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Demonstrating Rotational Inertia

 

Have you ever struggled to describe Rotational Inertia to your students? Even worse, have you ever struggled to understand Rotational Inertia yourself? Did you know Rotational Inertia is the same as Moment of Inertia? Yeah, I’m with you there. I did not know the name had been changed until recently. However, I do think Rotational Inertia is a more logical phrase than Moment of Inertia. Well, if you would like some help with the concept of Rotational Inertia, then I highly suggest the Rotational Inertia Demonstrator from Arbor Scientific because it is an easy way to demonstrate the concept of rotational inertia. The demonstrator is composed of three pulleys of different sizes all centered around the same axle. Attached to the pulleys are four spokes on which four masses can be placed. The distance from the axle, or axis of rotation, of the four masses on the spokes can be adjusted.
In order to understand rotational inertia, we should first review the equation for rotational inertia of a system of particles:
The rotational inertia of a system of particles equals the sum of the quantity of the mass of each particle times the square of the distance each particle is from the axis of rotation. While the Rotational Inertia Demonstrator does not appear to be a system of particles, the equation for the rotational inertia of a system of particles helps us to understand how the rotational inertia of the demonstrator changes when we adjust the locations of the four adjustable masses. The closer the four adjustable masses are to the axle, or axis of rotation, the smaller the “r” value in the rotational inertia equation and the smaller the rotational inertia of the demonstrator.
We also need to review the Rotational Form of Newton’s Second Law of Motion to better understand rotational inertia. The net torque acting on an object equals the rotational inertia of the object times the angular acceleration of the object. Please remember torque and angular acceleration are vectors.
Notice the similarities to the Translational Form of Newton’s Second Law of Motion. The net force acting on an object equals the inertial mass of the object times the linear acceleration of the object. Again, remember force and linear acceleration are vectors.
Force is the ability to cause a linear acceleration of an object.

Torque is the ability of a force to cause an angular acceleration of an object.

Torque is the rotational equivalent of force.

Rotational inertia is the rotational equivalent of inertial mass.

Angular acceleration is the rotational equivalent of linear acceleration.

But, what does it mean that rotational inertia is the rotational equivalent of inertial mass? Inertial mass is the measurement of the resistance of an object to linear acceleration. Therefore, rotational inertia is the measurement of the resistance of an object to angular acceleration. In other words, the greater the rotational inertia of an object, the more that object will resist an angular acceleration. Referring to the rotational inertia demonstrator, the farther the four adjustable masses are from the axis of rotation, the larger the “r” value in the equation for the rotational inertia of a system of particles, therefore the larger the rotational inertia of the demonstrator. The larger the rotational inertia of the demonstrator, the larger the resistance of the demonstrator to angular acceleration. In summary, the larger the distance the four adjustable masses are from the axle, the larger the rotational inertia, and therefore the larger the resistance of the demonstrator to angular acceleration.
This is demonstrated below by hanging a 100 g mass from the largest pulley in two simultaneous demonstrations. In the demonstration on the left, the four adjustable masses are close to the axis of rotation and therefore the rotational inertia of the system is smaller. In the demonstration on the right, the four adjustable masses are farther from the axis of rotation and therefore the rotational inertia of the system is larger. When both demonstrators are simultaneously released from rest, because the net torque caused by the 100 g masses is approximately the same, the demonstrator with the larger rotational inertia on the right has a smaller angular acceleration. In other words, the demonstrator with the larger rotational inertia speeds up rotationally at a slower rate. Going back to the Rotational Form of Newton’s Second Law of Motion, because the net torque is almost the same, a larger rotational inertia results in a smaller angular acceleration:
Notice we are always keeping the four adjustable masses the same distance from the axle, or axis of rotation. This is to keep the center of mass of the system at the axis of rotation of the system. When the four masses are not equally spaced from the axis of rotation, then the center of mass of the system is offset from the axis of rotation and the force of gravity acting on the system causes a torque on the system. The force of gravity causing a torque on the system makes understanding the demonstration much more complicated. In the examples shown below, the demonstrator on the left with four masses equally spaced from the axle rotates at almost a constant angular velocity. The demonstrator on the right has one mass farther from the axis of rotation and therefore the whole system actually becomes a physical pendulum. The system oscillates back and forth in simple harmonic motion. While this is interesting, it does not provide an obvious way to learn about rotational inertia. In summary, it is much easier to learn about rotational inertia from the demonstrator if all four masses are equally spaced from the axis of rotation.
Let’s look at another set of demonstrations below to learn about rotational inertia. As in the previous demonstration, on the right, we have a 100 g mass hanging from the largest pulley and all four adjustable masses far from the axis of rotation. On the left, all four adjustable masses are still far from the axis of rotation, however, the 100 g mass is hanging from the smallest pulley instead. In other words, both rotational inertia demonstrators have the same rotational inertia and the force of gravity acting on the string is the same, however, the net torque acting on each demonstrator is different. Recall torque equals the “r” vector times the force causing the torque times the angle between the direction of the “r” vector and the direction of the force. The magnitude of the “r” vector is the distance from the axis of rotation to where the force is applied to the object:
Because the 100 g mass is hanging from the small pulley on the left and the large pulley on the right, the “r” vector for the small pulley is smaller and therefore the net torque acting on the demonstrator through the small pulley is less. Therefore, according to the Rotational Form of Newton’s Second Law of Motion, the angular acceleration of the demonstrator on the left is less than the angular acceleration of the demonstrator on the right.
Our last set of demonstrations has both demonstrators with identical rotational inertias and masses hanging from the smallest pulleys. Also, both demonstrators have a 100 g mass hanging over the left side of the pulley. However, the demonstrator on the right has a second mass, a 200 g mass, hanging over the right side of the pulley. This means the demonstrator on the right has two different masses hanging off of the smallest pulley.
In order to determine what is going to happen, remember the Rotational Form of Newton’s Second Law of Motion includes net torque, not just torque. 
In this example, the net torque from the two masses on the demonstrator on the right actually has roughly the same magnitude as the net torque acting on the demonstrator on the left, however, the directions are opposite from one another.
Again, both demonstrators have the same rotational inertia, are using the same pulley, and have a 100 g mass hanging over the left side of the pulley. The pulley on the right adds a 200 g mass hanging over the right side of the pulley. For the demonstrator on the right, the 100 g mass hanging over the left side of the pulley essentially cancels out 100 g of the 200 g mass hanging over the right side of the pulley. This effectively means the right demonstrator essentially has a 100 g mass hanging over the right side of the pulley. Therefore, the net torques on both demonstrators have essentially the same magnitude and opposite directions. Therefore, the angular accelerations of both demonstrators should have roughly the same magnitude and opposite directions. You can see that is true in the demonstration.
But why do the two demonstrators have “roughly” the same magnitude angular accelerations? Adding the 200 g mass to the demonstrator on the right increases the total mass of the system. Because inertial mass is resistance to acceleration, increasing the total mass of the system actually decreases the angular acceleration of the system a little bit, even though the net torque should be roughly the same. Proving this requires drawing free body diagrams, summing the torques on the wheel, and summing the forces on each mass hanging, so I am not going to walk all the way thought that solution here.
There are many more ways you can make adjustments to the rotational inertia demonstrator to better help understand rotational inertia. For example, ask yourself what would happen to the angular acceleration of the demonstrator if the only change we make to it is to increase the mass hanging from the demonstrator? Increasing the mass hanging from the demonstrator increases the net torque acting on the demonstrator. The rotational inertia remains the same. Therefore, according to the Rotational Form of Newton’s Second Law of Motion,  , the angular acceleration of the demonstrator will increase.
What if the only change we make is to change the locations of the four adjustable masses from all being at their farthest extreme positions to having two of the adjustable masses near the axis of rotation and two adjustable masses far from the axis of rotation? Bringing two adjustable masses near the axis of rotation decreases the rotational inertia of the system and therefore, according to the Rotational Form of Newton’s Second Law of Motion, the angular acceleration of the demonstrator will increase. Notice, this will only work when the two close adjustable masses are opposite one another and the two far adjustable masses are also opposite one another. If this is not the case, the center of mass of the rotational inertia demonstrator will not be at the axle, or axis of rotation, which is a problem we addressed earlier.
The pulley sizes of the rotational inertia demonstrator are provided by Arbor Scientific. They are 20.22 mm for the small pulley, 28.65 mm for the medium pulley, and 38.52 mm for the large pulley. Given this information, we can even predict which way the rotational inertia demonstrator will rotate if we were to hang 100 g over one side of the large pulley and 200 g over the other side of the small pulley. Before releasing the demonstrator, the angular acceleration of the demonstrator is zero because it is at rest. Therefore the torque caused by the 100 g mass will be 0.3852 meters times 0.100 kilograms times 9.81 m/s2 times the sine of 90 degrees which equals roughly 0.38 N.
The torque caused by the 200-gram mass will be 0.2022 meters times 0.200 kilograms times 9.81 m/s2 times the sine of 90 degrees which equals roughly 0.40 N.
Therefore, the net torque caused by both masses acting on the demonstrator before it starts to accelerate is the difference between these two torques because they act in opposite directions.
Therefore, because the torque caused by the 200 g mass is larger than the torque caused by the 100 g mass, the rotational inertia demonstrator will rotate in the direction caused by the torque of the 200 g mass.
Please realize these torque calculations are only correct while the demonstrator is at rest. Once the demonstrator begins to accelerate, the force of gravity and the force of tension acting on the mass hanging are no longer the same and we would need to draw free body diagrams and sum the forces on each hanging mass.
If you enjoyed watching this video by Jonothan Palmer, the creator of Flipping Physics, please let us know in the comment section below and check out his YouTube page for more videos like this one.

