## simulation

• ### Demonstration Highlight: Diffusion Distribution Models

Today we’re taking a look at some models of diffusion: Demonstrations I6-21 and I6-25. These both use the behaviour of ping-pong balls to model the behaviour of molecules in a gas.

Each of these models uses ping-pong balls of different colors to represent different molecules in a gas. In I6-21, we have a mechanically shaken chamber divided by a plastic barrier. We can put balls of one color on one side and balls of another color on the other side. When the chamber vibrates, the balls bounce around like the molecules in a gas. When the barrier is removed, the balls begin to drift onto each other’s sides, and soon there is no distinction between the two.

This is also a good example of the principle of entropy – while it is very easy and probable to disorder this system, as the two sets of balls mix together, it is highly improbable (though not impossible, given a small enough number of balls) that all of the balls of each color will suddenly sort themselves out again! Thus, the system tends towards the more disordered state.

In I6-25, we start with columns of balls at the top of an array of pegs. The balls are held in place by a small plastic baffle. When the baffle is removed, the balls fall down through the array, scattering as they go. By the time they reach the bottom, they have spread out into a curve, roughly approximating a proability graph. The columns at the bottom with more balls are the areas more probable for balls to scatter into, and those with few or no balls are less probable. As with I6-21, we can use different colors of balls to show how gases diffuse together over time.

Now, you can try this in class or at home with this simulation from the PhET Collection at the University of Colorado. You can let a small or large number of particles of two different gases diffuse through each other, and watch their behaviour. How do the simulated particles here resemble the model “particles” of our demonstrations? What’s different? How can we explore the differences when talking about the behaviour or real gases?

And explore more such experiments in our Directory of Simulations!

• ### Demonstration Highlight: Discharging capacitor

Perhaps our most popular and dramatic demonstration of capacitance is demo J4-32: Discharging a Capacitor with a Bang. You can see it in action in this video with physics student John Ball.

Energy is stored in the electric field inside the capacitor. When a circuit is completed by placing a conductor across the poles of the capacitor, that energy is quickly released. Unlike a battery, a capacitor stores energy directly in its internal electric field, which can allo0w it to discharge very quickly. In this case, it does so so rapidly that it actually breaks down the air around the electrodes, discharging with a loud bang and flash of light.

You can experiment with capacitance safely, and learn more about the physics underlying their use, in these simulated Capacitor Labs:

At oPhysics: https://www.ophysics.com/em5.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: Elastic and Inelastic Collisions

One popular way to illustrate simple one-dimensional collisions in the classroom is our air track. We have two models of air track for larger and smaller rooms, and several demonstration setups for them, including C7-01: Elastic Collisions; C7-02: Inelastic Collisions, and C7-04: Collision Velocity Multiplier.

In an elastic collision, both momentum and kinetic energy are conserved. In an inelastic collision, momentum is still conserved, but kinetic energy is not; energy is lost to friction, internal interactions, etc.

There are several simulations on the internet that have been developed to help illustrate elastic collisions as well. They can be useful when used in class in conjunction with the demonstration, or to examine such collisions on your own time outside of class.

Andrew Duffy has developed a simulation that simulates the motion of a pair of carts on such a track, and you can see active graphs of the momentum, energy, velocity, or position. You can try it out here: http://physics.bu.edu/~duffy/HTML5/collisions_1D_bargraphs.html

Eric Neumann has a simulation with one to three masses colliding with each other and the walls. You can try it out here: https://www.myphysicslab.com/springs/collide-spring-en.html

In both cases, controls are available to let you adjust variables like mass, velocity, elasticity, etc. Try out different configurations and see if you can replicate your favourite in-class experiments; and see if you can find the limitations of the simulations as well!

• ### Demonstration Highlight: Electric Fields

Electric fields are an important topic in physics, and one that’s particularly challenging to demonstrate clearly in the classroom. You can find several demonstrations of this in section J3 of our catalog, wherein we qualitatively trace out electric field lines around a Van de Graaff Generator or a Wimshurst Machine, and have a variety of ways of gathering electrostatic potential and showing how it interacts with conductors in different configurations. One very popular one, demonstration J3-08, uses paper streamers around one or two Van de Graaff Generators to show how the fields bend and interact.

Understanding electric fields is important for everything from understanding the structure of matter to communications technology to the behavior of living cells. The electric field is a vector field of the electrostatic force (strength and direction) on a hypothetical charge placed at any given point. Thus, it is usually measured in Newtons per Coulomb or Volts per Meter.

