Coupled Pendulums

December 2, 2011

by:  Martin Sagendorf

One Pendulum…

Is interesting, but…

Two Pendulums…

Are much more interesting.

 

But Only If…

They are coupled together.

An Easy Way Is To…

Couple them at their pivot points.  This is accomplished by hanging the two pendulums from a horizontal string.

There Are…

Many illustrations of coupled pendulums on the web; search for ‘coupled pendulums’ – but the fine points of making a really successful demo are rarely discussed… so before we start:

Some Guidelines:

-       Make the pendulums absolutely identical: both the rod lengths and the mass values (the lengths are measured from the pivot points to the C.G. of the masses)

-       Use rod lengths of at least 1/3 meter (13”) – so the pendulums don’t swing too quickly

-       Use masses of at least 75 g (1 oz) – to provide a long swing time

-       Space the vertical supports for a horizontal string length of 500 to 600 mm (20 to 24 in.) – weighted or clamped-down ring stands will work – and will work especially well if their top ends are joined by a solid bar to minimize vibrations

-       The string should be fairly taunt – for example:  a 13 to 15 mm (1/2 to 5/8 in.) droop in the center with two 75 g masses hanging 100 mm (4 in.) apart

-       Use pendulum spacings of 75 to 125 mm (3 to 5 in.) – experiment for good results

-       For the best results, symmetrical setup spacing is critical – try to achieve positions symmetric within 4 mm (1/8 in.)

-       When pulling a pendulum to the side, two things are very important: first, don’t pull it too far (a mass rise of 75 mm (3 in.) is fine); second, the pendulum must be pulled at precisely a right-angle to the string

-       For the following exercises, when two pendulums are raised, they should be raised to the same heights

With Two Identical Pendulums:

Center the two pendulums with the pair spaced about 100 mm (4 in.) apart

-       (A.)  Raise and release one pendulum

Question:  What happens?  Why?

-       (B.)  Raise (on opposite sides) and release both pendulums

Question:  What happens?  Why?

With Three Identical Pendulums:

Center the three with a space of about 75 mm (3 in.) between each

-       (C.)  Raise and release the center pendulum

Question:  What happens?  Why?

-       (D.)  Raise and release one of the outer pendulums

Question:  What happens?  Why?

-       (E.)  Raise (on the same side) and release both outer pendulums

Question:  What happens?  Why?

-       (F.)  Raise (on opposite sides) and release both outer pendulums

Question:  What happens?  Why?

So Far…

We have dealt with identical pendulums… but what happens if we:

-       (G.)  Make a pendulum with a greater mass (but the same length) and use it in place of one of those

above

Question:  What happens?  Why?

-       (H.)  Make a pendulum just slightly longer (say, 20%) than one of the three and use it in place of one of

the pendulums above

Questions:  What happens?  Why?

In Action:

Construction Notes:

-       The horizontal string must be firmly attached (tied, hooked, or taped) to the vertical rods

-       The pendulum rods are made from coat hanger wire or from welding rod

-       Hooks are formed in the pendulum rods using a pair of pliers

-       The masses can be any object that can be affixed to the rod – preferably an object through which a hole can be drilled and, for easy identification during demonstrations, the masses should be different colors

In This Apparatus:

-       Length of horizontal string = 600 mm (23-1/2”)

-       Length of pendulum rods (from inside hook to far end) = 440 mm (17-7/16”)

-       Diameter and material of pendulum rods = 1/8” brass welding rod

-       Thread on end of pendulum rod = 6-32 for a length of ¾ in. (Note 1)

-       Nuts = brass 6-32 knurled (2 per rod)

-       Small mass = 5/8” x 2-1/16” steel rod (75 g) – 3 required (Note 2)

-       Large mass = 1” x 1-3/4” steel rod (175 g) – 1 required (Note 2)

-       Distance from inside of pendulum rod hooks to the centers of masses = 400 mm (15-7/8”)

Note 1:  A No. 6 screw diameter is 0.138”. – the 1/8 in. welding rod is 0.013” less – this is OK

Note 2:  Drilled thru No. 29 (0.136”)

A Comment on Dimensions:

The overall dimensions are not critical, but the apparatus should be large enough to be easily viewed in a classroom setting.

A Definition:

These are ‘Simple Pendulums’ because they are not ‘ideal’: i.e. their masses are not concentrated at single points and the restoring force is not a constant – however they do exhibit ‘Simple Harmonic Motion’.  This motion is an approximation at small angles – it is sufficiently accurate for our purposes.

And Further:

The details of Harmonic Motion and Simple Harmonic Motion are fascinating – the details of both can be found in any physics textbook.

‘Resonance’ is defined as the building up of large vibrations by the repeated application of small impulses whose frequency equals one of the natural frequencies of the body – in this case, a pendulum.  Identical pendulums are required to provide maximum energy transfer.  The mechanical energy is transferred by the ‘pulls’ on the supporting string – this is rather like a child’s swing where ‘pushes’ applied at the correct times will ‘add’ and act to increase the swing amplitude.

In Summary:

These demonstrations provide vivid illustrations of energy transfer between two and three resonant bodies.  Even better, additional pendulums, various masses, and variations of excitation will provide more interesting demonstrations and bases for experimentation.

Marty Sagendorf is a retired physicist and teacher; he is a firm believer in the value of hands-on experiences when learning physics.  He authored the book Physics Demonstration Apparatus.  This amazing book is available from Educational Innovations, Inc. – it includes ideas and construction details for the creation and use of a wide spectrum of awe-inspiring physics demonstrations and laboratory equipment.  Included are 49 detailed sections describing hands-on apparatus illustrating mechanical, electrical, acoustical, thermal, optical, gravitational, and magnetic topics.  This book also includes sections on tips and hints, materials sources, and reproducible labels.

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Posted by Tami O'Connor

101 Things Everyone Should Know About Science

November 26, 2011

by:  Dia Michels

Science affects everything—yet so many of us wish we understood it better. Using an accessible question-and- answer format, 101 Things Everyone Should Know About Science expands every reader’s knowledge. Key concepts in biology, chemistry, physics, earth, and general science are explored and demystified by an award-winning science writer and a seasoned educational trainer. Endorsed by science organizations and educators, this book is perfect for kids, grown-ups, and anyone interested in gaining a better understanding of how science impacts everyday life.  101 Things Everyone Should Know About Science, written by Dia Michels and Nathan Levy is offered by Educational Innovations for $9.95.

Sample Questions!

1.  Name some characteristics of all mammals
2.  Name three of the bodily fluids
3.  What are the three states of water?
4.  What mineral is found in a saline solution?
5.  What do we use calories to measure?
6.  What happens over time when iron is exposed to oxygen?
7.  At the same pressure, which is more dense—hot air or cold air?
8.  How does a semiconductor work?
9.  Each year, Earth revolves once around what?