 

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Newton’s Laws Revisited

Newton’s Laws Revisited

Newton’s Principia Mathematica, the book published in 1687, contains Newton’s three laws of motion.  Most people think he wrote it to explain forces on blocks, falling stones, and pulleys.  But that’s not true. The purpose of the book was to explain the motion of the planets and comets.  Ultimately, Newton proves that Kepler’s “laws” of planetary motion are actually a natural consequence of one single law of the inverse square relationship of gravitational force.

Newton’s famous diagram which explains satellite orbits

Fig 1. Newton’s famous diagram which explains satellite orbits. Imagine a cannon is fired from a mountaintop. It could go fast enough to fall around the earth rather than upon it.

In the preface to the book, Newton distinguishes between PRACTICAL MECHANICS, which would include fixing windmills and carts (today automobiles), and RATIONAL MECHANICS, which concerns itself with the motion of the planets and the Earth among the stars.  These days Rational Mechanics is called CELESTIAL MECHANICS. It was Newton’s breakthrough and his thesis was that the laws of physics would be the same whether on earth or up in the heavens.  This is the apple story that the gravity on the apple would also apply to the moon. That is the gravity of the earth reaches beyond the earth’s surface, as far as you like into space, and pulls the moon into a curved path.  In this video and article, I revisit Newton’s laws from within the historical context and from his own original purpose of devising them.  To explain the motion of the planets. Frequently he speaks of “motion” as the product of mass and velocity, these days we would call this momentum.
Practical Mechanics and Rational Mechanics in one picture

Fig 2. Practical Mechanics and Rational Mechanics in one picture. Perhaps there is only one type of mechanics after all? A Gravity Well was used in this demonstration.

1st Law

Although you already know it, I believe it is best if we restate it as follows:

All objects, including planets and meteors, will continue in their motion, in a straight line at constant speed, unless there is a force that acts on them.  
On earth, we rarely see this event because there is so often a force, like friction, pushing or pulling on objects.  Newton correctly hypothesized that there would be no air in outer space, and this would explain how the planets could continue in perpetual motion along their paths. He reasoned that there must be no air beyond the atmosphere near earth’s surface because as we climb mountains there is less and less air.  At distances such as the moon (60 earth radii) there would be so little air that the moon’s motion would essentially be through a vacuum.  This explains how it can move with no friction.
Although Newton never had this view, we can see that the earth’s atmosphere barely extends beyond its surface

Fig 3. Although Newton never had this view, we can see that the earth’s atmosphere barely extends beyond its surface. Basically, at this scale, it is a thin coat of white and light blue paint. The moon should be much further off, about 10 feet away on this scale.

2nd Law

An alteration from linear motion is caused by a force (a push or a pull) but the larger the mass, the less the force will change the motion.

a = F / m

It is best to write the equation in this form, at least initially, to demonstrate the proportionalities. Alterations of motion are caused by force but mass (inertia) resists.  As always, a force is a push or a pull.  An object like Jupiter might be traveling through space and have its straight-line path altered by the inward pull of gravity caused by the sun.
Jupiter with its four moons, moves in a nearly circular orbit, pulled by the sun’s gravity. The whole journey takes about 12 years.

Fig 4. Jupiter with its four moons, moves in a nearly circular orbit, pulled by the sun’s gravity. The whole journey takes about 12 years. The four moons circle Jupiter like clockwork and helped Newton calculate the density of the various planets. The closest one, Io takes less than 2 days to orbit the giant planet.

Now it is no longer moving in a straight line.  This relationship, a=F/m defines inertia as the effort required to alter an object’s motion, and it turns out that inertia can be measured by mass, which Newton called the quantity of matter.
Shaking objects quickly can demonstrate inertia. The smaller mass is easy to shake, but the heavy one takes a lot of effort.

Fig 5. Shaking objects quickly can demonstrate inertia. The smaller mass is easy to shake, but the heavy one takes a lot of effort. Inertia is measured by mass. Here I show that a 10g mass can be rapidly shaken, but not a 1000g mass. This defines inertia.

In our physics classes, we often overemphasize acceleration as a solution to this formula.  Then we get surprised when students don’t recognize changes in direction as alterations of motion.
In a typical lab, somebody might let a Fan Cart go, and measure the acceleration difference as the mass is increased.
A Fan Cart can be loaded with mass to demonstrate that the same force causes less acceleration.

Fig 6. A Fan Cart can be loaded with mass to demonstrate that the same force causes less acceleration. This is an excellent demonstration but is only half of the story of F=ma.

Speeding up is only one form of alteration of motion.  When I teach, I emphasize “alteration” not only because it is a more accurate word, but because it reflects Newton’s original meaning.  Even the translator agrees with me.
Fig 7. Newton’s second law, as it appears in Andrew Motte’s translation from the original Latin. The original phrase is mutationem motus.

Fig 7. Newton’s second law, as it appears in Andrew Motte’s translation from the original Latin. The original phrase is mutationem motus.

Motion in a circle is a very good example of a motion that is being altered. An object that is not going in a straight line will necessarily be subject to a force.  In the video, I show one of our devices, the “Exploring Newton’s First Law: Inertia Kit” which I use here to demonstrate that straight line at constant speed will happen if the force applied stops.
Movement in a circle is a good example of an altered motion.

Fig 8. Movement in a circle is a good example of an altered motion. Unless there is a constantly applied force, the ball will fly off in a straight line at constant speed.

