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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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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Air Powered Projectile in-depth look [W/Video]

The Air Powered Projectile in-depth look

One of the best ways to engage your students in the study of projectile motion is with direct experiment and observation. For this purpose I recommend the air-powered projectile. It safely and reliably demonstrates projectile motion by simply releasing compressed air. Here are five experiments to get you started.

launch
The soft nose cone provides a high degree of safety while the body’s sleek design minimizes the effects of air resistance.
soft_nose

MEASURE LAUNCH VELOCITY
Shooting the projectile straight up is the easiest way to determine launch speed.
The first thing you want to do is determine the launch velocity by shooting straight up. It takes about 5 seconds to go up and come back down when shot vertically. Use the formula v=vo+at , analyze the top of the trajectory. At this point velocity = zero. Then set gravity to negative 10m/s/s. Gravity is pulling opposite the initial launch velocity, which is the unknown. Plugging in 2.5 seconds for time (assuming the trip takes the same time up as down) we get a launch velocity of about 25m/s. You might be concerned whether this is a safe speed, but the soft nose c one, and the fact that there is no chemical propellant ensures this. You may wish to wear safety goggles anyways.
launch-1

The calculation of launch velocity is straight forward, requiring only algebra.
algebra

ANGLE vs RANGE
A classic experiment that I have done every year since I started teaching is to investigate which angle generates the greatest launch distance. Students will have their own hypothesis. Without doing any math, try to hypothesize which angle will maximize the range. This is an experiment that works in both high school and middle school. The theoretical result is that 45 degrees maximizes range.

r-a

Sample data for the Range vs Angle Experiment. Note the systematic error on the zero.
This is because the product of horizontal velocity and time in the air is maximized. The mathematical proof is a common homework problem in Honors Trigonometry classes and can be done without calculus. When you plot the data, a surprising result is that the complementary angles, like 30 and 60 degrees can have the same range as each other. This is because when the velocity is more horizontal, the vertical time is lessened, and vice versa.

wedges

Angled Wooden Wedges help a lot in this experiment. The angle of launch will be the compliment to these angles.
When performing this experiment, it is helpful to use the angled wooden wedges option. These help adjust the angle without the use of clumsy blocks of wood or coupling. Another addition you might want to invest in are the varied speed end caps. The different size caps affect the pressure limit that causes the seal to slip, launching the tube upward with the force of expanding gas. Larger endcaps can capture more of that force so it will go faster. This adds another variable which allows you to make new predictions. But with the same endcap, you get the same time, every time.

caps

Different sized end caps can change the launch velocity, adding a new variable.
ADIABATIC EXPANSION
The air powered projectile does not use any chemicals to launch. It only uses the compressed air of a bike pump, typically around 60 psi (pounds/square inch). When you launch the projectile, you will usually see some clouds appearing beside the base. They only last for a second, but can be made more visible by using a high speed camera. (Many students now have these in their smartphones.)

Adiabatic

Adiabatic clouds appearing during a typical launch event. This image was taken with an iPhone 5s in 120 frames/second mode.
The clouds are caused by the humidity in the air being turned into a vapor due to the rapid temperature change. When a gas expands rapidly, it cools. This is called adiabatic expansion. It is an important idea in thermodynamics and this is a really good example of it. You’ve probably seen it when you open a champagne bottle, or even a soda.

Because the force of launch only acts in the initial moment, the rocket is an excellent example of a free falling projectile (unlike missiles and rockets). The sleek profile minimizes air resistance and turbulence while increasing the accuracy of the experiment.