  • the sun
  • the moon
  • its axis
  • the Milky Way

10.  What are the four major directions? In which direction does the needle of a compass point?
11.  The continental divide separates:

  • which animals are nocturnal and which are diurnal.
  • the Northern Hemisphere from the Southern Hemisphere.
  • the direction water travels to the sea.
  • where it rains from where it snows.

12.  Why is it colder an hour after sunrise than it is at sunrise itself?
13.  What is a hypothesis?
14.  What is the goal of a double-blind, placebo controlled study?
15.  How can you use a lemon to light a light bulb?
 

Answers:

1. All mammals have backbones, are warm-blooded, have hair or fur, and drink their mother’s milk when they are born.

All mammals are vertebrates, which means they have backbones, unlike worms or insects. They are also able to maintain a constant body temperature, which is called being warm-blooded. Mammals have hair or fur at some point in their lives, and the females produce milk for their young through mammary glands. Mammals have large brains with modified skulls, complex teeth, and three ear bones. Their skulls have adapted over time to support their elaborate chewing muscles, and to better contain their large brains. Scientists believe that mammalian ear bones (the malleus, incus, and stapes) evolved from bones that were no longer needed, such as a bone to support gills. There are three orders of mammals: monotremes (egg-layers), marsupials (pouched mammals), and placentals (which account for the majority of mammals, including humans).

2. Blood, sweat, saliva (or spit), tears, breastmilk, semen, urine, mucus, lymph, plasma, serum, and digestive juices.

The human body is composed mostly of water, which our body uses to produce different fluids. These fluids help the body to work properly. Glands are organs in the body that create and release chemical substances through ducts. Glands produce sweat, saliva, tears, and breastmilk. Blood comprises two fluids and it also carries hormones, nutrients, infection-fighting cells, and oxygen. Plasma is the liquid component in the blood, while serum is the protein-rich fluid that remains after blood clots. Lymph is a milky fluid that contains lymphocytes, a type of white blood cell. It plays a critical role in the body’s immune system by filtering out and destroying toxins and germs. In mature males, the reproductive system produces semen, which contains the sperm needed to reproduce. Our kidneys process urine to carry wastes out of the body. Mucus is a thick secretion made by special tissues, including the inside of the nose and throat.

3. Liquid, solid, and gas.

Water exists in three states. We use the liquid state most often in our daily activities, for drinking, washing things, and cooking. Liquids do not hold a shape, but they maintain the same volume. In humans, liquid water makes up about 70 percent of our bodies. Ice, snow, and frost are frozen water. Water’s freezing temperature—the highest temperature at which water will become solid—is 32°F (0°C). Water vapor is water in its gaseous state. Until it reappears as a liquid or solid, it is invisible. Water evaporates into the air from bodies of water and from plant and animal respiration. Water vapor is an important regulator of the earth’s heat. Without it, and other so-called greenhouse gases, our planet would be very hot by day and very cold at night. A gas doesn’t hold its shape or maintain its volume. For example, if you pour one liter of water from a watering can into a bucket, it’s still one liter. If you take one liter of water vapor and release it into a two-liter bottle, it will spread out to fill the entire bottle. At sea level, water vaporizes at 212°F (100°C).

4. Salt.

Minerals (like salt) are natural compounds formed through geological processes. Saline is the term used to describe something, including a solution, that contains salt. The chemical name for salt is sodium chloride. Oceans are huge saline solutions, containing about 3.5 percent salt. Salt is also found in some rivers, lakes, and seas (e.g., the Dead Sea and Great Salt Lake). There are natural salt beds that are thought to have come from the salt water of evaporated ancient seas.

Salt manufacturers obtain salt either from these beds or by evaporating seawater. People have used salt as a seasoning and to preserve food supplies since ancient times. It was even used as money, in the form of salt cakes, by the Hebrews and other societies during Biblical times. There are references in the Christian Bible to salt and its value (e.g., “any man worth his salt.”) In Roman times, salt was an important item of trade and was used as money as well. Roman soldiers received part of their pay in salt, and newborn babies were rubbed with salt to promote good health. To compare a person to the “salt of the earth” is to say that they are valuable and have worth. Before refrigeration, rubbing salt into meat was the only way to preserve it. Salt is an excellent cleaning agent, drives away ants, is an effective antiseptic, and is used in skin treatments. Solutions of salts in water are called electrolytes. Both electrolytes and molten salts conduct electricity. Electrolytes also help the kidneys retain proper fluid levels and help balance the amounts of acids and bases in our bodies. They also help the cells in our bodies maintain a proper “voltage” so that the nerve cells can communicate with each other via electrical signals. Electrolyte drinks containing sodium and potassium salts are used to replenish the body’s water and electrolyte levels after water loss. Excessive water loss, resulting in dehydration, can be caused by exercise, diarrhea, vomiting, starvation, or surgery.

5. Energy.

We use calories to measure heat or energy. Scientists define the small calorie, or gram calorie (c), as the amount of heat it takes to raise the temperature of one gram of water 1°C. The large calorie, or kilocalorie (C), is equal to 1,000 small calories and is used to measure the amount of energy produced by the food we eat. Some items we consume have no calories, like water, coffee, or artificially-sweetened drinks, and provide us with no energy—although coffee and some diet sodas contain caffeine, which can create the illusion of energy. Other foods, such as cake and doughnuts, have lots of calories, but they provide little energy since they are very low in nutrients. These are known as empty calories. Any extra calories we consume beyond what is needed for our daily activities are stored by the body as fat.

6. It rusts.

Rust is the common name for a very common compound, iron oxide. For iron (chemical symbol Fe) to become iron oxide, three things are required: iron, water, and oxygen. Iron oxide, (Fe2O3) is so common because iron readily combines with oxygen (so readily, in fact, that pure iron is only rarely found in nature). Iron or steel rusting is an example of corrosion, an electrochemical process. Water speeds the process because it allows for the formation of hydroxide (OH-) ions. The rust that forms is much weaker than iron; when iron becomes severely rusted, it will crumble away. To prevent rusting (or the oxidation of iron), rustproof paint can be applied—a common occurrence on the Golden Gate Bridge in San Francisco. In other applications, nickel and chromium are added to iron to bind together the atoms and prevent them from rusting.