Newton’s second law can also explain why all objects fall at the same rate independent of mass, even a book and a piece of paper.   Normally, they do not succeed at falling at the same rate because of air friction on the paper. But a book and a piece of paper will fall at the same rate if we evacuated the room, but there is an easier way.  If you put the paper on top of the book, then the book will push the air out of the way for them and they will fall together.  A piece of paper will fall at the same rate as a book. We see the solution here.
A massive object m has a greater weight, due to the force of gravity mg.  But that same object also has more inertia, also symbolized by m, and that makes it harder to move around, even for the earth’s gravity.  These two cancel out and the acceleration, yes, in this case, it is acceleration, is simply g.
Now you might not believe that an inanimate object like the earth could have trouble moving things around, but that is precisely the case.  Here, I have an Inertia Balance, which shows you that more massive objects are harder to move about even for objects like tables and springs or metal bands.  The rate at which it can bound the greater inertia is less.
Fig 9. The inertial balance set can be used to demonstrate that even inanimate objects, like these metal strips can have a difficult time bouncing larger amounts of mass around.

Fig 9. The Inertial Balance set can be used to demonstrate that even inanimate objects, like these metal strips, can have a difficult time bouncing larger amounts of mass around.

3rd Law

It is now time to state Newton’s 3rd law properly.  For every action force, there is a reaction force that is equal in magnitude but opposite in direction.

In Newton’s words, when you push on a stone, the stone pushes equally back on your finger.
It is possible to show the third law more accurately.  Set up a situation where two people pull on the same scale, their scales will always agree.
What if you ask your partner to pull with 20N and you only pull with 10 N.  This is impossible to achieve, but the result will be that they will move in the direction of the person pulling harder
Newton did discuss the tides and the motions of the planets, especially Jupiter, how it would perturb the sun, causing it to wobble.  But he did not know about Pluto, which is a great way to illustrate the third law in terms of gravitation.
As Charon goes around Pluto, it causes it to wobble.

Fig 10. In the video, I show this animated gif of Pluto and its moon Charon, taken from the New Horizons Spacecraft that photographed it in 2015. As Charon goes around Pluto, it causes it to wobble. This is because they both pull on each other with equal force.

There is also Newton’s own example, the cart, and the horse.  In the Principia, Isaac Newton discussed how his 3rd Law can best be understood in the context of a horse pulling on a cart.  Paul Hewitt immortalized this example still further by using it as the basis of a cartoon:
Paul G. Hewitt drew this cartoon, inspired by Newton’s own example of his third law.

Fig 11. Paul G. Hewitt drew this cartoon, inspired by Newton’s own example of his third law. Find this in his masterpiece book called Conceptual Physics.

Newton’s third law explains jumping.  When I jump I push down on the ground with my feet, which pushes me upward with a force equal to my push.
. It is possible to demonstrate Newton’s 3rd Law by putting two Newton scales together.

Fig 12. It is possible to demonstrate Newton’s 3rd Law by putting two Newton scales together. These are quite funny, they told me that I weight 800N.

A lot of the names we give for exercises seem to violate Newton’s 3rd Law.  For example, have you ever done a pull-up, what are you doing to the bar when you do this?  Pulling down!  It is the bar that pulls you up!  Have you ever done a push-up?  What are you doing when you do this?  Yes, pushing down, the ground is doing the push-up.
Another way to understand Newton’s third law is through the example of the air-powered projectile.  When a burst of air is pushed out of the bottom of the tube, the projectile is pushed up by that same air.  All rockets work on this principle, but the air-powered projectile is not truly a rocket because it only ejects the gas once and provides no flame, etc.
Newton’s 4th Law

Now, what about the planets, Jupiter, and the tides?  Newton explained that gravity reaches up from the surface of the earth and out into space, expanding and diminishing.  The acceleration weakening in proportion to the distance squared.

The gravitational field of a massive planet extends through space, but all the while weakens as the square of the distance from that planet.

Fig 13. The gravitational field of a massive planet extends through space, but all the while weakens as the square of the distance from that planet. The distance is initially measured to be the radius of the planet, so the gravity would not be twice as weak when you are an extra meter above the surface, but a full earth’s radius.

This is usually written similar to the form of F=GMm/r2 and most people incorrectly believe that Newton didn’t know the value G, but that is another Isaac Newton myth.
Newton guessed that the density of the earth was between 5 and 6 times that of water. Which is correct.  He then used the volume of a sphere to estimate the mass from mass = Density times bulk – his word for volume.
Most people who teach physics are aware of Henry Cavendish’s experiment to determine the universal constant G.

Fig 14. Most people who teach physics are aware of Henry Cavendish’s experiment to determine the universal constant G. Except, that he was interested in measuring the density of the earth. The symbol G was introduced much later. This device is called a torsion balance. The way it works is that two heavyweights W were attracted by the two cute little one’s C a telescope T was used to observe the twisting of the rope. Fun fact, Henry Cavendish is also the discoverer of Hydrogen.

The one thing that Newton could not understand was how gravity acted through space.  We now better understand that it is a gravity field that extends from the sun to the planets.  This is the Einsteinian model, that mass bends the fabric of space-time.  Recently confirmed, by the detection of gravitational waves that distort the gravity field, and travel at the speed of light.
The warping of spacetime is the current best explanation for how gravitational forces seem to reach out and pull on masses.

Fig 15. The warping of spacetime is the current best explanation for how gravitational forces seem to reach out and pull on masses. In Newton’s time, he had to appeal to the idea that the law worked so it must be true.

One of the best ways to demonstrate the modern answer to Newton’s conundrum about “occult forces” and through the Einsteinian Model of the warping of space, time is with the Gravity Well.  This device is surprisingly easy to build.  I have my own set of planets which I like to send around the large 1 kg sun ball that is provided.  However, the set comes with colored marbles which will illustrate the point just as well.
The corrections made by Einstein to Newton’s gravity theory were very slight, but they were not negligible.  There were three specific predictions.  1) Light would be bent by gravity a very specific amount. 2)  The orbit of Mercury would process (spin) over many years. 3) There would be gravity waves that would travel at the speed of light.
The first of these was demonstrated during a solar eclipse, two years after the publication of Einstein’s Theory of General Relativity. The Newton theory predicted less deviation of light than the Einstein theory.  The experiment was done by Arthur Eddington, taking pictures of stars during a solar eclipse.  Their positions were deflected by the sun’s gravity.
Arthur Eddington’s famous photograph of stars during a solar eclipse proved that Einstein’s new theory was more accurate than Newton’s old one.

Fig 16. Arthur Eddington’s famous photograph of stars during a solar eclipse proved that Einstein’s new theory was more accurate than Newton’s old one.

The second of these errors was already known to astronomers.  Because the sun is not the only object in the solar system, the other planets deflect one another from their orbital paths.  This error is called precession of the perihelion.  Einstein correctly reasoned that Mercury would show the biggest error when compared to the Newton solution because it was so close to the sun.  He was right, and so was his new theory.
The orbit of Mercury is an ellipse, but this ellipse precesses slightly over the centuries.

Fig 17. The orbit of Mercury is an ellipse, but this ellipse precesses slightly over the centuries. The theory of Newton also predicts this (due to the presence of other planets) but the theory of Einstein worked better. The error was about 1 degree over 2 years.

The third prediction of general relativity is that there would be gravitational waves that would propagate at the speed of light.  This was demonstrated only as recently as 2016 in the LIGO laboratories and has already been rewarded with a Nobel prize.  These gravitational waves were detected twice, and the signal was the same.
Two gravitational wave signals detected at the same time in different states.

Fig 18. Two gravitational wave signals detected at the same time in different states. The event was supposedly a pair of black holes in another galaxy colliding and rippling the fabric of space-time. Physicists will immediately recognize that these vibrations would be inaudible frequencies.

These such vibrations can also be demonstrated with the Gravity Well.  Here is a video in which they are demonstrated with a drill. A strobe light is used to help make the waves more visible.

 


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Five Demonstrations for the First Day of Class!