HIGHLY ACCURATE CALCULATED LANDING SITES
In video we launch the air powered projectile at 30 degrees, and from the first experiment, we already know the initial velocity, Vo=25m/s. We use Vo sin30 to find the initial upward velocity (12.5m/s) and Vo cos30 to find the horizontal component (21.6 m/s).

board

A typical projectile motion problem can now be performed experimentally, with a high degree of accuracy and while being highly engaging.
At the highest moment, it is only moving horizontally, so we once again can use v=vo+at. Only this time the plug step is 0=12.5-10t giving a time of 1.25 seconds to reach the top. Twice that is 2.5 seconds, the total time of flight.
The product of the horizontal component and the total time of flight is the distance traveled. (The horizontal velocity never changes.) The range, x=vhoriz * time = 21.6m/s * 2.5 sec = 54 m.
That the theoretical prediction. Take it with you, and some measuring tape (or the yard lines on the football field) and see what really happens.

field

The impact location proves to be within 2 meters of the expected value.
When we did the experiment we got a result of 56 meters. That is less than 4% error, very good!


james_lincolnJames Lincoln

Tarbut V’ Torah High School

Irvine, CA, USA

James Lincoln teaches Physics in Southern California and has won several science video contests and worked on various projects in the past few years.  James has consulted on TV’s “The Big Bang Theory” and WebTV’s “This vs. That”  and  the UCLA Physics Video Project.

Contact: [email protected]

 


 

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Measuring Forces on an Inclined Plane

The Forces on an Inclined Plane Demonstrator is a new piece of physics equipment that can help make the abstract concepts of vector components of forces a tangible reality.  The innovation of the device is that it can be manipulated at will.  The angles can be set and reset quickly and the forces measured fairly quickly.

 

The device breaks the weight of an object into its component forces and allows for accurate data to be taken without having to set up clumsy and cumbersome ramps.

Each module comes with a built in scale (that measures how the Normal Force varies with the angle of inclination) and a parallel spring scale (that measures how the Parallel Force increases with the angle of inclination).

The module contains three unique features.  Built in scale, protractor, and spring scale  mount.

The measurements rely heavily on Balanced Forces.  Balanced Forces result in zero acceleration.  The action of gravity pulling the cart downhill is balanced by the equal and opposite action of the spring scale pulling the cart uphill.  Similarly, the component of the weight that is wasted in the hill is balanced by a reaction force which is perpendicular to the hill.  This is called the Normal Force (normal meaning perpendicular).

The sine and cosine relationships will come naturally out of well-calibrated data.

 

Lab Ideas

 

Create Graphs of Sine & Cosine:  The two forces measured by the device will trace out the sine and cosine curves (with an amplitude mg) as the device is rotated through angle.

 

Verify Specific Predictions:  Test out the special triangles: 45 45 90, 30 60 90, 3 4 5, to reinforce the behavior of the forces as the vary with tilt angle.  For example, 5N tilted to an angle of 37 degrees will have a normal force of 4N and a downhill force of 3N.  But what will happen for 53 degrees?

 

In an open-ended lab the students invent their own procedures and hypothesize the relationships without formal instruction.

 

Open-Ended Lab:  Have students try to invent the formulas for themselves.  Taking data from the digital balance and from the spring scale to determine the relationships from scratch.  This style of lab is consistent with the NGSS Standards and the AP Physics 1 curriculum.

 

 

 

Tips for Success

 

While taking measurements the user will have to “tare” the scale every time.  This is because the plate that sits on the scale is itself an object with weight.  Once the angle is selected, simply lift the cart and tare then reweigh.

 

It is also important to recalibrate the spring scale when making a measurement of the component downhill.

How it looks to correctly set 45 degrees.

 

Be careful not to confuse the screw that holds the up the incline plane with the angle indicator.  The angle is measured best by the lower edge of the plane being in line with the angle in question.

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James Lincoln

James Lincoln is an experienced physics teacher with graduate degrees in education and applied physics. He has become known nationally as a physics education expert specializing in original demonstrations, the history of physics, and innovative hands-on instruction.

The American Association of Physics Teachers and the Brown Foundation have funded his prior physics film series and SCAAPT’s New Physics Teacher Workshops.

Lincoln currently serves as the Chair of AAPT’s Committee on Apparatus and has served as President of the Southern California Chapter of the AAPT, as a member of the California State Advisory for the Next Generation Science Standards, and as an AP Physics Exam Reader.  He has also produced Videos Series for UCLA’s Physics Demos Project, Arbor Scientific, eHow.com, About.com, and edX.org.