We have an article in our Directory of Simulations with several ways of experimenting with electric fields virtually. Try out this one at oPhysics, by Tom Walsh. You can model our paired Van de Graaff Generators above as a pair of identical charges, and see the structure of the resulting electric field. Compare how this would change if one of the generators had the opposite charge, or if we used four generators instead of two.

Check out other simulators as well, and see what you can find!

• ### Demonstration Highlight: Electromagnet

Sometimes powerful things come in small packages, and this electromagnet is no exception! It features in two popular demonstrations in our collection, J6-01: Electromagnet with Bang and J6-04: Low-Power High-Force Electromagnet. These two demonstrations are frequently used, separately or together, in a variety of physics classes.They also featured in our popular Physics of Fantastic Worlds program!

This small electromagnet is powered by a single flashlight battery. But it is quite strong. In the first demonstration, we see a heavy block of steel being held up by the electromagnet. When we flip the switch to turn the electromagnet off, though, it falls to the table with a bang.

In the second, the electromagnet and a small steel plate are mounted on handles. If students grab the handles and touch the plate to the magnet, they cling together so tightly that even quite strong people cannot pull them apart. But flip the switch to turn off the electricity, and they fly apart!

But what is an electromagnet, and why does it work? Let’s find out.

The battery produces an electrical potential that causes a current to flow through the wire in the coil when the switch is closed. A current can only flow when the circuit is complete.

Maxwell’s Equations of Electromagnetism tell us that moving electrical charges, such as an electric current, create a magnetic field around it. This magnetic field acts just like the magnetic field of the permanent magnets we’re familiar with, like refrigerator magnets. The strength of the magnetic field is determined by the amount of current passing through an area.

(image credit: Wikimedia user Chetvornohttps://commons.wikimedia.org/wiki/File:Magnetic_field_of_wire_loop.svg)

Here we see a diagram of the magnetic field around a single loop of wire. We can see that the field wraps around the wire, so the direction of the force from the magnetic field will be different depending on where you are around the wire.We can see this field in motion in this animation from Penn State - click here!. See the animation "B Field Lines Due to a Current Loop."

The direction of the field also depends on which way the current flows; try this out in this simulator at JavaLab - click here!

• Imagine the field around that single loop in the illustrations above turned on its side, lined up with more like it.If you flipped one of the wire loops around, its field would be oriented the other way, leaving a slightly weaker point in the field; but if you flipped all of them at once, the field of the entire coil flips directions. Try this out with the simulator!

• You can also flip the battery aroundin the simulator to change the direction of the currentflowing through the wire.

Compare for yourself: what happens if you change the direction of the wire, or change the direction of the current, or both at once?

The force from a single wire is not very strong, especially with only a small electric current. You could make a stronger electromagnet by having a power source with a higher electrical potential to make a stronger current;but that might not be very practical, and would certainly be more expensive.

But if we have many loops of wire, and line them up so that the fields all are aligned, then the small magnetic force from each wire will add up to a much stronger force. This is how a strong electromagnetlike the one in the photographs aboveis built.

You can also try this at home; check out instructions to build your own small electromagnet on our outreach page, and try some experiments with it! Get the PDF here!

• ### Demonstration Highlight: Fourier Analysis

Joseph Fourier and the Fourier Transform

Joseph Fourier was a French scientist in the late 18th and early 19th centuries. He made important contributions to subjects ranging from algebra to thermodynamics, including early studies on the greenhouse effect on Earth’s climate, but today is best remembered for his discovery that many mathematical functions can be approximated more simply as a sum of basic trigonometric functions (sines and cosines).

This process is particularly useful to us because of the realization that you can analyze the structure of any waveform by breaking it down into a series of sine waves. By doing this, we can represent the wave as a list of simple sines and cosines, and their relative amplitudes and phases. We can build up a complex waveform by taking a single sine wave, then adding harmonics of it (sine waves whose frequency is an integral multiple of the fundamental sine wave) in different amplitudes and different phases.

We can then work with these sine and cosine waves mathematically in order to manipulate the original waveform. This is used in modern technology for many things, from audio equalizers on music players, to cleaning up errors in digital photographs, to analyzing the complex interference patterns from spectroscopy and crystallography used to identify substances in the laboratory.