On the first day of school, it is a good idea to show a demonstration that gets students thinking and sets the stage for what the class is going to look like over the course of the year.  In this video, I’ll tell you about five demonstrations that you might want to show to your students on the first day of class.  The idea is to give a preview of what is coming in the school year.  Some of these demos are puzzles.  The idea is that the students have to guess not only the outcome but develop a model that explains the phenomena.  The topics covered are waves, thermodynamics, electromagnetism, and the nature of science.  This video should be helpful for anyone who teaches any physical science. Although I personally am a physics teacher, I would do some of these demos with my 8th-grade physical science class.
Hand Boiler
Salt vs. Fresh Water Melting

Which will melt ice faster, salt water or fresh water?  Ice will be placed into cups of water, as often is done, and begin to melt.  That the water will not be stirred is an important consideration.  The result is surprising both for the outcome and for the mechanism.  The result is that the freshwater melts the ice faster.  As the ice is melted it becomes cold fresh water.  Cold fresh water has a higher density than regular water and so the cold water sinks – but this will not happen in the salt water.  Salt water has a higher density than cold fresh water and that causes the cold water to stay on top.  This acts as a refrigerator for the ice, only being bathed in cold water and prevents further melting.  I owe this demo to Bernard Cleyet a fellow Physics technician from UC Santa Cruz, although the food dye illustration is an original contribution.

Fresh water vs. Salt water

The set up of two cups of water – one fresh and one salt – will result in a surprising conclusion.

Sale Water vs. Fresh Water

Make it visible by dribbling the ice with blue food dye, or any color really. It appears that the cold water does not leave the ice in the case of salt water.

Two Candles

Find two candles, a tall one and a short one.  Although a candle on a stand would work fine.  Light them both and place them in a glass jar.  Now, they are both going to go out eventually…but which one will go out first.  And why?

Two Candles

The set up for the two candles demonstration. A great puzzle for the first day of class.

An incorrect explanation might be that CO2 is denser than ordinary air, which is true, and that would cause the lower candle to go out first.  But the flame is also hot and that causes the CO2 to rise.  This is the dominant effect.  It causes a buildup of CO2 which does not allow the candle to get oxygen and the top candle snuffs out.

This demonstration speaks to the nature of science, we have multiple variables happening at the same time and we cannot use a single fact to explain a phenomenon.  It is necessary to parse out the variables and decide which one is making the main effect.  I owe this demonstration to my own physics teacher, Scott Dukes.

Two Candles

CO2 fills the top of the jar first because – being a hot gas – it has a very low density and is buoyed up by the surrounding oxygen and nitrogen in the normal air, smothering the top candle.

 It is actually possible to cause the lower candle to go out first.  If there is a very large chamber like an aquarium, then the CO2 has time to cool down and it will sink.  This will cause the lower candle to go out first.  It is hard to be sure this is what we are seeing, however.  It might be due to a convection effect (swirling).
The Magic of Electricity

In this demonstration, we show that electricity can communicate over vast distances causing us to power objects that are far away.  A magnet on a spring is dipped into an Air Core Solenoid coil and a similar coil is set up on the other side of a table.  When a magnet is dipped into one of the coils it generates a current which is supposed to have an effect in the other coil, only that doesn’t happen!  You have to connect the wire.  When the wire is connected, the electric current generated in the first coil can travel to the second coil and enable its motion at a similar frequency.  You will notice in the video that I am moving my magnet at close to the normal frequency of the bouncing spring.  These wires that connect the two magnets can be as long as you like and they will still communicate the effect.

Air Core Solenoid

The bouncing magnet demo is easily illustrated with two Air Core Solenoid coils. The most important part is to not connect the wire. This highlights that it is not the shaking of the table that is causing the effect and also that there really is electricity traveling through the wires. For the sake of the camera, I kept these wires closer than I normally would in class.

This demonstration provides a tantalizing preview of all the things that electricity can do.  It is the first step toward understanding that having a masterful control over nature is not done through longer levers or bigger hammers, but through the control of electrons, whose motion is easily amplified.  Although Michael Faraday did a similar demonstration (he only had a compass on the receiving coil), I owe this demonstration to Bill Layton of UCLA.
When I think of all the amazing things that electricity has empowered us to do, I think of how it is the modern version of magic made real, although we do not always find it impressive anymore.  We have light at night, the ability to see through people without harming them, and self-applied electrical messages.  But, to belabor the point, perhaps the ability to see each other over any distance at any time is the greatest accomplishment.  Facetime is probably the most magical achievement of electricity.  Even more so than the laser light show.
The demonstration can also be performed with a hand-cranked generator. Which I show in the video.  The generator does a much better job of generating electricity than the “dip the magnet” approach.  In the generator is a small DC motor which is cranked backward to produce electricity.  If electricity is sent into the generator it will act like a motor and the crank will turn.  In the video, you will again notice that I use the generator with the same frequency as the bouncing magnet.
You can read more about Electromagnetism by checking our “Three Right-Hand Rules of Electromagnetism” blog.
Hot and Cold Mixing Cups

In this demonstration, I say how even though it is a very simple demonstration, it gives us a common language that we can share as a class.  By this I mean, we need a window into the definition of temperature.  When we say something is hot or cold, what do we mean?

To perform this demonstration, take some cold and hot water in equal amounts and add a drop of food dye to each.  In my case, I used blue and red food dye for dramatic effect. However, two dyes of the same type will work fine. What difference do we expect to see between the hot cup and the cold cup?

Water Temperature

Two cups, one hot and one cold will show very different results when food dye is added. For some purists, using the same color of food dye might be preferable, but since the result is the same I do not see any harm in going with red for hot and blue for cold.

The result is that the hot water mixes the dye much more quickly.  Hot water is hot because its water is moving around faster.  While this does demonstrate the point very well, there is a bit of a cheat in the explanation.  What we are really witnessing is convection: the movement of a hot substance.  However, we still need energy to cause that movement and that is powered by the molecular motion of the hot substance.

In the common language, temperature is a measure of molecular motion.  This gives us an experiment to call back to as a class, one that we can all relate to, one that we can use to help us imagine molecules moving about in future lessons.

In a deleted scene, I take the temperature of each of the cups.  It is important to use temperatures below 65 degrees Celsius.  Above this, the water becomes scalding hot.  I recommend 60 and below.  The cold water is easily made from pouring off ice water.  Usually, you get between 1 and 4 degrees.  But what would happen if I mixed water at 2 degrees with water at 60 degrees in equal amounts?  The result is an average.  31 degrees is half of 2+60 degrees, and that is very close to the result.  Some chemists out there will want me to work in Kelvin, but the result is the same through the averaging process whichever scale you use.

Pendulum Wave

A very exciting demonstration is the pendulum wave apparatus.  Challenge your students to explain how it works.  Different length pendula have different periods, this causes a traveling phase change which gives the appearance of a sine curve.  The different phases result in different apparent wavelengths as the pendula go in and out of phase.

The pendulum wave apparatus works by having several pendula of different lengths.  Each of these will vibrate with a slightly different period than its neighbor.  As the pendula swing, they seem to create sine curves of different lengths.  This effect grows and shrinks over time because of the phase relation between each pendulum.  The result is that we get the appearance of a wave from oscillatory behavior.  The meaning behind this demonstration is that waves and simple harmonic motion (such as pendula) are closely related phenomena.

pendulum wave apparatus

The pendulum wave apparatus does not really show wave behavior but a phase relationship between neighboring pendula. This is a good way to have students visualizing what waves look like however and a very fun science toy to investigate.

