all starting from the same point like the velocity of a ball does. But as we saw in the photos of the demonstrations above, the addition is the same no matter how we slide them around! Changing the axes doesn't change how the underlying mathematics works.

Now try experimenting – change the magnitude of one vector and see how that change affects the sum. Try changing the angle. See if you can do it in reverse – note what the sum of two vectors is, change one of the vectors to that magnitude, then change the angle to see what angle you need to get the original vector’s magnitude out.

• ### Demonstration Highlight: Astro Blaster

This little toy, C7-18 in our collection and sold in many shops as the Astro Blaster, is a fun way to demonstrate some interesting and complicated collision physics. John Ball presents it in this video:

This device has four balls of graduated masses on a central shaft. When the whole assembly is dropped, the smallest ball on the end flies with considerable velocity, potentially rising to significantly greater than the initial height.

The balls are highly elastic, and when they collide, they transfer much of their energy to the smallest ball, which has a slightly larger hole in it and thus is the only one free to move off the shaft. Since it now carries the kinetic energy of the greater mass of falling balls, it can bounce higher than it started! Meanwhile, the rest of the balls fall quietly (more or less) to the surface.

It is believed that the use of this kind of collision in physics classes was initiated by Stirling Colgate of Lawrence Livermore National Laboratory. It was also popularized by an article in The Physics Teacher by Richard Mancuso and Kevin Long,  https://aapt.scitation.org/doi/abs/10.1119/1.2344238 .

Once you’ve seen it in action in the video, you can also try it out in this simulation. Or try it at home with a couple of elastic balls, one high mass and one low mass, such as a small rubber ball and a well inflated basketball. If you can drop them together (this takes practice), you should see the smaller ball bounce away with much greater velocity. Just try not to break anything!

• ### Demonstration Highlight: Brass Barbell

This week we’re taking a look at a classic illustration of center of mass: the Brass Barbell. This simple device is a brass rod with solid brass discs on either end, one larger than the other. It can sit balanced on a stand; but, because the disc on one side is larger and thus more massive than the other, its center of mass, the point at which it balances, is not in the geometric center of the rod.

You can see this in this video with Dave Buehrle:

As Dave explains, what we see here is the equilibrium of torques – the relationship between the force of gravity pulling down on the mass with how far that mass is from the center. When the barbell is balanced at a point where those torques are equalized, it stays at rest and doesn’t fall off the stand.

You can try this out in the classroom, at home, or anywhere else! You just need a long rod with different weights at either end - try a broom, a screwdriver, or a pencil with a big stick-on eraser.

• ### Demonstration Highlight: Centers of Mass

Continuing the theme of Center of Mass, this week we’re taking a look at two more popular demonstrations. Demo B1-01 shows us that how an object hangs when suspended is dependent on its center of mass. We can use this to locate the center of mass of an irregularly shaped object, as you see in the picture here.

Demo C1-02, in turn, looks at the center of mass of an irregular object in motion. As this very familiar irregularly shaped object tumbles through the air, its ends seem to be moving every which way. But the center of mass follows a parabolic path, just like a simple thrown ball.

The UNSW School of Physics has some videos analyzing this. You can see how the ends of an object or the limbs of a running athlete move through the air, while the center of mass traces out that same parabolic path. And they found the center of mass of a runner the same way we did with the plunger: just see where it balances!

https://www.animations.physics.unsw.edu.au/jw/centre.html

• ### Demonstration Highlight: Chaotic Pendula

Welcome back to the Demonstration Highlight of the Week! This week, we’re taking a look at demonstration G1-60: Chaos with Two Bifilar Pendula. You can see the demonstration in action in this video featuring doctoral student Subhayan Sahu.

We have two essentially identical sets of physical pendulums suspended from a single rod. The physical laws governing their behaviour are quite simple, merely the conservation of linear and angular momentum and the force of gravity. The two pendulums are started into apparently identical oscillations, but starting the pendula with identical initial conditions is nearly impossible. So no matter what, their motion soon diverges. No matter how closely the motions of the two pendulums are started, they eventually must undergo virtually total divergence. This extreme sensitivity to initial conditions is a form of chaos, the mathematical study of irregularity in dynamical systems.

Wikipedia has a surprisingly good article on the mathematics of the double pendulum. (https://en.wikipedia.org/wiki/Double_pendulum) Also, Eric Neumann has created an online simulation that can be used to model one of the legs of the pendulum. Try experimenting with the simulation as well, and see how sensitive it can be to its initial conditions. (https://www.myphysicslab.com/pendulum/double-pendulum-en.html)

• ### Demonstration Highlight: Double Cone

The Double Cone is a sometime-puzzling and always fun demonstration of equilibrium and inclined surfaces, and a good way to challenge your students to think hard about an apparently paradoxical result. We have both large (demonstration B1-06) and small (demonstration B1-07) versions in our collection, for use in any size of classroom.

The device consists of a solid wooden double cone, resembling two cones placed base to base. They rest on a sloping track. When released in the middle of the track, the cones appear to roll uphill! And in one sense they do, but in a more fundamental sense they do not.

The track consists of two rails in a triangular shape, joined at the base and widely separated at the upper end. The key to the demonstration is the carefully planned difference between the angle of the slopes of the cones, the slop of the ramp, and the angle of the separation of the rails. As the double cone rolls “up” the ramp, the center of mass is actually getting lower

Check out this animation at +plus magazine https://plus.maths.org/content/defying-gravity-uphill-roller to see an excellent diagram of how this works, and why.

You can read more about the physics behind this in several physics journal articles:

N. Balta, New versions of the rolling double cone, TPT 40, 156-157 (2002).

S. Ghandi & C, Efthimiou, The ascending double cone: a closer look at a familiar demonstration, EJP 26, 681 (2005)

J. Havill, Defying Gravity: The uphill roller, +plus magazine (2006)

• ### Demonstration Highlight: Eddy Current Pendulum

Today we’re looking at an exciting demonstration of electromagnetic induction: The Eddy Current Pendulum, seen in this video starring physics student Dan Horstman:

We have a very strong permanent magnet mounted at the bottom of an aluminum stand. We can install a variety of pendula to swing from the top of this stand. As the pendulum swings, the bob passes between the poles of the magnet. With a wooden bob, the pendulum swings freely, just like we would expected it to do without the magnet there; this is unsurprising.

A conductive copper pendulum bob, though, shows very different behaviour. While copper is not innately attracted to a magnet the way iron is, it is an electrical conductor. As the copper plate passes through the magnetic field, it experiences a changing magnetic flux. The laws of electromagnetism tell us that a conductor in this situation will have an induced electric current.

Loops of current, called eddy currents, form in the pendulum bob. These currents have their own magnetic fields, which interact with the magnetic field of the permanent magnet and slow the pendulum’s motion. The energy of the pendulum’s motion is gradually dissipated in this way, and the pendulum slows and stops.

This is a nice way to see electromagnetic induction in action. This effect also has many practical uses. Just like the magnetic field slows and stops the swing of the pendulum, eddy currents can be used to make brakes for vehicles! Automobiles, trains, and even roller coasters can use this process to slow their wheels without friction, reducing wear.

But there are other cases where you actively want to prevent eddy currents – if you’re trying to avoid losing energy! For example, conductive components of electrical transformers might be made with insulating gaps to make it harder for eddy currents to form, so you lose less of your electrical energy to heating up the transformer. Metal pendula with interruptions can model this behaviour as well.