This all sounds very complex; but the fundamentals of it are quite simple, and you can try it for yourself!

Each of these pairs of images represents a single waveform. In the first picture, we see the full wave. In the second, we see the Fourier Transform of that wave – the spread of sine waves of different frequencies that can be assembled to build that waveform. Each spike in the Fourier Transform graph represents a sine wave; the height of each spike is how large the amplitude of that sine wave should be to make the full wave.

When the waveform we put in is just a sine wave itself, of course the Fourier Transform of it is a single line – it’s just that same sine wave again!

This more complicated sawtooth wave is made up of many Fourier components – multiple sine waves. As the frequency goes up, the amplitude goes down.

Each of these sine waves is a harmonic of the first one; the frequency of each is two, or three, or four, etc times the frequency of the first, or fundamental, sine wave. That fundamentalhas the same frequency as the original sawtooth wave.

These graphs were all created with an oscilloscope and waveform generator in our facility; check one out here!

Match the Wave!

Now try it for yourself! Here are some more waveforms:

and some Fourier transforms. Can you guess which Fourier transform came from which wave?

Even without a complex electronic synthesizer, you can try this at home with a simulator.

This interactive simulatorin the PhET collection lets you build up waveforms by adding Fourier components: https://phet.colorado.edu/en/simulation/legacy/fourier

And the Falstad collection has another interactive simulator to discover the Fourier components of many different wave forms, and see how the breakdown of components changes when the wave does. You can also turn on the sound generator and compare how different waveforms sound to your ear. Try it out, and see what you can change in a wave to change what you hear – and what you can change and have the wave still sound the same. Can you hear a chance in frequency? A change in phase? http://www.falstad.com/fourier/

Try out both, and see what waves you can build and explore!

• ### Demonstration Highlight: Fourier Synthesizer

Welcome back! In this entry in our Demonstration Highlights series, we’re taking a look at Fourier Synthesis. You may recall that we addressed Fourier Analysis in a previous entry, the process of analyzing a waveform by breaking it down into harmonic components. This time, we’re taking the process in reverse. In Fourier Synthesis, we assemble a wave form by adding sine waves together.

Our Fourier Synthesizer demonstration, H4-01 in the demonstration index, lets you generate a sine wave of any frequency between 100Hz and 1,000Hz. The synthesizer then generates harmonics of this frequency, waves with integer multiple frequencies – e.g. 120Hz, 240Hz, 480Hz, etc. You can then choose to add any or all of these harmonics to the output of the synthesizer. For each of these harmonics, you can then adjust two variables: the amplitude of the harmonic, and its phase (whether it is in synch or out of synch with the original waveform).

As Joseph Fourier showed us last time, you can create approximations of any other wave by assembling harmonics in this way.

You can try this at home with the updated Making Waves simulation in the PhET Collection at the University of Colorado. This simulator works much the same way as our demonstration, allowing you to select the amplitude of each harmonic, and display them both individually and in sum. Try it here: https://phet.colorado.edu/en/simulations/fourier-making-waves

In the top third of the screen, you set the amplitude of each harmonic. The middle third shows graphs of each harmonic, and the bottom third shows the sum of all of them. Try building a square wave, or a sawtooth wave, and see how close you can get!

• ### Demonstration Highlight: Friction on an Inclined Plane

Welcome back! This week, we’re visiting some simple and classic demonstrations of friction: C6-01, the friction box, and C6-02, the friction block.

The coefficient of friction is defined formally as the ratio of the force required to move two surfaces over each other, and the force pushing them together. The coefficient of static friction, the ratio when objects are at rest, may be different (and significantly higher) than the coefficient of kinetic friction, when they are in motion with respect to each other.

One way we can see this is by having the two surfaces at an angle with respect to gravity. By changing the angle, we change the force acting on the surfaces. We can see that as we increase the angle, and thus the force, the box or block will start to slide down the surface. Once it is in motion it will continue to slide, even if the angle is decreased slightly; the kinetic friction is less! But interestingly, it is unaffected by changing the mass of the box, since while the total mass and force may change, the ratio stays the same.

You can experiment with this at home; find any rigid surface that you can prop up to change the angle, and find flat-bottomed containers that can rest on it or slide down it, then add mass to the containers to see what happens. Compare the effects, if any, of changing the mass, the angle of the slope, and the material of the containers.