At the end of the video, I perform the “Snake Pendulum” demonstration.  This is achieved by giving a much larger amplitude to the far end of the Pendulum Wave Apparatus than the close end.  However, since period does not depend on length in a pendulum, we get to see all the same effects as before.  Different here is that the size of the swings is not all the same.  This illustrates that the effect is not amplitude dependent.
Learn more about waves and sound by reading some of our previous blogs.
pendulum wave apparatus

The snake pendulum effect. The same wave patterns result but with different amplitudes. This effect is made possible by the fact that the pendula do not change their periods of oscillation with time.

BONUS: Hand Boiler

In the video, I also demonstrate using the Hand Boiler.  The instructions on the box are incorrect (explaining about Charles’ Law).  The correct explanation is that the phase change from liquid to gas causes an enormous expansion. In a liquid, the molecules of the substance are touching, but in a gas, they are separated by a vast empty space.  The phase change is made possible by the very low pressure inside of the glass allowing for rapid/easy boiling with just a little input heat (liquids boil more easily at low pressures).  As the liquid is evaporated by the heat of a person’s hand, it changes into the gas phase, causing an expansion into the chamber which pushes the rest of the liquid out and up the neck.  There is not much boiling going on, mostly evaporating.  The appearance of boiling is more about air seeping in and jumping up the glass neck.  As shown in the video, there are several colors and shapes of hand boilers, however, they all use the same liquid.  The gas phase is clear, the dye is left behind in the remaining liquid.

Hand Boiler

The hand boiler can demonstrate a simple heat engine, but what it does not do is demonstrate Charles’ Law. Rather it is an illustration of phase changes causing volume changes. The added volume of the gas increases the pressure in the base and pushes the rest of the fluid up the stem.

Hand Boiler

The hand boiler can be controlled with warm water and not just the heat from a hand. Do not, however, use hot water which might cause it to crack.

The hand boiler can also be used to demonstrate distillation.  Since the dissolved dye will not vaporize, a clever experimenter can manage to warm one end of the hand boiler and cool the other.  This will collect clean clear liquid on one side while concentrating the dye on the other.  The liquid inside is not water, but ethyl alcohol, which is the same type of alcohol that we drink.  I do not recommend drinking this alcohol however, it is likely to be taken from petroleum rather than plants. They also tend to “denature” the alcohol by adding a bad flavor, best to avoid this.  Sometimes these hand boilers have been used as a love meter, or a “pulse glass,” meaning that it checks that you are alive or at least that you have warm hands.  I am not sure how having warm hands is a measure of love, but it certainly can help identify blood flow and blood pressure.  Supposedly this device was used by Benjamin Franklin and may have been of his own design
Do not forget to recognize that the process by which this works is similar to how the drinking bird works.  But do NOT use the explanation on the box.  Charles Law (a gas’ volume increases linearly with temperature) has almost nothing to do with the effect.  In fact, it is almost a non-effect when you consider that we are using the kelvin scale.  For example, imagine we start at 24 celsius then increase to 30 celsius from our hand’s heat (human body is 37C).  That is only a change of 6 degrees out of 300 degrees on the kelvin scale. This amounts to a 2 percent volume change!! That is not enough to fill up that glass bubble.  Therefore, we are mathematically demonstrating the failure of Charles’ Law to explain the hand boiler’s behavior and we correctly recognize phase changes causing volume changes as the main factor.  Just like the two candles demo, the hand boiler can illustrate that the wrong theory can be used to explain the right effect.  This is best avoided, please put a sticker or paint over the explanation on the box.
If you liked this video please subscribe to the Arbor channel, and share it with your friends on social media, especially teachers who can use these types of ideas.

 


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Three Right Hand Rules of Electromagnetism

 

 
Teaching electricity and magnetism is complicated by the challenge that the magnetic forces are perpendicular to the motion of the particles and currents.  This requires a three-dimensional perspective which can introduce a variable of a “wrong” direction.  To prevent errors, let us be “right” and use the right-hand rule.
Some would claim that there is only one right-hand rule, but I have found the convention of three separate rules for the most common situations to be very convenient.  These are for (1) long straight wires, (2) free moving charges in magnetic fields, and (3) the solenoid rule – which are loops of current.  Calling these “rules” is the right name. They are not laws of nature, but conventions of humankind.  We use rules to help us solve problems, laws would be the underlying cause as to why the rules work.
Rule #1 – Oersted’s Law

Danish Physicist and Chemist

Our story begins with Oersted’s Demonstration, which was performed for the first time during a lecture in 1821.  What Oersted showed for the first time that when a current carrying wire passes over a compass the needle – which is a magnet – the needle deflects.  When it is underneath the magnet it deflects the other way. The direction that the magnet points is called the magnetic field around the wire.  And you can predict that with your right hand.

Replicating Oersted’s demo is quite easy to do. The compass is dialed to the north, the current flows from North to South and the compass underneath is deflected toward the West. In this case, I am using about 5 amps.

Point your right hand’s thumb along the flow of current – defined as the imagined flow of positive charge.  Now curl your fingers as if they were wrapping around the wire.  The direction that your fingers point, is the field.  I sometimes like to call this the RIGHT-HAND CURL, or Ampere’s Law.  Ampere himself described it as the face of a clock:  if the current flows into the face of the clock then the magnetic field would wrap clockwise.

As the current flows upward, the magnetic field will wrap around. Again, your thumb is the flow of current, and your wrapping fingers are the curl of the field.

Here is the situation in real life with the wire pointing upward and the compasses wrapped around. Normally they just point North, but when I turn the current on we see them all pointing around it, just as we predict with our right hand.

 A good way to demonstrate this phenomenon is with a set of the Small Clear Compasses.  When these are wrapped around a vertical wire, with no current, they will all initially point North.  But, if the current is switched on, the compasses will align in a loop around the current.  It is important to note that the compasses do affect each other, so finding the right distance between them can help make the demonstration more dramatic.
Rule #2 – The Lorentz Force

This second right-hand rule is usually applied to freely moving charges, called cathode rays, or otherwise to push on electric currents.

This cathode ray tube computer screen was originally all red. But these magnets have deflected the electrons from landing on their proper pixels. Note that the silver-colored cow magnet is more powerful than the plastic-coated ceramic iron magnet.

A goldfish is made green by application of a magnet. This is because the electrons (cathode rays) are hitting different pixels (phosphors) on the screen when they are deflected by the magnet.

A cathode ray tube computer screen is one vivid way to demonstrate the Lorentz Force. The screen is illuminated by moving electrons and moving charges are pushed about by magnetic fields.  This is a surprise to many people who think that magnets only affect metals such as iron and nickel.  (After using the CRT just leave it unplugged for a few minutes and that will restore almost all of the original screen color.)

The Electric Swing Apparatus proves that magnets affect currents and can demonstrate that the direction of that force obeys a right-hand rule.

Since electric current is made of moving charges we can also push it around with magnets.  One way to show this is with an Electric Swing Apparatus.  This will highlight that the current, field, and force are all three at right angles.

The magnetic field acts on the current in 3D. The direction of the force can be predicted with your right hand. Let your thumb be the current, I. Next aim your pointer finger in the direction of the magnetic field, B. Then the force will be directed along your middle finger, perpendicular to both of these.

The fingers are directed correctly along the vectors using the right hand.

Using your right hand, the current flows from positive to negative – thumb.  The magnetic field – pointer finger – is directed from North to South (that usually means from red to blue).  The force on the current is perpendicular to both of these and is predicted by your middle finger.

This 2nd rule is usually called the Lorentz Force named after H. A. Lorentz, a contemporary of Einstein, although its effects were known at the time of Michael Faraday.

Now, some people and some books prefer to use the palm to represent the force, that would be current field force (open hand).

The right-hand palm is a common alternative form of the same right-hand rule.

Another way to demonstrate this is with the Electricity and Magnetism Light bulb demo.  When there is alternating current, the wire vibrates, but when it is direct current we can apply force in a specific direction.  Using your right hand, it is possible to predict the direction the current is flowing.