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See Energy Transformation with a thermal camera or steel spheres [W/Video]

You can calculate the thermal energy created when the ball hit the bat by using the Law of Conservation of Energy. Before the collision, the center-of-mass of the bat (mass 1kg) was moving at about 70mph (31m/s) and the ball (mass 0.15kg) was moving at about 90mph (40m/s). Now, calculate the initial kinetic energy.
[Answer: 600J]

After the collision, let’s estimate the speed of the bat at 50mph (22m/s) and the speed of the ball is 30mph (13m/s). Calculate the final kinetic energy. [Answer: 255J]. Now use the Law of Conservation of Energy to find the thermal energy created during this ball-bat collision. [Answer: 345J]

This thermal energy is detected by the camera as a higher temperature on the bat and ball. The camera shows higher temperatures as white.

Now you can try to estimate the thermal energy created the collision of the Colliding Steel Balls? What information do you need to find or estimate? Paper burns at about 200˚C. Do your numbers suggest that the paper’s temperature could rise that much?

 


About the Author

Dr. David Kagan has been at CSU Chico for over thirty years. During this time, Dr. Kagan has served in numerous roles including: Chair of the Department of Physics; founding Chair of the Department of Science Education; and Assistant Dean in the College of Natural Sciences to name a few. He is a regular contributor to The Physics Teacher having had over thirty papers published in the journal. Kagan continues his deep devotion to quality teaching by avidly engaging his students with methodologies adapted from the findings of Physics Education Research. In addition, he has remained true to his lifelong obsession with baseball by using the national pastime to enhance the teaching and learning of physics.


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Help Students Reach the Ultimate Form Of Scientific Inquiry

Back to School Means Back to STEM

The Next Generation Science Standards (http://www.nextgenscience.org/next-generation-science-standards) identifies eight practices of science and engineering as essential for all students to learn. These are:

 

  1. Asking questions (for science) and defining problems (for engineering)
  2. Developing and using models
  3. Planning and carrying out investigations
  4. Analyzing and interpreting data
  5. Using mathematics and computational thinking
  6. Constructing explanations (for science) and designing solutions (for engineering)
  7. Engaging in argument from evidence
  8. Obtaining, evaluating, and communicating information

 

One of the best ways to implement all of these practices is through the growing practice of Project Based Learning (PBL), defined by Edutopia as “a dynamic classroom approach in which students actively explore real-world problems and challenges and acquire a deeper knowledge” (http://www.edutopia.org/project-based-learning). The duration of these projects can be as short as a single class period or last throughout an entire school year, but typically last from 1-3 weeks.

 

This past summer, Grade 6 – 9 science teachers, math teachers, and administrators from Warsaw (IN) Community Schools partnered with science and math educators from Ball State University during a two week summer institute to design classroom projects, strengthen science and math content knowledge, and refine inquiry practices. The Arbor Scientific “Pull-Back Car” (http://www.arborsci.com/pull-back-car) was featured in a “mini” PBL activity to illustrate how science, technology, engineering, and mathematics (STEM) can be integrated into an authentic data collection and analysis activity.

 

Participants were divided into 12 groups and each group of 4-5 participants was given a pull-back car. Each participant played the role of a quality control engineer, whose job description may include taking “part in the design and evaluation of the product” and being “responsible for making sure that the materials meet the requisite standards and that the equipment works correctly” (http://www.wisegeek.com/what-is-a-quality-control-engineer.htm). Each group served as a team of quality control engineers who were instructed to design and conduct tests on these cars to determine if Arbor Scientific should continue selling them.

The engineering teams addressed four questions about the cars:

  1. 1. How consistent is the distance an individual pull-back car travels after being pulled back a specified distance?
  2. 2. How consistent is the amount of time an individual pull-back car travels after being pulled back a specified distance?
  3. 3. How straight does an individual pull-back car travel?
  4. 4. Do all pull-back cars behave similarly?

 

Each team was charged with designing an experiment to answer their quality question, conducting the trials, analyzing their results, summarizing their findings on poster paper, and reporting their results to the large group.   Groups scattered in and around the building to design and conduct their trials.