Then, compare your results to what you find from a simulation, like this one by Tom Walsh: Static and Kinetic Friction on an Inclined Plane. You can change the mass, the coefficients of friction, the angle, and even the force of gravity (in case you want to see what your experiment would look like on the Moon). Also, try giving your mass an initial velocity up the slope – does friction slow it down? What happens after its velocity reaches zero?

• ### Demonstration Highlight: Galileo's Pendulum

This week, doctoral student Subhayan Sahu returns with another pendulum demonstration – this time, Galileo’s Pendulum. Different presentations of this device can be found in our demonstration directory as C8-03 and G1-20. See it in action in Subhayan’s video below:

A pendulum is mounted on a backboard with two pegs on it. The pendulum is hung from the upper peg, with the lower peg interrupting its swing at the midpoint.

This is a fun way to challenge students to think about conservation of energy in a pendulum. The potential energy of a stationary pendulum at the top of its swing is dependent entirely on its height, not its length. So when the peg effectively changes the pendulum length, the bob still has the same energy and so reaches the same height, but the period changes!

You can explore a similar effect with this simulation in the PhET Collection: https://phet.colorado.edu/sims/html/pendulum-lab/latest/pendulum-lab_en.html The Pendulum Lab lets you start a pendulum moving with any given height; then you can change the length, mass, and even the force of gravity. Try it out and see what happens!

• ### Demonstration Highlight: Gravitational Lensing Model

In astronomy, gravitational lensing is the phenomenon whereby gravitational forces around a mass bend light in a way similar to a conventional refracting lens does. When a large mass lies between an observer and the light source they're observing, sometimes that mass can bend the incoming light, causing the source to appear in a different location, or even in multiple locations at once. This can even allow an observer to see a light source that would otherwise be unobservable due to being directly behind another object.

We have a model of this in our collection, as demonstration E1-21, a glass lens that is specially shaped to produce a similar effect to gravitational lensing. Light is bent more the closer it is to the lens' center axis. As a light source moves behind the lens, you can see the source appear to be displaced, or even see one source appear to become several, or become a ring of light around the center of the lens. All of these phenomena can be seen from gravitational lensing in space as well.

In this drawing, you can see a cross section of part of the lens. The changing curvature produces the gravity-like effect of increasing refraction towards the center.

Try experimenting with this simulation https://slowe.github.io/LensToy/ to see it in action in a starfield!

• ### Demonstration Highlight: Guitar & Oscilloscope

Our Guitar and Oscilloscope demonstration is a fun hands-on way to show a visualization of a waveform while students also hear it. It illustrates how waves on a string become sound waves in air, and how the decay times of different components of a complex waveform affect its sound over time. You can see it in action in our new demonstration video, starring physics student Alana Dixon.

A guitar produces sound from the vibration of the strings. When you strum or pluck a string, the string vibrates. The frequency of this vibration is determined by the string’s length, its tension, and its weight. The body of the guitar, and the air chamber within, can couple and resonate with these vibrations. The energy therein is passed to the air, creating the sound waves we hear across the room. A pickup has been attached to the guitar; this pickup uses magnetic induction with the strings to detect the vibrations and transform them into an electrical signal. This is then amplified by the amplifier and displayed by the oscilloscope. An oscilloscope displays a changing electrical voltage as a moving point on a graph. It allows us to display visually how the signal changes over time.

When we pluck a string, we can see the resulting sound wave reflected as a waveform trace on the oscilloscope. There is a slight difference, though: the pickup is showing the vibrations from the string, and the vibration of the body as well since it is connected to the body, but this is not always exactly identical to the wave as transmitted through the air! The particular shape of the guitar body and sound hole can emphasize slightly different elements of the sound as they couple with the outside air. But for the purposes of our experiments, it’s close enough.

The frequency produced by a vibrating string is determined by three factors: the length of the string, the tension in the string, and the linear density of the string. These define boundary conditions for the waveforms. Guitar strings have different linear densities (the weight per unit length) to help them produce a wider range of sounds. Then we adjust the tension in each string to tune the guitar to the exact frequencies we want. You’ll notice, though, that the waveforms we see here are not simple sine waves. The sound of a guitar is a very complex waveform that changes over time. The complexity of the waveform is in part due to the design of the instrument. There are several modes of coupling within the guitar, as energy passes from the vibrating strings to the surface of the guitar (the soundboard), from there to the air inside the body, and between the body and the outside air. And the complex shape of the instrument creates multiple possible resonances at various frequencies. All of these can reinforce certain harmonics of the fundamental wave, and these components add up to form the complex waveform we see on the oscilloscope screen. Additionally, the different components of the wave last different amounts of time. After the string is plucked, its vibration slowly dies down, but the vibrations it has set up within the instrument also last for different amounts of time – each component has its own decay time. As these components change in amplitude, the shape of the overall waveform changes, and that gives the guitar its complex sound and varying sound.