This Edison-style light bulb has currents that are readily deflected by magnets.

For the flow of currents, which are the imagined flow of positive charge, it is appropriate to use your right hand.  But when it comes to negative currents, such as electrons, it is appropriate to use your left hand, which generates the opposite result that a positive charge would experience.  If one wishes to demonstrate the Lorentz force on a CRT, it helps to know to emphasize “use the left-hand rule for negative charges.”
Rule #3 – The Solenoid Rule

An air core solenoid can act just like a bar magnet. Repelling north and attracting south. In fact – if you trace the magnetic field with a compass, you can see that it truly matches the behavior a bar magnet perfectly

Using a third right-hand rule, we can we predict which side of the coil is north.

Let your curling fingers be the direction the current is flowing.  It is looping around.  Then your thumb will be NORTH end of the electromagnet.

This solenoid will behave exactly like this a bar magnet with a clearly defined North and South end. A compass emphasizes that – as far as the magnetic field is concerned – this is a magnet no different than the others.

The North end of the solenoid repels the North end of this bar magnet, in exactly the same manner as would another bar magnet. If the fingers of the right-hand point in the direction of current flow then the thumb will be the North side of the electromagnet.

Electricity and Magnetism are connected phenomena, but at right angles to each other.  So we use the convention of the right hand to predict the direction of the fields relative to each other.

Left Hand Rule

The right-hand rules assume “Conventional Current”, that is… current flows from positive to negative. College-based courses all go with that concept. NOT ALL high school physics courses use that concept. For example, some high schools use the “left-hand” rules because it deals with ELECTRON FLOW, that is… current flow from Negative to Positive (the direction that electrons flow from a battery for example).

The hand rules work the same but they are based on two different current concepts. In this blog we focused strickly on the right hand rule.


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The physics of a roller coaster loop

 
Each year millions of people will visit amusement parks in order to ride some of the fastest, highest, most extreme roller coasters. These machines thrill us because of their ability to accelerate us from a standstill to unbelievable speeds in a matter of seconds while changing from one direction to the next in an instant.
There is so much physics going on in the loop of a roller coaster. Angular velocity, centripetal acceleration, conservation of energy, and more! In this Cool Demo, we are going to look at how we can collect the data by using a Hot Wheels track and by placing a PocketLab Voyager on the Hot Wheels car.
By placing magnets at each connecting section of the track you can now generate “gate” times with PocketLab’s magnetometer. Using a 3D printer you can print a new set of connectors that are designed to house a small magnet. ( 3D print files are available to download in the resource section) When the car passes over these sections of the track you will be able to see a change in the magnetic field. Using this change and time we can come up with “timing gates” at each of these sections, and knowing the distance the car has traveled we can calculate the speed of the car.
The most obvious section of a roller coaster, or in this case, the Hot Wheels track is the loop. Although the loop of the Hot Wheel track is a circle, in reality, roller coaster loops have a tear-dropped shape that is geometrically referred to as a clothoid.
As the car passes through the loop, you can see the track bends into a tear-dropped shape. Once the car passes through the loop we are able to measure the angular velocity or the rate of change of the angular rotations, as it’s moving through that loop using the PocketLab’s Gyroscope.
Roller coaster rides are notorious for creating g-forces. The PocketLab also has an accelerometer, so as the car passes through the loop you can also measure the g-forces a person would be experiencing if they were traveling in the car. Traveling around a circle creates a centripetal force that the rider experiences as a g-force. The force is a function of speed and radius.

The Flip Flap Railway was built in 1895 and was the first roller coaster to have a loop. It was “famous” for its extreme g-forces that it produced on its riders of approximately 12 gs. The circular nature of the coaster’s loop along with its small diameter of 25 feet caused riders to experience neck injuries from whiplash. There are some interesting accounts where riders are hanging on for dear life in a death grip on the sides of the railcar and surviving a 12g ride which is absolutely nuts! Modern looping roller coasters all use teardrop-shaped loops to reduce the g-forces. The Flip Flap Railway was the last coaster to use a truly circular loop.

 
Looking at the Data:
  1. The time it took the car to travel through the loop = 0.34 seconds.
  2. The average angular velocity (gyroscope) through the loop = 1,170 degrees/seconds
  3. The average acceleration through the loop = 3.7 g
Data analysis:

Looking at the angular velocity inside the loop can be done in two ways:

  1. We can calculate the average loop velocity using our timing gates. (The time we exit the loop – the time we enter the loop and using the circumference of our track. Plugging in the geometry in our time we get 1.9 meters per second as our average velocity.
  2. Using the (1.9 m/s) velocity we can calculate the average angular velocity of 18.5 radians per second or 1060 degrees per second.

To get the g-force we need to calculate the following:

  1. Taking the timing gate data to calculate the G-Forces that would be felt inside the loop; (18.5 radians per second)²(0.1 meters per second) = 3.9 g.

The PocketLab Voyager has an array of sensors built into a small package. This allows you to measure data in scenarios such as this Hot Wheels Loop track experiment. Simply connect it to your smartphone or tablet through Bluetooth and you will be able to see the data live in the palm of your hands. On-board memory is also included for when you the PocketLab Voyager is out of Bluetooth range. The best thing about PocketLab Voyager is that that it comes packaged with some many features compared to equipment that costs thousands more.

Download lab resources:
  1. Click here to download – 3D print file (track connector Magnet Single)
  2. Click here to download – 3D print file (double track connector loop)
  3. Click here to download – Hot Wheels Loop Experiment Instruction

Explore the world around you with the sensors built into the PocketLab Voyager:

  • Measure Acceleration
  • Angular Velocity
  • Magnetic Field
  • Range Finder
  • Altitude
  • Barometric Pressure
  • Ambient Temperature
  • Humidity
  • Light
  • Dew Point
  • Heat Index

More Labs using PocketLab Voyager:

If you enjoyed this lab using a Hot Wheels track, we have two more you can download using a Constant Velocity Car and Air Powered Projectile.

  1. Click here to download – PocketLab Voyager with Constant Velocity Lab
  2. Click here to download – PocketLab Voyager with Air Powered projectile

 


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Demonstration of The Photoelectric Effect!

 

In 1905 Albert Einstein had his miracle year, publishing 5 papers, including the Special Theory of Relativity, the Mathematical Description of Brownian Motion, and the E=mc2 formula.  One of these papers was titled “On a Heuristic Point of View about the Creation and Conversion of Light.” [Ref 1]  In section 8 of this paper he develops a mathematic model that describes how light creates cathode rays.  What was heuristic was that he described light as “energy quanta” (photons) for the first time but what was worth a Nobel Prize, was that he was correct.

Figure 1.A –Max Planck presents Einstein with the 1929 Planck Medal for extraordinary achievements in theoretical physics.

Figure 1. B – Albert Einstein c1905 at the patent office desk where he worked as a third-class clerk, and occasionally worked on his “miracle” papers.

It is quite easy to demonstrate the photoelectric effect with an electroscope and a short wave UV-C lamp. By placing a negative charge on the electroscope, and shining the short wave UV light on top, it will discharge. Short wave UV is usually blocked by glass, but visible light is not, thus a pane of glass can be used to show that it is not just regular light that is causing the discharge.

Figure 2 – The electroscope is discharged by shining short wave ultraviolet light upon it.

It helps that on the top of the electroscope there is a zinc plate which has been scrubbed with steel wool.  This removes the zinc oxide layer and makes it more sensitive to the light.  Also note that if the experiment is tried with a positive charge, for example with a piece of glass rubbed with silk, it will fail to discharge.  This is because the photoelectric effect is only for electrons and will only work on negative charges because they are at the surface, but the positive charges are held deep in the nucleus by the strong force. In fact, the photoelectric effect is a great way to identify positive vs. negative charge.