7. Cold air.

Cold air is more dense than warm air. Air is made up of nitrogen, oxygen, and other molecules that are moving around at incredible speeds, colliding with each other and all other objects. The higher the temperature is, the faster the molecules move. As the air is heated, the molecules speed up and push harder against their surroundings and each other. If the volume of the area is not fixed, this increases the space between the molecules, making the air less dense. For example, when the air in a hot-air balloon is heated, it expands (molecules speed up and spread apart). Now less dense than the surrounding air, the balloon rises. When the heater is turned off, the air in the balloon cools, the molecules slow down and move closer together, and the balloon descends.

8. By conducting electric impulses in a controlled fashion.

Semiconductors have had a monumental impact on our society. You find semiconductors inside most microprocessor chips—the heart of any normal computer. Anything that’s computerized or uses radio waves depends on semiconductors. Semiconductors, often created with silicon, allow the transmission and control of electric impulses in microscopic circuits. The smallness of these circuits has led to portable technology that could not have been built with the previous technology of vacuum tubes. For example, the computing power of a modern laptop computer would have required a large building full of power-hungry equipment and a large maintenance staff were it not for semiconductor technology. A diode is the simplest possible semiconductor device, and is therefore an excellent beginning point if you want to understand how semiconductors work. A diode allows current to flow in one direction but not the other. You may have seen turnstiles at a stadium that let people go through in only one direction. A diode is a one-way turnstile for electrons. Most diodes are made from silicon. You can change the behavior of silicon and turn it into a conductor by mixing a small amount of an impurity into the silicon crystal. A minute amount of an impurity turns a silicon crystal into a viable, but not great, conductor—hence the name “semiconductor.”

9. Earth’s orbit around the sun is called Earth revolution.

This celestial motion takes 365.26 days to complete one cycle. Earth’s orbit around the sun is not circular but elliptical. An elliptical orbit causes the distance from Earth to the sun to vary annually. Because Earth’s axis is tilted in relation to its orbit, the Northern Hemisphere receives longer and more direct exposure to the sun for half the year. For the other half, the Southern Hemisphere receives the warmer weather. The moon revolves around Earth much in the same way that Earth revolves around the sun, but it takes only 28 days for the moon’s revolution. Earth’s axis is the invisible line extending through its center from pole to pole. Earth spins, or rotates, on its axis one rotation every 24 hours, causing day and night. The Milky Way is the galaxy to which our solar system belongs.

10. The four major directions are north, south, east, and west; a compass needle points north.

A compass, often used when hiking or sailing, is a navigational tool used to tell direction. Magnets in the compass align themselves along a magnetic north-south orientation, which causes the needle to align with the magnetic North Pole, so it points north. The compass card inside the glass has the four headings shown as N, E, S, and W (going clockwise) and subheadings of northeast, southeast, southwest, and northwest. Numbers appear every 30 degrees. Long vertical marks occur every 10 degrees, with intervening short marks at 5-degree points. The compass card containing the magnets is mounted on a small pivot point in the center of the card assembly. This allows the compass card to rotate and float freely. The enclosure of the compass is filled with white kerosene to provide a medium to dampen out vibrations and unwanted oscillations. A lubber line is etched onto the glass face of the instrument to enable exact reading of the compass. When a compass points north, it is pointing towards magnetic north, or in the direction of the earth’s magnetic field. True north, also known as geographical north, is the actual northernmost point on the earth, or the center of the North Pole. The two measurements differ because the Earth’s magnetic “north pole” is actually in Canada. In order for an explorer to determine his actual location, he has to know the difference between true north and magnetic north, which changes depending on the longitude.

11. The direction water travels to the sea.

The North American continental divide is a mountain ridge that runs irregularly north and south through the Rocky Mountains and separates eastward-flowing from westward flowing waterways. The waters that flow eastward empty into the Gulf of Mexico by way of the Mississippi and other rivers. The waters that flow westward empty into the Pacific Ocean. Every continent with the exception of Antarctica has a continental divide. Some continents may have more than one.

North America also has an eastern continental divide, which runs along the Appalachian Mountains. Rivers to the west of this divide drain into the Mississippi and other rivers that flow into the Gulf of Mexico. Waterways to the east of the divide flow into the Atlantic Ocean.

Nocturnal and diurnal refers to the active time for an organism. An animal that is active during the day and rests at night is diurnal. An animal that primarily rests during the day and is active at night is nocturnal. The equator, an imaginary line drawn around the earth halfway between the north and south poles, separates the northern and southern hemispheres. Rain is liquid precipitation while snow is solid crystals. There are several factors that affect whether precipitation falls as snow or rain, such as temperature and elevation.

12. Because the planet continues losing heat after sunrise.

We think the minimum temperature should occur at sunrise because the earth has been cooling down all night. The temperature drops throughout the night because of two processes. The earth no longer receives energy from the sun, and the earth radiates energy to space. Overnight, the balance is strongly negative, and the earth loses heat. At sunrise, solar energy again arrives, but the heat loss due to radiation to space dominates until about an hour after sunrise. At that time, incoming solar radiation increases enough to overcome the radiational heat loss.

13. A proposed explanation for why something happens.

In common usage today, a hypothesis (which is Greek for assumption) is a provisional idea whose merit must be evaluated. Science happens in many ways. In some instances, a scientist observes a phenomenon—such as, food left at room temperature spoils more rapidly than food kept cool—and then develops a hypothesis for why. Other times, scientists set out to answer a question—such as, will mice be healthier if they eat vegetables or chocolate. Whether the hypothesis comes from an intellectual pursuit or an observation, the job of scientists is to perform tests in order to validate or negate their ideas. Through rigorous testing, scientists can help us learn what is speculation and what is real.

14. To eliminate the chance of bias.

In a single-blind experiment, the individual subjects do not know whether they are so-called test subjects or members of an experimental control group, but the researchers do. In such an experiment, there is a risk that the subjects are influenced by interaction with the researchers. This is known as the experimenter effect. Double-blind describes an especially stringent way of conducting a scientific experiment. In a double-blind experiment, neither the individuals nor the scientists know who belongs to the control group. Only after all the data is recorded (and in some cases, analyzed) are scientists permitted to learn which individuals are which. Performing an experiment in double-blind fashion is a way to lessen the influence of prejudice and unintentional cues on the results. Strictly speaking, in this type of experiment, every scientist who interacts with or treats a subject should be “blinded.” This doesn’t mean that they are really sight-impaired, it means they don’t know who is receiving a particular test or intervention.

15. Turn the lemon into a battery.

A lemon can be used like a battery by placing a copper penny and a steel paper clip (or a zinc-coated nail) into slits cut into the lemon skin, then connecting the penny and clip with a small piece of wire. The two different metals react with the acid in the lemon juice and cause electrons to travel from the negative terminal (the steel or zinc) to the positive terminal (the penny). An electric potential is created when the different metals are immersed in the lemon, and you can measure this with a voltmeter. One lemon alone will probably not produce enough power to light a bulb, but if you link four or more lemons together in a circuit by connecting the negative terminal of one lemon to the positive terminal of the next, and so on, you may get enough electricity to light an LED bulb, or some other small device.