To understand this better, we can examine some simulations of how a string responds to being plucked, and its behaviour over time.

This simulation from Falstad http://www.falstad.com/loadedstring/ lets you pluck a string and see how the resulting wave in the string gradually decays. It will display graphs of both the amplitude and phases of various harmonics that make up the wave. Try adjusting the damping to see how that changes the decay over time!

If you’d like to learn more, check out this breakdown https://www.acs.psu.edu/drussell/Demos/Pluck-Fourier/Pluck-Fourier.html  by Dr. Daniel Russell of Penn State with both graphical and mathematical treatments of the initial conditions of a plucked string and its evolution over time.

Fred W. Inman. A Standing-Wave Experiment with a Guitar

The Physics Teacher 44, 465 (2006); https://doi.org/10.1119/1.2353595

Michael C. LoPresto. Experimenting with Guitar Strings

The Physics Teacher 44, 509 (2006); https://doi.org/10.1119/1.2362942

Polievkt Perov, Walter Johnson and Nataliia Perova-Mello. The physics of guitar string vibrations

American Journal of Physics 84, 38 (2016); https://doi.org/10.1119/1.4935088

Michael Sobel. Teaching Resonance and Harmonics with Guitar and Piano

The Physics Teacher 52, 80 (2014); https://doi.org/10.1119/1.4862108

Scott B. Whitfield and Kurt B. Flesch. An experimental analysis of a vibrating guitar string using high-speed photography

American Journal of Physics 82, 102 (2014); https://doi.org/10.1119/1.4832195

• ### Demonstration Highlight: Hill Track

Welcome to the latest Demo Highlight of the week! This week, we’re taking a look at a popular demonstration used to introduce the concept of energy: C8-04, the Hill Track. Dave Buehrle introduces it in the video below.

The ball starts out with a certain amount of gravitational potential energy based on its height above the base. As it rolls down the track, it converts this potential energy into kinetic energy. This includes both the kinetic energy related to its linear motion along the track, and the rotational kinetic energy of the ball spinning as it moves. So if the ball is released on the high end of the track from a height exactly equal to the height of the hill in the middle, it doesn’t quite make it over the hill, it doesn’t quite reach that same height. Some energy has been lost to friction, but importantly, some energy is still in the form of kinetic energy as the ball is still rotating. Thus, for the ball to get over the hill, it has to start out slightly higher than the hill to compensate for this.

The PhET Collection at the University of Colorado has a simulation related to this demonstration. The Energy Skate Park simulator (https://phet.colorado.edu/en/simulation/energy-skate-park) is a simpler (non-rotating) system that lets you experiment with a simulated skateboarder on a variety of tracks, including one with a hill in the middle. Try it out at home, and see how the initial position affects how your skater moves!

This demonstration, though simple, is also used in advanced classes. You can see it cross-listed as demonstration P2-41, and it is often used in the teaching of quantum mechanics to illustrate the concept of potential wells.

• ### Demonstration Highlight: Hookes Law and SHM

Welcome back to the Demonstration Highlight of the Week! This week, we’re taking a look at G1-31: Hooke’s Law and Simple Harmonic Motion. You can see it in action in this video starring PhD student Subhayan Sahu.

In this demonstration, we have a spring that is reasonably well described by Hooke’s Law – that is, within its usual range the spring responds linearly to force. We hang a series of 200 gram masses from the spring, and by measuring the displacement and the period of oscillation we can determine the spring constant, k.

You can try this kind of experiment at home as well! If you don’t happen to have a spring handy, the PhET Collection has a simulated one you can use: https://phet.colorado.edu/en/simulation/masses-and-springs .

This demonstration is an excellent example of how we can use multiple measurements in scientific experiments. The value of k (or, of kis known, of g) can be determined from the displacement, or from the period of oscillation. By measuring both, we can test our assumptions about the system.

• ### Demonstration Highlight: Inertial Reference Frame

Welcome back! Today we’re taking a look at a popular demonstration related to the concept of relativity.