 

1

After completing the data collection portion of the activity, groups returned to their tables to analyze their data and report their results.
2
After each group had completed their tasks, each group presented their findings. Examples of summary posters are shown below.
Screen Shot 2014-08-21 at 2.01.19 PM
Once the participants had a good idea of how consistent the cars were, these cars were again used later in the summer institute to investigate additional inquiry questions, such as:

  1. 1. How does the distance the car is pulled back before release affect the total distance it travels?
  2. 2. How does the distance the car is pulled back before release affect the total time it travels?
  3. 3. How does additional weight affect the distance the car travels when pulled back a specified distance?
  4. 4. How does additional weight affect the total time the car travels when pulled back a specified distance?
  5. 5. How does the angle of incline affect the distance the car travels when pulled back a specified distance?
  6. 6. How does the angle of incline affect the total time the car travels when pulled back a specified distance?

 

Despite slight inconsistencies in the behaviors of the cars, participants in this summer institute agreed that the Arbor Scientific Pull-Back Car is an excellent inexpensive product that can be used in many different investigations – especially when one wants to integrate aspects of STEM. These cars can be used at any grade level and provide countless opportunities for students to engage in authentic scientific inquiry. They also provide an inexpensive way for math teachers to incorporate real world data collection and analysis. As a science educator, I heartily recommend this product and can honestly say that I consider it the ultimate inquiry device!

Download this article as a PDF


Dr. Joel Bryan

Ball State University

Muncie, Indiana

Dr. Bryan teaches at Ball State for the Department of Physics and Astronomy. He taught all levels of high school physics (Pre-AP, AP, conceptual) and a variety of mathematics courses for 13 years before receiving his Ph.D. in curriculum and instruction at Texas A&M University.


 

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g ball

Measuring the Acceleration with the g Ball


What is this about?
Galileo claimed that all objects fall toward Earth with the same acceleration. Modern measurements indicate that this acceleration is about 9.8m/s2. Using the G-Ball by Arbor Scientific, you can measure this value and compare the acceleration of other objects with different masses and in different states of motion.

What do I need?
You need a G-Ball, a meter stick, other objects to drop such as a baseball.

What will I be doing?
First, you will measure the acceleration due to gravity by simply dropping the G-ball and getting the time to fall.  Next, you’ll throw the G-ball horizontally at different speed and see if the time of fall changes.  Finally, you will drop the G-ball and a baseball to see which object accelerates more rapidly.

What do I think will happen?
Assume that you drop the G-ball from rest from an initial height of 1.0m.  Use the accepted value of g = 9.8m/s2 and the kinematic equation  to predict the time of fall.  Did you get 0.45s?

If you toss the G-ball horizontally, at different speeds do you think:

  1. The time for the fall will increase if the G-ball is thrown faster.
  2. The time for the fall will stay the same if the G-ball is thrown faster.
  3. The time for the fall will decrease if the G-ball is thrown faster.

Take a moment to write down your thinking and explain your answer.
If you drop a G-ball and a baseball at the same time which one will hit the ground first?  Again, take a moment to write down your thinking to explain your answer.

What really happened?

  1. Following the instructions packaged with the G-ball, use it to time a fall of 1.0m.
  2. Repeat this process several times to get an average value.
  3. Comment on your value compared with your prediction.
  4. Time the fall for the G-ball tossed horizontally from a height of 1.0m.
  5. Repeat this tossing the ball horizontally at several different speeds.
  6. Do the values vary more than they did for the dropped G-ball?  Comment on your results and compare them with your prediction.
  7. Drop a G-ball and a baseball from the same height at the same time.
  8. Repeat this several times until you are sure which one hits the ground first.
  9. Comment on your results compared with your prediction.

What did I learn?
If you found that the time for the fall was about 0.45s, then you have verified the accepted value of the acceleration due to gravity is 9.8m/s2.  Did you discovered that regardless of the speed you threw the ball horizontally the time of the fall was the same?  If so, you have shown that the horizontal motion does not affect the vertical motion.  Finally, if you saw that all objects fall at the same rate, you have verified Galileo’s experiment – just like he supposed did at the Tower of Pisa.