Dia Michels is the founder and president of Platypus Media, an independent press in Washington, DC, whose goal is to create and distribute materials that promote family life by educating grown-ups about infant development and by  teaching children about the world around them. She is an award-winning science writer who has written or edited over a dozen books for adults and children. She has spoken at national and international conferences for such groups as American Association for the Advancement of Science, national Association of Biology Teachers, La Leche League International, Smithsonian Institution, and the Museum of Science.

Nathan Levy is the author of Stories with Holes, Whose Clues? and Nathan Levy’s 100 intriguing Questions. A gifted educator, Nathan worked directly with children, teachers, and parents in his 35 years as a teacher and principal. He has developed unique teaching strategies that encouraged the love of learning. He has also mentored more than 30 current principals and superintendents, as well as helped to train thousands of teachers and parents in better ways to help children learn.

2 Comments | Biology, Chemistry, Earth Science, Elementary Level, High School Level, Middle School Level | Tagged: | Permalink
Posted by Tami O'Connor

Two Prisms – Four Demos

November 26, 2011

by: Martin Sagendorf

Most everyone knows that an equilateral prism will refract white light into its constituent colors: a spectrum ranging from red to violet.  But, if one uses an additional prism, there’s much more to be discovered.

All that’s required:

-       a source of white light

-       a slit mounted on a large piece of cardboard

-       two equilateral prisms

-       two small pieces of card stock

-       a square of ground glass.

SIMPLE REFRACTION

The light source and slit are arranged as shown.  A fairly narrow (1/4”) color spectrum will be displayed on the ground glass.  Note that the light beams are DIVERGENT.

DOUBLE REFRACTION

The color spectrum from one prism is now passed through a second prism.  The various color beams are further spread to result in a somewhat wider (5/16”) spectrum display on the ground glass.  The light beams are even further DIVERGENT.

A SINGLE COLOR EXPERIMENT

Isaac Newton wondered if any single color of a spectrum could be further broken into more colors.  To investigate this, he placed ‘STOPS’ in the light beams between the two prisms – allowing only one color to pass to the second prism.  The result was that once white light was broken down into its constituent colors, the colors could not be further broken down.  Here only one STOP is used – leaving only red, with a small fringe of blue.

RECOMBINING SPECTRUM COLORS

Isaac Newton also wondered if the colors of the spectrum could be recombined to again make white light.  To do this he used a second prism arranged as shown.  He proved that this was possible.  What’s interesting is that the light beams exiting the second prism are not on the same line, but they are PARALLEL.  And, because the slit is not infinitely narrow, these beams are not infinitely narrow and therefore can mix to create white light.

THE COMPONENTS

  • A 100 Watt halogen bulb provides a good light source.  It must be shielded because the room light should be a low-level to see the spectrums on the ground glass.  As shown, a box top is used – a fully enclosed bulb would be better, but there must be provision for removing the heat generated (about 90 Watts for a 100 Watt bulb).  Experiment to find a slit width that works well for your set-up.

  • Two razor blades (single or double-edged) spaced with their edges about 1/32” apart make a good slit.  Tape the blades over a one inch by ¼ inch cutout in a piece of cardboard.  And be sure to use black tape to cover any openings in the blades.
  • Two equilateral prisms.
  • Two 3” x 3” square pieces of thin cardboard to act as STOPS.
  • A 2” x 2” or 3” x 3” piece of ground glass or frosted vellum paper.  Ground glass is easily made using automobile engine valve lapping compound – place some compound between two pieces of ordinary window glass and rub them together.  Only one side should be frosted.  The sharp edges and corners of the glass pieces can be ‘broken’ with fine sandpaper wrapped around a small piece of wood.

NOTES:

A standard tungsten filament light bulb will not work as well as a halogen bulb – the halogen provides a much better spectrum.  Rotate the bulb to obtain the highest illumination of the slit.

The STOPS can be hand-held or taped to small blocks of wood.  In either case, the vertical edges that block the light must be parallel to the color lines so only one color is passed.

The ground glass can be taped to a small piece of wood – in this case, the vertical dimension should be increased to 3”.

It is important that the heights (the centerlines) of the bulb filament and the slit be the same.  And since the bulb’s filament will be four or five inches above the bench top, some large books or other flat objects can be stacked so the vertical center of the optical components match the center height of the slit.

The distances shown in the illustrations work well.  The distances to the ground glass can be increased for larger images, but with subsequent decreases of image intensity.  Obviously, a darker room will allow easier viewing of fainter spectrums.  As shown in this photo:

The spectrums shown are slightly curved because the prisms’ faces are very slightly curved.

IN SUMMARY

These are great demos in that they not only illustrate some fundamental properties of light, but that they also provide for many variations of the set-up.  The distances and angles shown provide a starting point for experimentation.  For example, increasing the distances will enlarge the spectrum display – but, which works best to do this?

IN THE CLASSROOM

These experiments can be done as a demo for the class as a whole, but even better, since the components are so inexpensive, several set-ups can be provided for lab groups of three or four students.  Equally fun for the instructor is the creation of the lab worksheet guiding the students through the investigations.

Marty Sagendorf is a retired physicist and teacher; he is a firm believer in the value of hands-on experiences when learning physics.  He authored the book Physics Demonstration Apparatus.  This amazing book is available from Educational Innovations – it includes ideas and construction details for the creation and use of a wide spectrum of awe-inspiring physics demonstrations and laboratory equipment.  Included are 49 detailed sections describing hands-on apparatus illustrating mechanical, electrical, acoustical, thermal, optical, gravitational, and magnetic topics.  This book also includes sections on tips and hints, materials sources, and reproducible labels.

Leave a Comment » | High School Level, Middle School Level, Physics | Tagged: , , , , | Permalink
Posted by Tami O'Connor

If you Want a Good Thermometer, Don’t Use Your Body

November 26, 2011

by: Martin Sagendorf

An Easy Question:  Which is warmer – which is cooler?

In the strictest sense, it’s a matter of energy.  And we use temperature as a measure of energy level.  As we all know, the greater the energy level, the higher the temperature… But, although this is absolutely true; sometimes it’s not exactly what we perceive in everyday life.  When asked, we all can testify that when we touch a piece of metal we’ll say it feels cold.  But is it really cold?  Is it or isn’t it ‘cold’?

The Answer Is…

… very simple.  If the piece of metal is at room (ambient) temperature it cannot be ‘cold’ – it must be at the same temperature as the temperature of the room.