We’re accustomed to thinking about the motion of a projectile from a perspective outside of its motion, the generally safer option in real life! The PhET collection of physics simulations has a lovely one for seeing how different parameters like mass, gravity, and air resistance affect the motion of a projectile; try it out here: https://phet.colorado.edu/en/simulations/projectile-motion

When we observe and measure motion, we are inevitably making the measurement against some frame of reference. An inertial reference frame is the technical term for a frame of reference in which an object is observed to have no outside forces acting on it, so that it is moving freely in space. Sometimes we have to go to great lengths to determine what such a frame of reference might be – and in the case of this demonstration, it is literally a metal frame!

In demonstration P1-02 in our collection, two spring-powered cannon have been pointed so that if a projectile came out of either of them and moved in a straight line, the projectile would pass through a hole in a transparent barrier and then land in a sophisticated projectile catchment mechanism, also known as a sock. But of course, if we just launch a ball out of the cannon, that doesn’t happen! As soon as the ball leaves the cannon, it starts to fall due to the acceleration of gravity, following a parabolic path, so it slams into the transparent barrier far below the hole.

But, if we raise up the whole aluminum frame that holds the cannon, barrier, and catchment, and then drop it, we can fire the cannon while the aluminum frame is falling. Now, from the perspective of the frame, there’s no separate acceleration pulling the ball down, because the frame is falling at the same rate that the ball is! So the projectile moves “straight” across the frame, through the hole, and lands in the catchment. Meanwhile, from our own perspective outside the experiment, we see the ball following a parabolic path just like always, while the whole experiment falls down.

• ### Demonstration Highlight: More Fun with Polarization

Earlier this year, we took a look at new videos of our popular demonstrations of the polarization of light, demos M7-03 and M7-07. This week, we’re returning to the topic to check out some simulations that let you try this at home!

The first simulation, by Tom Walsh at the oPhysics site, lets you model a wave as it passes through a series of polarizing slits. You can independently adjust the angle of up to three such slit-filters, and see how the resulting wave responds. Experiment with it at https://www.ophysics.com/l3.html.

The second simulation, created by Andrew Duffy and hosted by Boston University, shows a graph of light intensity as it passes through a series of polarizing filters. Again, you can independently vary the angle of each of three filters, and now you can see how this changes the intensity of the light after each. Try it at http://physics.bu.edu/~duffy/HTML5/polarized_light.html.

Speaking of trying things at home, this isn’t a purely academic question – this is how polarized sunglasses cut the glare from sunlight reflecting off the road without preventing you from seeing where you’re going! Try rotating a pair of polarized sunglasses and see how their effect changes with angle. It may look something like the animation below. We do this in the classroom, too – check out demonstration M7-18

• ### Demonstration Highlight: Parallel Plate Capacitor

Today we’re visiting the ever-popular Parallel Plate Capacitor, in its simplest form found in our demonstration index as J4-01, or with a dielectric plate at J4-22. A capacitor stores energy in the electric field between its plates. The capacitance of a capacitor is technically the amount of charge stored per volt – in a sense, how capable it is of storing charge at a given potential. In a parallel plate capacitor, the capacitance goes up with greater surface area, and goes down with greater separation between the plates.

The parallel plate capacitor consists of two large aluminum plates with an air gap. The capacitor is charged with a potential of around 1000 Volts using a low-current DC power supply. The plates may then be separated and the voltage observed, demonstrating that for a fixed amount of charge, the voltage is proportional to the plate separation.

But if you insert a dielectric sheet into a charged capacitor, the voltage goes down, which means the total capacitance of the system has gone up! The capacitance of a system depends on the dielectric constant of the medium – for air, this is very nearly the same as pure vacuum, but some materials have a much greater dielectric constant. This plastic plate has a dielectric constant nearly 5 times that of air.

Now, try out these simulations to see if you observe the same behaviour!

The first, from the PhET collection at the University of Colorado, places a capacitor in a simple DC circuit. In the first simulation tab, you can adjust the input voltage and plate size, and measure the electric field, capacitance, and energy stored. The additional tabs show variations: you can add a dielectric to the capacitor, or place multiple capacitors in series and parallel.

The second simulation, at oPhysics, additionally lets you control many characteristics within an idealized circuit. Compare the results you get for different combinations of capacitor size and input voltage between the two simulations.