With any form of visible light, you will not get the electroscope to discharge. It does not matter how bright the light is, even lasers will fail.  It takes ultraviolet, specifically the short wave UV-C, because even blacklights are not energetic enough to liberate the electrons.

The thing with light is, the shorter wavelength the more energy it has, and this was already well-known, from Max Planck’s formula  E = h f  but what was worth a Nobel prize, was the idea that the light hits one electron at a time.  Not as waves, but as individual pieces of light.  ONE particle of light hitting ONE electron at a time.  Einstein called this particle a quantum of light, meaning that it is a discrete exchange of energy.  We now call this a PHOTON.

Figure 3 – Albert Einstein took Max Planck’s formula for the quantization of energy in black bodies and extended it to describe light.  This implied that light delivered its energy in bundles of E=hf.  This was a new and heuristic idea, but it explained the photoelectric effect.  KE is the energy of the escaping electrons and W is the energy required to liberate them from the metal.

Figure 4 – The Phet Simulation of the photoelectric effect is a great way to engage students with the details of this modern physics concept. It is based on the experiments of Robert A. Millikan who proved Einstein’s perspective by experiment.

It is also possible to demonstrate the photoelectric effect with a small neon bulb.  These will turn on at about 70 volts.  Hook one to a high voltage source and then dial it back until it is just about to turn on.  Now it will be so sensitive, that just a little extra energy will make the electrons jump and conduct. This will NOT work for red and green light.  It must be blue, or ultraviolet.  That’s right, blue light ACTUALLY DOES have more energy than red and green light.  This is because light travels as photons, and the shorter the wavelength of light, the more energy per photon.

Figure 5 – The energy of blue light can cause electron conduction in a small neon bulb. The bulb stays on because plasma conducts better than rarefied neon.

Reference

http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Einstein_1905_heuristic.pdf


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Reflection, Refraction, Diffraction & Interference…… That’s COOL!

The Mini Ripple Tank is a great way to address the wave-energy standards and to teach about the properties of waves by showing how water waves behave.  This is in keeping with the history of physics and the modern experimental approaches to science instruction.

The Mini Ripple Tank eliminates the clumsiness of the larger ripple tanks of old and gives the opportunity for students and teachers to interact with the wave properties quickly and engagingly.  Because of the competitive price, and variety of available experiments.  It is even reasonable to buy a class set.

Fig 1.  Plane waves are being produced and are readily visible on the built-in screen.

Getting Familiar

The Mini Ripple Tank contains a small pan for water and a vibrating source.  The strobe light below projects waves of various frequencies on a fold-down screen.  Both the strobe and the wave frequencies can be varied, generating many interesting effects.  There is also a synchronizing mode which links the two (this is very helpful when measuring wavelength).

Fig 2. Water is filled up to half of the height.  The adjustable strobe projects from underneath.

The device comes with three distinct wave generating mechanisms: single source, double source, and plane waves.  The single source is the most fundamental and is helpful in instructing on wave basics and Huy gen’s Principle (plane waves are a sum of circular waves).  The double source can be used best at teaching interference experiments (more below) as well as testing out the diffraction formula.  The plane wave source is the one I tend to use the most often because it sets up a standard wave that can readily land upon the other implements which are used to redirect the waves.

Fig 3. The nine components.  Left to right: the two lenses and the prism, the two barriers and the parabolic mirror, and the double and single sources, as well as the plane wave source.

As for general tips, it is helpful to use a document camera for larger classes, also adding blue dye can sometimes improve visibility, and try to not overload the tank with water – either fill halfway or just enough to barely cover the lenses and prism.  Experiment a lot with wave and strobe speeds to improve the visibility of the desired effects.  

Refraction by the Lenses and the Prism

The bending of light waves by glass is well-known, but is this a property of all waves?  Yes! Demonstrate this dramatically by bending water waves with lenses and prisms.  The shallower the water, the slower the waves.  This is analogous to the denser the medium, the slower the light waves (with few exceptions).  

Fig 4. The prism can bend the waves by slowing their propagation.  

Again, remember to keep the water shallow.  Some experiments can include measuring the focal lengths of the two lenses (positive for convex, negative for concave), measuring the index of refraction for the prism (by wavelength change, speed change, or Snell’s Law), and measuring how water depth affects refractive index.  

Fig 5. The refraction formulas that can be used for quantitative experiments.  The first formula might be the least familiar – wavelength changes with index of refraction.  The second formula compares a standard speed c with the new slower one v to define the index n.  The third is the famous Snell’s Law.  

Somehow it is very satisfying to see the focusing of water waves when using lenses.  The ray approach to drawing images known as geometric optics does not provide a hypothesis as to the wave nature of light, but this experiment convincingly demonstrates that refraction and focusing is something that waves do!  Refraction and lens effects are a powerful piece of evidence that demonstrates the wave nature of light.  

Fig 6. The convex and concave lenses demonstrate convergence and divergence of waves respectively.

Reflection by Barriers and the Parabolic Mirror

The law of reflection can be readily demonstrated by the Mini Ripple Tanks (by stacking the barrier pieces) however, the best demonstration is the focusing of waves by the parabolic mirror.

When a plane wave enters parallel to the axis of a parabolic mirror, it will be reflected to the focus of that mirror.  This is the basis for Newtonian Reflector telescopes that remain the standard style in modern times.  A reversal can also be achieved by placing the single source at the focal point and reflecting out plane waves.  

Fig 7.  Reflection of plane waves off a parabolic mirror will focus them to a point.  

Diffraction by Barriers

le-slit diffraction of waves is easily demonstrated with this simple device.  Just place the barriers in the path of the plane wave source and the effect is immediately present.  Manipulating the opening and wavelength can help illustrate the variables: more diffraction occurs the smaller the opening is allowed to be.

Fig 8.  Single slit diffraction shows the bending of a plane wave source as it passes through an opening, illustrating Huygen’s Principle that plane waves are a sum of circular waves.

The diffraction formula for quantitative experiments is best applied to the two-source case, however, and while this is only a case of interference and not diffraction, it does provide an opportunity to apply the formula experimentally.    Here, we see both versions of the formula, the angular version, and the small angle approximation.  I prefer the second one because lengths are usually easier to measure than angles.    

Fig 9. The diffraction formulas:  The symbol d represents the distance between the sources, and lambda as always is wavelength (which is the dependent variable in this experiment).  Theta is the angular distance to an interference fringe as measured from the spot half-way between the sources.  X is the linear distance between the interference fringes, these are the locations of constructive interference.  L is the linear distance from the point between the sources to the point of interest, and because there is more than one location of constructive interference, m is the index number which labels these points as m=1,0,-1,2, etc, (any integer).  

Fig 10. An interference pattern is easily generated with these two sources.  The diffraction formulas above will apply to this double source interference pattern, even though no diffraction is occurring.  This demonstration can be converted into a quantitative experiment.

 


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Powering Imagination and Creativity OneCar at a Time

 

The OneCar is Arbor Scientific’s answer to the various needs of STEM Educators. It is an open-ended creativity-driven approach to science teaching that addresses cross-cutting concepts and offers an opportunity for tinkering and design.

Pictured here is one of the eight OneCar Packets which comes in every kit. Each can be used to construct eight different cars. Students can be creative.

The kit itself is jam-packed with 8 sets of experiment options, enough for large classes and extras for spare parts. A typical starter lab would be building the battery-powered motor car.

A motor in its housing slides into the chassis. These cars can be assembled and disassembled each class period.

This might be used for speed and acceleration experiments. But the options expand rapidly as more options are introduced.

The OneCar offers 8 ready to go experiment options. These can be extended and combined in creative ways to allow for the open-ended labs that STEM teachers have been searching for.