But First:

Let’s discuss ‘perceived temperature’: this is what we ‘think’ the temperature is.  It isn’t always the actual temperature (of the object we touch).  Thus we enter a wonderful combination of both physics and biology.  Physics describes the absolutes.  Biology describes the biological reactions (interpretations) of our physical world.

It’s a matter of thermal conductivity and our nerves.  Some materials are good conductors of heat (energy) and some are not.  Our nerves sense only temperature – so if thermal energy is rapidly removed from the tissues surrounding our nerve endings (like at our finger tips), our nerves sense that the temperature ‘they feel’ is cooler – e.g. the material is removing thermal energy from the body tissue surrounding the nerve ends at a rate faster than our body can re-supply energy to the tissues – thus our nerves sense this as ‘cooler’.

Now:

A truly illustrative and memorable way to present the question:

Use a construction that provides a means of ‘feeling’ the temperature of three different materials: all three of differing thermal conductivities – low, medium, and high – a simple box having squares of ceramic, wood, and aluminum.  The ceramic and aluminum pieces exhibit nearly the same thermal conductivity, but the aluminum has just a little better thermal conductivity.  The wood has a relatively low thermal conductivity.

This box is 17” wide, 8” high, and 3” deep.

In The Classroom, Discuss:

Thermal energy in materials

Temperature (as a measure of thermal energy)

Conductivity (of thermal energy)

[note that you haven’t yet presented the biological aspect of the students’ upcoming measurement of what’s warmer or cooler]

The Exercise:

Begin by drawing a three column ‘Vote List’ on the classroom board (ALUMINUM – WOOD – CERAMIC).

[this is a little of a deliberate distraction, but flip the switch to ON and count to five seconds before starting]

Have the students, one-by-one, ‘test’ (by touching) the three materials and marking their vote on the board.

Total the votes.

Ask the class if this makes sense… that the aluminum (or perhaps the ceramic) piece is the coolest?  Ask, “Why is this so?”… “Is it because the metal or ceramic is heavier?”… Or, “Is it because the wood is darker in color?”

Now, turn the box to show its insides – that there’s nothing inside the box.  The three pieces of material MUST be at the same temperature! – Room Temperature.  If any students still doubt you, use an IR thermometer to prove your point!

And Finally:

The really fun part of the lesson:  Ask the class, “Why did so many people think that one material is ‘cooler’ than the other two materials?”  Don’t give the answer – guide the discussion – let the class discover the answer.

Marty Sagendorf is a retired physicist and teacher; he is a firm believer in the value of hands-on experiences when learning physics.  He authored the book Physics Demonstration Apparatus.  This amazing book is available from Educational Innovations – it includes ideas and construction details for the creation and use of a wide spectrum of awe-inspiring physics demonstrations and laboratory equipment.  Included are 49 detailed sections describing hands-on apparatus illustrating mechanical, electrical, acoustical, thermal, optical, gravitational, and magnetic topics.  This book also includes sections on tips and hints, materials sources, and reproducible labels.

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Posted by Tami O'Connor

Ghost Eyeballs

October 14, 2011

by: Norman Barstow

Educational Innovations’ Growing Spheres can be used to add a note of ‘horror’ to your classroom or home Halloween experience.  Once fully expanded, Growing Spheres have an index of refraction almost identical to that of water. This means that when the Growing Spheres are placed in water, they are nearly invisible.

Materials:

  • A large (2 qt or larger) translucent plastic storage container and lid.
  • Growing Spheres : GB-720 or GB-730 (these are the size used for the photos)
  • Water
  • Label for the container lid: GHOST EYEBALLS

Procedure:

1. Fill the storage container about ¾ full with water.

2. Add a pinch or two of Growing Spheres.

3. Wait about a day to let the spheres expand in size.

‘THE HORROR’

Place the container of ‘ghost eyeballs’ either on your school desk or at home on a table or chair on the front porch.  Place a ghost mask and/or ghost costume near the container of eyeballs.  Invite your students or trick or treaters to reach into the bowl and touch the ghost eyeballs.

CAUTION:

The eyeballs won’t be visible at first, but after several hand insertions, the water will get a little dirty and the eyeballs will be visible.

HUMOROUS FOLLOW-UP.

When I finished taking the pictures for this Blog entry, I put the Growing Spheres into the soil of a large plant we have in the house.  When we’re away for the summer, we leave the plant with a friend.  One day, after a rainy spell, our neighbor noticed the spheres sticking up out of the soil. “What,” she thought, “Snake eggs?”

So she rushed a sample over to a local nursery where she learned that these snake eggs were actually a form of water gel crystals.

What Are Water Gel Crystals?

When placed in water, over time these hard crystals expand to about 300 times their size, producing gel-like spheres. Students love to feel the slippery, spherical gel! The Large size start with a diameter of about 3.0 mm and end with a diameter of about 20.0 mm.  For a lesson activity, ask students to determine the change in volume, using V = 4/3 pr3.  These polymer spheres are great for starting seeds and growing plants so that the roots can be seen! They can be colored using food coloring. The polymer is similar to our super-absorbent, polyacrylamide polymer (#GB-5B and #GB-3) and can be dried and reused. These spheres are available in four sizes: Regular (~1.4 cm expanded), Large (~2.3 cm expanded),  Jumbo (~3.3 cm expanded) and Gigantic-Sized Spheres (start with a diameter of ~15 mm and grow to a diameter of ~57 mm!)


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Posted by Tami O'Connor

Make Your Own Time

October 10, 2011

by: Martin Sagendorf

A Definition:

Clocks measure time – it can be a continuous measure of events passing or the measure of the interval between two events.

Of Hours:

After years of evolution, our modern clocks now divide the day into 24 equal length hours.  And, as we know, there are two systems in use today: Americans use the “double-twelve” system while the rest of the world uses the 24 hour system.

As An Aside:

The word “hour’ comes from the Latin and Greek words meaning season, or time of day.  A “minute” from the medieval Latin pars minuta prima (first minute or small part), originally described the one-sixtieth of a unit in the Babylonian system of sexagesimal fractions.  And “second” from partes minutae secundae, was a further subdivision on the base of sixty – i.e. “a second minute”.  (ref. Pg. 42 The Discoverers by Daniel J. Boorstin)

The “Double-Twelve” Clock Face:

Has 12 at the top – probably because at noon the sun is at its highest point in the sky.

But…

We can make a clock with 12 o’clock anywhere we wish and the clock will still work just fine.

Here we have a clock with 12:00 where 5:00 usually is.  Now, if the hour hand points to 12 and the minute hand points to 2, the time would be 10 minutes past 12.