What else should I think about?
Why did you have to be careful to throw the ball horizontally?  What would have happened if you accidentally gave the ball a slightly upward initial velocity?  What about a slightly negative initial velocity?

If the mass of a falling object doesn’t affect its motion, why does a feather fall slower that the g ball?

Catch it in the Web!
The Brainiacs dropped cars to test Galileo’s ideas about falling objects. Check it out!

A feather and a hammer were dropped at the same time on the moon. See the result!

About the Author

Dr. David Kagan has been at CSU Chico for over thirty years. During this time, Dr. Kagan has served in numerous roles including: Chair of the Department of Physics; founding Chair of the Department of Science Education; and Assistant Dean in the College of Natural Sciences to name a few. He is a regular contributor to The Physics Teacher having had over thirty papers published in the journal. Kagan continues his deep devotion to quality teaching by avidly engaging his students with methodologies adapted from the findings of Physics Education Research. In addition, he has remained true to his lifelong obsession with baseball by using the national pastime to enhance the teaching and learning of physics.


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A Visit to Isaac Newton’s Home [W/Video]

When I visited England this summer, I had the opportunity to walk in Isaac Newton’s footsteps at his birthplace, Woolsthorpe Manor.

James at Woolsthorpe Manor

It is a little tourist museum far from the major train stops. You will probably have to take a long taxi ride from the train station at Grantham, but it’s not so far from London that it’s more than a day trip.  Woolsthorpe means wool farm, and it still is a wool farm where you can find long-haired Lincoln Sheep grazing in the meadows.

It is everything you would imagine a farm in the idyllic English countryside to be, with lightly rolling green hills, a stone cottage, and barns. The home and birthplace of Isaac Newton still stands as it did during his lifetime: a proud stone cottage with many adjacent stables and farm houses. Today, every part that is not empty is a museum.

james3-1

During the plague years, 1665-1666, Newton fled his college at Cambridge and retired home to his mother’s stone cottage beside a grove of apple trees.  He was a self-taught student of mathematics, and by the time he returned, he was the top mathematician in Europe.

It was in the apple orchard here in Woolsthorpe that Newton developed his Three Laws of Motion and Law of Universal Gravitation. The apple tree that inspired the latter is supposedly still growing here. It is gnarled with age but still gives apples.

The markers tell the story of how the tree that inspired the young Newton’s gravity theory fell victim to gravity itself during a major storm.

At well over 400 years old, this tree miraculously still bears apples and inspires those who make the pilgrimage. As the sunlight broke through the clouds and the birds sang far from the city sounds it was easy to imagine what this place was like in Newton’s time and how one could think clearly here.

The peace stretches far across the land, and there is a contemplative feeling in the air; it seems like a place where there is nothing much to do except think of ideas.

Newton was born here on Christmas Day 1642, and grew up here learning to build little mechanical toys.

Young Newton often neglected his farm duties, such as mending fences and tending to the sheep, in favor of reading and experimenting. His father passed away before he was born, and his mother remarried and left him in the care of his grandmother. These stories and others can be learned while visiting the museum that was his home.

The main building itself has five rooms, and these are decorated in the style of the era, with signs and exhibits throughout. There is even a little hands-on science museum where visitors can try out some of the classic experiments associated with Isaac Newton.

Also on site, you will find a human sundial, a place for a picnic, and the famous experiments on optics that were Newton’s other great contribution to physics. There are prisms, reflecting telescopes, and light color mixers.

When Newton came of age, he left the countryside to attend Trinity College in Cambridge. Here, you can find cloned relatives of his apple tree, grafted, through vegetative propagation. One of the trees is in the Cambridge University Botanic Garden.

Cambridge is a great day trip too, and Trinity College is beautiful, thanks to King Henry the VIII’s money. Near the front gates you will find another apple tree, right outside Newton’s office, where he lived and worked as a research professor for almost 30 years.

james17-1

So where is Sir Isaac Newton now?