For example, the motor can be used to drive a fan or be powered by a rechargeable capacitor. The lessons can go beyond physics or include chemistry lessons such as air pressure and electrochemistry or even acid-base reactions. Perfect for Physical Sciences courses. There is more too. The Potential energy in a rubber band lab or the classic mousetrap car can be readily created using this kit.

The rubber band-powered car can be used to investigate potential energy.

The mousetrap car is a classic lab in physics used to teach energy and simple machines. Adding a lever arm and CDs for wheels is a common innovation.

You can also build a solar-powered car. Challenge your students to discover what can be done to optimize its traveling speed? Face it south? Angle the collar panel? Use a mirror to reflect the sunlight?

A solar powered car can be created and manipulated to optimize its efficiency. The solar panel can be either connected directly to the motor or, in this case, used to charge up one of the supercapacitors. Note how the solar panel is angled to be perpendicular to the sun, just like solar panels on rooftops.

All of these options can be mixed and matched. That is the whole idea of open-ended inquiry education. The OneCar gives students many opportunities to be creative in solving engineering challenges. Many of the above images come from videos on our website: ArborSci.com/OneCar.   Take a look and see how fun and easy it is to build these designs.

 


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Lab4Physics Classroom Edition Powered by Arbor Scientific

The Lab4Physics App is a helpful tool for teaching physics and physical science. It is a lab app for smartphones and tablets, and because of the familiar controls and friendly, easy-to-use interface, all your students can use it

 

The App works by using the built-in features of cell phones and tablets that convert easily to probeware, such as the accelerometer, which we will explore first.


Fig 1.  The Lab4Physics home screen.  When you open the app, there are lots of experiments you can try (which are categorized on the left) or you can go straight to the tools (right) and perform your own experiments.

 

ACCELEROMETER

 

If you shake the phone up and down, the accelerometer records this motion in 3D. Deleting the X and Z axis, we will now graph only the Y-vertical motion.

Fig 2.  It is easy to use the accelerometer to measure the earth’s gravity field strength.  Here the phone was held vertical then slowly turned to lay flat.  The gravity constant 9.8 m/s2 is measured.

The app allows you to zoom in, both vertically and horizontally, and slide the image around, just like a picture or map.  Because this interface is so familiar, students will already know how to do this.

Fig 3.  The phone’s Acceleration is measured in 3 dimensions, but typically you only need one.

Because the accelerometer is so easy to use, you will find yourself using it in many different applications, such as spring and pendulum experiments.  Note that when facing the phone, X is right and left, Y is up and down, and Z is toward and away.  The positive axes are right, up, and toward, which you can remember with thumb X, open fingers Y, palm-slap Z.

Fig 4.  Zoomed-in on the image of the above data.  Vertical zoom for precise amplitude measurements and horizontal zoom for precise time (period) measurements.

Fig 5.  A plastic bag is a convenient container for the phone when performing spring and pendulum experiments.  The touchscreen still works fine through the plastic.

 

SONOMETER

 

Using the microphone, Lab4Physics can analyze the intensity and frequency of a sound that the phone records. With this device, you can see the waveform of the frequencies that the phone picked up. Use this to compare the amplitudes of loud and quiet sounds or the frequencies of a high and low pitch.  This works as an instant oscilloscope. It is also possible to measure the period as the time between peaks, it helps to zoom in for this.

Fig 6.  The Sonometer makes a measurement of the author’s whistling ability.  The period can be measured as the peak to peak time, or the Highest peak frequency can be displayed automatically by using the Intensity vs. Frequency feature.

The waveform displayed looks transverse, but the sound is a longitudinal wave.  Therefore, it is important to explain how this wave was generated.  It was the motion of the vibrating microphone that moved a small magnet that generated the electricity that became the signal displayed. The device also can calculate the frequency of the loudest part of the signal it is detecting.  This can be used to test who sings with the highest or lowest frequency or just to check the frequencies of musical instruments.

Fig 7.  A tuning fork, which is supposed to be the musical tuning standard A 440Hz, is revealed to be very nearly correct by the Lab4Physics App’s Sonometer feature.

 

CAMERA / MOTION TRACKING

 

One of the most useful features is the ability to track an object’s motion.  Utilizing the phone’s camera, film an object (usually with a ruler in the picture), and by tracking at a specific point on the object, you can follow its motion through the frames of footage.

Fig 8.  An accelerating toy car has its motion tracked through ten frames of footage generating the expected parabola of an accelerating object.

 Because the frames are equally separated by time intervals the app can turn this data into a distance vs. time graph.  From this data, it further generates the acceleration and velocity graphs.  Even a Data Table is provided so you can sort out anomalous data or analyze further.

 

SPEEDOMETER

 

Lab4Physics also has a speedometer which is a streamlined alternative to stopwatches.  Students can, for example, set up a series of positions and click the split button to get the individual times for when the object is at that position.  Using this, graphs are generated for position and velocity.

Fig 9. A typical Speedometer experiment. Tracking the position of a toy car through space. Changing it from going slow to fast can show up on a position vs. time graph.

 

EXPERIMENTS AND LABS

 

Lab4Physics has lots of ready to go labs to instruct your students, or you can use them to give you ideas.  Here we explore some of the labs on waves.

Fig 10.  Left, a screenshot from the app shows the four labs on waves.  Choosing Do-Re-Mi takes us eventually to this screen, right, which shows how we will be exploring the frequency of a musical instrument.

 The labs take the students through the experiment in five or six steps.  They are self-contained and complete and let you know how much time the activity should take.

 


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test

Cool Stuff Demos with Violet Lasers

 

If you are talking about optics in the classroom and students are learning about how light waves behave, take a look at the blue-violet laser, which produces wavelengths at 405 nm.

“I definitely want one of those blue LASERS! Ahhhh… to write my name on a phosphorescent board the FIRST day of class in the dark from the back of the room. That WILL get their attention!”   -Buzz Putnam

 

Sure, it is a different color and that is always cool, but why use this over any other Laser?

  • Cover most of the visible spectrum – If you only have the red (650nm) and green (532nm) Lasers, you are still missing a large part of the visible spectrum. At 405nm, the blue-violet Laser provides a good representation of the shorter wavelengths present on the opposite end of the visible spectrum from red.
  • Diffraction grating differences – You can compare the red, green, and blue-violet Laser colors by pointing them through a diffraction grating to observe where the different wavelengths end up.
  • More Fluorescence – Unlike the green Laser, the blue-violet Laser can produce fluorescence on a wide variety of materials. In other words, the blue-violet wavelength of 405 nm excites the electrons of most materials to a higher energy level than the green Laser.
  • More phosphorescence – For your next trick, we recommend shining the Laser on something with “glow-in-the-dark” properties, such as a sheet of glow-in-the-dark paper. The effect, called phosphorescence, is due to the same characteristics of excited electrons that we saw in florescence. Only with phosphorescence, it takes longer for the material to transition back to its ground state, and therefore you see it longer with those types of materials. The green Laser does not produce these same effects. Show your students both situations and ask them why!

 

Why pay $79 for a violet LASER

Arbor Scientific has carefully screened all of our Lasers to make sure they offer a higher level of safety and peace of mind. There are low-cost versions available on the market today that could pose serious risk to your students due to a lack of infrared (IR) filters. Even pointers that use IR filtering could still be harmful, due to shoddy manufacturing that provides poor conversion efficiency (when converting from infra red to visible light). While all Lasers should be handled carefully to prevent users from harm and should never be pointed at unprotected eyeballs, these lower cost Lasers are particularly problematic in the academic atmosphere where there are many people in close proximity. For the safety of your students, please always make sure you have taken all the proper precautions possible, including the use of effective IR filtering.

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