Or:

We can rearrange the face:

Or:

We can replace the numbers:

Or:

We can divide the day into ten hours (times 2).

Suitable Clocks & How:

-       Good candidates are battery operated clocks with face diameters of 8 inches or less.

-       There are a variety of these clocks – all I’ve seen can be disassembled if one is careful.  When a front cover face must be removed, it is usually secured by three small tabs at the inner part of the face – use a worn common screwdriver to gently pry inwards, over a tab location, between the side of the cover face and the clock body – this will release the tab and allow the cover face to be gently ‘worked’ outwards.  Other clock designs are held together by multiple screws from the rear – be careful, some of these have real glass for the cover face.

-       The hands can be pried-off by using one’s fingernails on opposite sides of the hub of each hand.

-       A new dial face should be of ‘card stock’ (8-1/2” x 11” is readily available) – standard weight paper is too light.

-       A dial face must be a little smaller (1/16” on the diameter) than the opening into which it is placed – this will prevent buckling from expansion due to high humidity.

-       The dial face can be hand-drawn or computer-generated (using any of the popular computer drawing programs).

-       A punch or a craft knife can be used to cut out the center hole.

-       Sometimes the original dial face can be removed – sometimes not – it is not really necessary.  In either case, multiple small pieces of double-sided tape are used to fasten the new dial face.

-       When reinstalling the hands, they must be synchronized – the easiest way to do this is to set (press on) all the hands pointing to the (original) 12:00 position.

And More:

Over the years I, and my students, have made dozens of different clock faces – there seems to be never-ending variations.  You, and your students, will think of many different ones – just think of anything that represents numbers.  And, what’s neat is that each individual clock can have the maker’s name and/or school name included on its face.

Marty Sagendorf is a retired physicist and teacher; he is a firm believer in the value of hands-on experiences when learning physics.  He authored the book Physics Demonstration Apparatus.  This amazing book is available from Educational Innovations – it includes ideas and construction details for the creation and use of a wide spectrum of awe-inspiring physics demonstrations and laboratory equipment.  Included are 49 detailed sections describing hands-on apparatus illustrating mechanical, electrical, acoustical, thermal, optical, gravitational, and magnetic topics.  This book also includes sections on tips and hints, materials sources, and reproducible labels.

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Posted by Tami O'Connor

The Tipping Point

October 6, 2011

by:  Ron Perkins

The bottle balancer is a fascinating conversation piece that illustrates the principle of center of gravity!  A small hole in an oak board allows you to balance a 2-liter soda bottle at an angle that appears to defy gravity. This can be used as a teaching tool or a centerpiece at your next party!  Hold the special angle cut of the wooden, bottle balancer board against a flat horizontal surface.   When a full, sealed, 2-Liter soda bottle is inserted into the wooden hole from above, it will catch the bottle flange and the wood/bottle assembly balances at a surprising angle.

Explanation:

In order for an object at rest to NOT tip over, its center of gravity, or its center of mass must be directly over its base.   A goose-necked desk lamp is usually quite stable, unless it is configured so that the lamp part is stretched horizontally, far from the large base.  Then, it becomes less stable and often tips over.   The wood/bottle assembly example is more complicated than the lamp example because if the bottle is moved, the flowing liquid results in a change of its center of mass.

Consider a thought experiment!  To simplify the Soda Bottle Balance, consider the soda in the bottle frozen and the bottle super-glued to the wooden board so that everything balances on the angled edge of the board.  Balancing will only occur if the center of mass is directly above the flat angled edge of the wood.    How do you find the center of mass?  Loosely tie a string to your forefinger with a hanging weight tied to the other end of the string, e.g. a large metal nut or a bunch of washers.  Balance the object (in this case, the glued and frozen bottle balancer) on your forefinger above the string.    The center of mass will be somewhere along the straight line that includes the string.    Then, balance the wood/bottle assembly on your forefinger at a different point.    Again, the center of mass will be somewhere along the straight line that includes the string.    Where the two lines intersect is the center of mass.   This imaginary point must be directly above the object’s base in order for the object to be stable and not tip over.   Sometimes the center of mass is within the object and sometimes it is a point in space outside the object, as in the wood/bottle assembly.

What happens when you release the carbon dioxide gas from a balanced 2-liter soda bottle?   A sealed 2-liter soda bottle has a mass of more than 2000 grams of material and contains about 10 grams of carbon dioxide under pressure (Wikipedia).   If the bottle is opened and the gas released, the mass of the bottle becomes less by about 0.5%.   However, approximately half of this decrease in mass is to the left of the center of mass and half to the right. The release of gas results in very little change in the center of mass.   In trying the experiment, one must find a method of slowly releasing the gas in the bottle without disturbing its balance.   One method would be to make an extremely small hole in the balanced bottle by pressing a small hot needle into the bottle, allowing gas to slowly escape without losing liquid. This way the bottle assembly stays balanced as the gas begins to slowly leak from the bottle.   Observe what occurs!  Sounds like an interesting experiment!    Please let Educational Innovations know the results!

Note:   

As the pressure is released, the bottle may sag causing the soda to flow, drastically changing the center of mass of the bottle.   Also, if the gas is released too quickly, foaming will occur as dissolved gas quickly comes out of solution, resulting in loss of liquid.

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Posted by Tami O'Connor

The Law of Dulong and Petit

September 3, 2011

by: Dr. Jean Oostens

Atoms were proposed in antiquity without any experimental evidence by Democritus, a Philosopher.  This must have been a problem for Newton and Leibnitz who posited that there was always a mean of considering smaller and smaller intervals of space to calculate the “instantaneous velocity”.

The introduction of the precision balance in chemistry by Lavoisier paved the way for Dalton to formulate his laws on the “definite and multiple proportions” governing chemical reactions.  This supported the atomic theory, without giving it general acceptance.

Specific heat was defined as the quantity of heat needed to increase one gram of a substance by one degree.  There was no definite pattern when specific heats of various substances were compared.  Until two French scientists, Dulong and Petit in 1819 calculated specific heat by atomic mass.  There appeared a number of cases where the results were quite similar: about 6 calorie per mole.  This was equivalent to stating that any atom is as good as any other to store heat!  This was a small step towards acceptance of the existence of atoms.   An explanation for this, and the reason for the exceptions, had to wait the early 20th century explanation by Albert Einstein.  By that time, atoms had gained wide acceptance from the work of Rutherford, and soon by Bohr.
—————————————————————————————————————

The Lesson:

You are given several chunks of metal, each containing 0.6 1024 atoms (i.e. one mole) of one element.   How will each of those samples, when dropped in a standard quantity of hot water (typically 200 mL and 70 C) affect the temperature?