Some of his books and locks of his hair can be found at Cambridge and Woolsthorpe. Even a copy of his death mask resides at Woolsthorpe. The memorial and grave of Sir Isaac Newton is at Westminster Abbey in London. This is not far from where he was president of the Royal Society of London. Which also has markers that honor their famous former president.

Of all the sights, none can equal the quiet, contemplative air of the orchard in front of the stone cottage at Woolsthorpe Manor. As a physicist, this is truly a place for spiritual fulfillment.

It was during the plague years, that Newton escaped here and was inspired to write his Laws of Motion and Theory of Universal Gravitation. Spend an afternoon here and you too, may have a great idea.


james_lincoln  James Lincoln

Tarbut V’ Torah High School

Irvine, CA, USA

James Lincoln teaches Physics in Southern California and has won several science video contests and worked on various projects in the past few years.  James has consulted on TV’s “The Big Bang Theory” and WebTV’s “This vs. That”  and  the UCLA Physics Video Project.

Contact: [email protected]


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SpillNot: The Physics Behind the Slosh

Although the problem of why coffee spills might seem trivial, it actually brings together a variety of fundamental scientific issues. These include fluid mechanics, the stability of fluid surfaces, and interactions between fluids and structures (we’ll set aside the biology of walking for now). The SpillNot is a cool tool for getting your students interested in the everyday physics behind why drinks spill while we’re carrying them and what has to happen to prevent spillage.

Download James’ SpillNot PDF

Why spilling happens: When the rigid cup is accelerated horizontally the low viscosity fluid remains at rest and is left behind to rise up on the cup’s wall. The greater the acceleration is compared to gravity, the more fluid is left behind such that the ratio ahoriz/g is the same as the slope. Later, when the person stops walking forward, the cup is decelerated but the fluid (now in motion) remains in motion toward the other end of the container. In some cases there is an amplifying resonance when the accelerations match the natural frequency of the fluid’s back and forth sloshing. Try it!

Why the SpillNot doesn’t spill: Instead of accelerating the cup sideways, the handy lever tilts the base of the apparatus so that the cup’s walls are always perpendicular to the fluid’s surface. The device tips when you accelerate it so that the largest force on the cup comes perpendicularly from the base. Now, even when though the fluid has been sloped compared to the horizontal, the cup has been, too! Simply put, the SpillNot prevents spilling by rotating the bottom of the cup so that the sloshing of the fluid never falls over the edge.

Simply put, the SpillNot rotates the bottom of the cup so that the sloshing of the fluid never falls over the edge. Most teachers are familiar with the demonstration of centripetal force that involves a cup or water in the bottom of a bucket is maintained in the bucket even when the bucket is spun in a vertical circle that goes overhead. This is not a difficult demonstration to do, but the SpillNot makes it more fun and students can safely try the experiment themselves. Of course I recommend practicing with clear water first versus using hot coffee. For the most part spilling is nearly impossible unless one goes out of his way to jounce the string. So long as there is tension in the string, spills generally will not happen.

The SpillNot is best for qualitative demonstrations of centripetal force. The idea that it can successfully take an object through a vertical circle so long as its acceleration exceeds the acceleration due to gravity is well demonstrated. But quantitative measurements are technically nuanced and not as convenient. The radius of the circle is often hard to measure and is different for every case of spin. Additionally, the normal force N on the object is not the same as the force acting on the strap. Therefore, one will have to account for the added mass of the apparatus itself if one wishes to measure the force directly; for example by using a spring scale hooked to the loop. Otherwise, one can indeed use the SpillNot to make direct verification of Centripetal Force as being mv2/r.