Our capacitor has 22cm diameter circular plates, rather than the square plates used in the simulations. In the simulations, try setting the plate area to be the same as ours and see how it responds to other voltages.

• ### Demonstration Highlight: Pendula of Different Masses

Welcome back! Physics PhD student Subhayan Sahu returns this week for another installment in our series highlighting oscillation demonstrations. This week’s highlight: Demonstration G1-14 Pendula With Different Masses. Check out his video below:

These swinging cubes are made of a variety of materials, from aluminum to lead. We can see that for a simple pendulum swinging under gravity, the period is dependent only on the length. So long as these pendula all have the same length, they have the same period!

You can try this for yourself in the PhET Collection’s Pendulum Lab simulation. In the lab, create two pendula with the same length and mass. Pause the simulation while you position them to the same height and release; you’ll see they have the same period. Now reduce the mass of one while keeping the mass of the other fixed; the period stays the same! Now try changing the length of one pendulum to see how that changes the period.

• ### Demonstration Highlight: Potential Well

This week we’re taking a look at demonstration E1-11, our model potential well. This fibreglass model was designed to let us simulate the motion of bodies in an inverse square potential, such as the gravitational potential around a massive object in space.

You can see the demonstration presented in this new video starring Liz Friedman.

An object in motion has a kinetic energy, based on how fast it is moving. It also has potential energy, based on the force of gravity the object experiences from nearby objects. The force of gravity acts on a moving object – as the object speeds up, it is converting the gravitational potential energy into kinetic energy. The force of gravity on an object is inversely proportional to the square of how far away it is – the force is maximum at the center.

A potential well is an area where potential energy is locally at a minimum. That is, when an object reaches the center of this well, it cannot gain additional kinetic energy to leave. Here, we have made a model of the potential well around a dense object. The curve of the fiberglass surface represents the increasing force as your approach the center.

The surface of this “potential well" is shaped so as to produce an inverse square gravitational force. When a ball enters the well enters the well, it is attracted to the center; if it has no initial velocity, it will fall directly to the center. But if it enters with some velocity tangential to the center, it will fall into an elliptical orbit that gradually decays to the center as the ball rolls around the well.

When you roll the ball across the surface, you use some initial force to start it moving. Once it is rolling on its own, though, the only forces acting on it are the force of gravity, pulling downwards, and the normal force and frictional force of the surface supporting it. So the ball accelerates as it rolls down the surface, exchanging potential energy for kinetic energy, until it either falls into the hole or it has enough kinetic energy to escape the potential well entirely.

The ball can follow many different paths within the potential well, all determined by its initial velocity vector – how fast it is moving to start with, and in what direction. Watch for that in the video!

• ### Demonstration Highlight: Projectile Motion - Pellet and Falling Target

Welcome back! This week, we’re visiting an old favourite: C2-22, the classic so-called “monkey and hunter” demo. This is based on a traditional textbook problem: if an animal is hanging from a tree and see someone aiming directly at it (humanely, with a tranquilizer gun, we hope), and drops from the tree; but the projectile drops at the same rate as the animal, they will still collide.

Obviously, this is a somewhat artificial problem, as it requires an animal that knows what a dart gun is but decides to drop to the ground rather than ducking behind the tree, and it also requires a shooter who for some reason doesn’t understand physics and was pointing directly at their target rather than anticipating the physics behind this problem in order to hit it in its original location! But it is a fun way to explore parabolic trajectories and projectile motion.

In our demonstration, as the pellet leaves the launcher it momentarily disconnects a switch. At the far end, a plastic toy with a metal cap is hanging from an electromagnet. The pellet is aimed directly at the toy. When the pellet trips the switch, the toy starts to fall. But of course once the pellet leaves the launcher, it also starts to fall.

Because the acceleration due to gravity is approximately independent of the mass of the falling object, and assuming that air resistance is negligible, the two objects fall at the same rate, even though one also has sideways motion and the other does not. So the pellet will strike the toy, assuming they both started out high enough that their paths intersect before reaching the ground.

We can adjust the initial height of the toy and the angle of the launcher to show that this still works regardless of angle, so long as the two are in line and they have time to complete the trip.

You can try this out at home with this simulator by high school AP physics teacher Tom Walsh: https://www.ophysics.com/k10.html . You can independently vary the horizontal and vertical position, angle, and velocity to see which configurations work and which do not.