Step 1  Use a good balance (at least 0.1 gm resolution) to determine which element you are dealing with.  If possible confirm your identification with an additional cue.

Step 2 . Select one of the computers available, and look at the readings of the two temperature probes (lower left corner of the screen).  They will tell which pair of element your are assigned to investigate.

Step 3.  Prepare your two standardized water containers.  Fill the two Styrofoam cups with equal amount of tap water. Check that the two temperature sensors read the same within 0.1 C.   Then bring the two cups to the microwave oven and heat for 2 minutes.  Exchange the positions of the cups in the microwave oven and repeat another 2 minutes of heating (this will uniformize the temperatures).

Carefully bring back the two cups (the water may be very hot) to your station and insert the temperature probes into their respective cup.  You need to note which cup is to receive the required element (Gold => Yellow and Silver => Grey for example).   When the probes reach an equilibrium, after 5 to10 seconds, verify that the two temperatures match within a degree or less.  If necessary, use a 60 mL syringe to transfer water from one cup to the other and then the other way.  The idea is to have the same quantity of water at the same temperature within reason.

Step 4.  Start the measurement.  Hit the “START” button with the mouse and wait 10 to 15 seconds during which an horizontal line should appear, with both traces nearly on top of each other (if this is not so, go ahead anyway: you can always get another chance).

Drop your two samples the same time, one in each cup and watch until the completion of the three minutes.

Compare your results with the other teams’ and draw conclusions of the exercise.

This experiment on Dulong and Petit Law was performed by the students of Professor Shuffett’s Chemistry class at Lindsey Wilson College (Columbia, KY). It uses the mole set from Educational Innovations and takes advantage of existing data acquisition capabilities at that college.

About the Author:  After 20 years of research in Particle and Nuclear Physics, Dr. Oostens included in his activities, teaching at several college and universities all over the US. After moving to Kentucky 17 years ago, he co-founded a local Alliance, STASCKY (Science Teachers Alliance – South Central Kentucky).  He hasserved as STASCKY’s secretary since its inception.

For more than forty years he has kept a small research activity in collaboration with Los Alamos National Laboratory in New Mexico.  His involvement there started when Dr. Louis Rosen started a non-programmatic (i.e. not defense) group to attract more talents from all over the world. In 1970, he invited Dr. Oostens to participate in that project as the first non-American to work there. Dr. Louis’ idea was predicated on a high intensity 800 MeV accelerator called LAMPF (for Los Alamos Meson Proton Facility). Later on, the proton beam was used to create a flexible neutron source, LANSCE, that attracted a variety of researchers from all fields.

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Posted by Tami O'Connor

How to Make a Rocket (Scientist)

July 1, 2011

by:  Tami O’Connor

A few months ago I had occasion to conduct two hands-on workshops for elementary and middle school teachers at the NSTA National Convention in San Francisco on behalf of Educational Innovations.  One presentation focused on film canister rockets.  This is a tried-and-true way to teach Newtown’s First and Third Laws of Motion and also brings to light concepts such as the four forces of flight; thrust, drag, weight, and lift.  It also reinforces instruction on 3-D shapes and 2-D plane figures such as circles, cones, cylinders, rectangles, and triangles.

I presented the lesson to the teachers in much the same way I would to my students.  The first thing we did was to brainstorm the features all rockets have.  After a bit of discussion it was agreed that they all have a nose cone, a cylindrical body, fins, and an engine.  I then handed out a paper template imprinted with the pattern of a nose cone and fins, a regular 8½ x 11 sheet of white paper, a piece of goldenrod paper, and a white translucent film canister.  Also required are scissors, tape, ¼ piece of an Alka Seltzer tablet, and paper towels.

The only canister that works with this rocket is the type that has the lid that fits snugly inside the canister.  The canisters that have a lid that wraps around the outside rim, however, will not allow enough pressure to build up inside the chamber.

The first step in building a film canister rocket is to construct the body of the rocket.  The easiest way is to curl the white 8 ½ x 11 paper into a cylindrical shape using the film canister (without the top) as a guide.  The paper can be rolled around the film canister and then taped along the edges.  The easiest way to recover the film canister is to blow into one end of the rolled cylinder, forcing the canister out the other end.

When I conduct this activity I am careful not to offer any suggestion as to whether students should roll the paper in the long or short direction, nor do I discuss how much tape should be used.  The results are very interesting.  Students (adults and children) are very creative, especially when they are not bombarded too much instructional advice.

At this point, you should use Scotch tape to affix the film canister to the cylinder.  This is one of the most critical steps.  First, the canister must have the open end extending far enough from the end of the cylinder so that no tape overlaps the opening of the canister.  If any tape extends over the opening, the lid will not form a complete seal, and sufficient pressure to launch the rocket may not build up.  Second, if the canister is not taped securely, it will launch into the cylinder and propel only the canister rather than the entire rocket.

The next step is to cut out a nose cone and fins.  I use the attached template in my workshops.  The nose cone is actually a circle with a ¼ pie slice cut out.  For those old enough to remember, it closely resembles a Pac Man figure.  The nose cone is made by curling the PacMan so the edges of the missing pie piece begin to overlap forming a cone shape.  Though the template I passed out had cut lines for the nose cone and fins, I give very little direction as to the size of the nose cone or the total number of fins each student should use.

When the construction of the rocket is finally completed, it’s time for the launch!  I have students lay the piece of goldenrod paper on their desk and clear from the launch area any papers or other things that might get wet.  I invite students one at a time to the front of the room so everyone can see the results of their construction techniques.  During teacher workshops where time is limited, I have everyone launch at the same time.

When we’re ready to launch I hand out approximately ¼ piece of an Alka Seltzer tablet.  It is important when working with students to remind them not to put anything in their mouths (especially Alka Seltzer!).  Since the Alka Seltzer is the last step in the process I have students place the tablet piece on the desk and leave it there until I specifically tell them to pick it up!

While holding the rocket upside down students are instructed to fill an eyedropper or pipette with water and add a squirt or two into the film canister.  The amount of water is not critical in the grand scheme of things.

The next step is far more critical, so it is important that students are paying attention at this point.  Once the Alka Seltzer is added to the water in the film canister, it will begin to fizz and give off Carbon Dioxide gas.  The total release of gas is not immediate and therefore will continue for more than a minute which allows plenty of time for the student to secure the cap onto the film canister.  If students become flustered and attempt to jam the top onto their canister while holding the paper cylinder portion of their rocket rather than holding the canister portion they will likely damage their rocket.  Thirty seconds is much longer than most people think.  Having the students relax is the key!  The important thing to remember is to grip the rocket around the film canister and NOT the paper cylinder.