B A sample procedure for the horizontal circle.

a) Hold the apparatus (loaded with ½ filled cup) out horizontally at an arm’s length
b) Hook a spring scale into the loop of the SpillNot (this can be used to measure m, the mass of the device and cup, and then later to measure the Tension, T)
c) Spin with the device in hand with a sufficient velocity such that the device raises
d) Have a partner time five full cycles with a stop watch, determine t for one cycle
e) During the spin, note the average value of the force on the scale (T)
f) Measure the horizontal radius (if the velocity is sufficient then Rhoriz = R is nearly true, otherwise Rhoriz = R cos θ)
g) Compute the velocity using the formula vcircle = 2πR/t or, more accurately, 2πRhoriz / t
h) Compare T with mv2/R, determine the percent difference, account for experimental error. (One such error is the assumption that either R or T is horizontal or that the mass of the apparatus is all the way out at R, which it is not!) Diagnosing errors is an important skill in physics. Note, that the centripetal force is only caused by Thoriz = T cos θ.

Alternatively, one could use the tilt of the SpillNot to determine the force. This can be accomplished by perhaps taking a picture or still-frame of a person swinging the apparatus. Then, with a protractor, measure the angle at which the rope falls below the horizontal. One can then compare a and v2/R by using tan(Ɵ)=a/g

This lab does not have much to offer pedagogically beyond what a ball on a string can teach, however the device itself is the hook that gets kids interested. It is novel and exciting to be spinning a cup ominously out with the plane of the fluid nearly perpendicular to the floor!

Another lab idea that you might try is the small vertical circle demonstration. In this case the radius is much easier to measure because, for all practical purposes, it is simply the height of the SpillNot plus the small rope. Assuming the cup has a fairly low level, one can determine the minimum speed required to spin the device without spilling. It may be wise and more fun – to do this lab outside. The slowest speed possible will be noticed when, at the top, the cup looses contact with the base. The free body diagram at the top of the spin generates Fnet = mv2/r = N+mg (down or centripetal taken to be positive). The statement “losing contact” implies that there is normal force coming from the base. Thus setting N=0 results in g=v2/r. Measure vcircle = 2πR/t similar to step g in the horizontal circle lab. In this case however I would recommend frame by frame video analysis of a video in which the students spin the device progressively slow until the cup falls off. By counting frames, t can be determined (frame rates can vary from camera to camera). Be careful however, the velocity changes throughout the circle. It will reduce error to use only the top half of the circle. In that case, vsemicircle= πR/t. Post lab analysis might involve comparing g with v2/r and accounting for error; which is usually about 15%.

Despite that the SpillNot does not offer itself easily to quantitative laboratory work, you will be impressed by how easy it is to use. It is not a quantitative demonstration tool. On the contrary, its best use is to demonstrate that the study of physics can be used to solve practical problems in ordinary life. The bonus is that it makes the classic centripetal force demonstrations much easier to perform.

In conclusion, the SpillNot’s ability to demonstrate centripetal force is not unprecedented. Many teachers will already be aware of the demonstration of the “Greek Waiter’s Tray” or water in the bottom of a bucket (both vertical and horizontal circles), and of course loop-the-loop rollercoasters. What is unique about the SpillNot is that you don’t spill whereas spilling is quite common among these other demonstrations, especially when a novice handles the apparatus. A novice, however, can successfully handle the SpillNot. Of course there is always the possibility that students will try to push the limits of the apparatus; but this is not a bad thing! In fact, having students learn what it takes to spill is a good lesson in the scientific method.


James Lincoln

Tarbut V’ Torah High School
Irvine, CA, USA

James Lincoln teaches Physics in Southern California and has won several science video contests and worked on various projects in the past few years.  James has consulted on TV’s “The Big Bang Theory” and WebTV’s “This vs. That”  and  the UCLA Physics Video Project.

Contact: [email protected]


 

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Download James’ SpillNot PDF

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Can the Frictional Force Between Two Interleaved Phone Books Lift A Car? [W/Video]

Students often underestimate the force of friction, despite the fact that friction is the force that acts every day to bring their school buses and cars to a stop. In this video, two phone books are interwoven page- by-page and the friction between the thin sheets of paper is put to the ultimate test – can the frictional force between two interleaved phone books lift a 3, 500 lb car? Watch the video below to see what happens.

Think of the total area between 2 phone books. That is a lot of friction!

Is It Possible To Pull Them Apart?

Watch Mythbusters try the experiment again using two military tankers.

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