Once the top of the canister is secure the rocket should be placed in the center of the goldenrod paper and the student should step back and wait.  The results are wonderful!!!  Inside the closed film canister pressure continues to build until the container can no longer contain it.  At this point, the top separates from the canister.  Since the top is unable to move with the table behind it, the rocket is propelled upward with a loud popping noise.   Since Goldenrod paper is an indicator for bases, students will notice the launch pattern that is left behind on their launch pad!  Kids find this almost as cool as the rocket launch!

After the activity is over students will note with interest which rockets flew the highest.  This is when the true lesson begins!  Here is the opportunity to identify the many variables and the effects of each variable on the rockets’ flight characteristics.  Examples will include the width of the nose cone, the length of the cylinder, whether any excess paper from the cylinder was trimmed and discarded, and the amount of tape that was added to the rocket during construction.

Since the film canisters are reusable, and the construction materials are quite inexpensive, students should be given the opportunity to redesign their rockets based on discoveries they made during the launch trials and the class discussion.  This is one activity that generates so much enthusiasm with every age group that I fit it in whenever possible.  I’ve brought this activity to Girl Scout meetings with varied ages, Daisys to Cadettes. And with 16 years of teaching experience from 1st grade to 7th, I managed a successful launch in each and every class!  This activity is so adaptable that there is certainly no shortage of learning!

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Posted by Tami O'Connor

Invite Newton Into Your Classroom

May 28, 2011

by: Matthew Morris

Newton was a revolutionary thinker of his time. He is responsible for the three laws of motion that we still use today;

1. Objects that are not in motion remain stationary unless acted upon by another force.

2. There is a direct relationship between the force acted upon the object and the mass of that object times the acceleration the object feels (F=ma).

3. For every action there is an equal and opposite reaction.

Nobody before Newton could explain why objects acted the way they did, but with these three laws he quantified movement in terms everyone could understand.

But there was a problem with his theory; if all motion had to be caused by some force acting on it, then why do objects fall towards the earth when you release them from a fixed position? This free falling object was in fact free, meaning free of outside forces acting upon it (besides wind resistance). There were no visible forces acting upon that object. So why do they move downward if nothing is acting on it? But Newton explained this motion with gravity. He said that gravity is a force that the earth has upon all objects, something invisible that pulls us down at all times at a constant acceleration. There is a myth that the way Newton thought of the idea of gravity was when he was thinking about it under an apple tree when an apple fell on Newton’s head and at that moment, he figured out that there must be a force pulling the object down. This is also why apples are used to demonstrate Newton’s force, but no one knows definitively if the myth is true or not.

At the time Newton didn’t know that the acceleration of Earth’s gravity would later be calculated at approximately 9.81 m/s2. Also, at the time, he couldn’t explain what this force was made of, but only that it was invincible and constant. It was many years later that Einstein explained gravity with the theory of relativity stating that space and time were really one thing called spacetime, that bound all objects together like a web such that when an object has mass, it stretches the spacetime causing objects around it to feel a ‘pull’ towards the center object. Also Einstein discovered that this force increases as the outer object gets closer to the center object. Think of it like a blanket being stretched really thin and a ball being placed in the center and another ball being rolled across the blanket from one side to the other. This would cause the one moving ball to move towards the ball in the center because of the bend in the blanket, or spacetime.

So, looking back at Newton and the apple, the earth’s mass causes a big bend in spacetime, which causes other objects, such as apples, to be pulled downward at all times, even when they are on the ground already. Hey, something has got to keep them from floating upward.

Now that we’ve explained the motion, let’s define it in equations so that we can predict how the object will act during a free falling motion. The first and most important thing to remember about free falling objects is that the mass doesn’t matter. A bowling ball and a pencil will fall, or accelerate at the same rate towards the earth. Meaning if you go on the roof of your building and drop a bowling ball and a pencil off of it at the same time, they will hit the earth at the same time. But someone might say, “What about a feather? It won’t fall at the same speed as a bowling ball.” And they would be right. But what they are forgetting is air resistance. The bowling ball has very little air resistance because it is very aerodynamic, but the feather is not very aerodynamic. If you were to repeat this test in a vacuum then the resistance due to air (drag) would be removed as a factor, and the objects would fall at the same speed and hit the ground at the same time.

So back to the equations; Using calculus, we can start with the equation for the acceleration of gravity and integrate an equation to define the velocity of the object and then integrate it again to find the position of the object. If we define x as time measured in seconds, then the equation for the acceleration of the object looks like this A(x) = 9.81. One might notice that there is no x in the actual equation and this is because no matter how long the object is falling, the acceleration of the object at any time will always be 9.81 m/s2. So by integrating that function of x, we get V(x) = 9.81x + C. In this case, we are defining the velocity of the object in a function of time. C represents any starting velocity of the object, such as if the object was thrown downward. This can also be defined as V0, or initial velocity.  Then if we integrate that function again we get a position function that looks like this, S(x) = 4.905x2 + Cx + K. In this last equation, K represents an initial position, such as if you defined the height of the object being 10 meters above the starting point, then K = 10. And C still represents the initial velocity.

From these equations, we can know that, if we eliminate the wind resistance, any object, the free falls for 1 second will have an acceleration of 9.81 m/s2, a velocity of 9.81 m/s, and a position of 4.905 m. After 2 seconds it will have an acceleration of 9.81 m/s2, a velocity f 19.62 m/s, and a position of 19.62 m. And at 3 seconds, an acceleration of 9.81 m/s2, a velocity of 29.43 m/s, and a position of 44.145 m. You can predict all of these values at any time using these equations just by plugging in the number of seconds into x.

Keep in mind that all of these equations are generalizations of free falling objects. Certain objects, in real life, because of wind resistance, will fall at different rates. Also, due to wind resistance objects will reach something called terminal velocity where the velocity cannot go any higher because the wind speed it feels restricts any increase in velocity. For humans, the terminal velocity is typically around 54 m/s or about 120 mph. For a raindrop it is around 25 m/s. Also, the earth’s gravity, though seemingly constant, isn’t actually constant. It has very miniscule changes as you change locations on the earth’s surface due to the density of the Earth at that spot. But these changes are so small students shouldn’t even bother trying to account for them.

So, what is a Newton anyway? It is the force created by the weight of an average apple (mass of approximately 102g). Technically speaking, a Newton is the force required to accelerate a mass of 1 kilogram at a rate of 1 Meter per second per second.  What better way for your students to visually understand Sir Isaac Newton’s idea of F=ma, than to drop a 1 Newton foam apple onto someone’s head? They will remember it forever!    Educational Innovations sells The Newton Apple as singles and in a five pack.  The five pack includes a full Starter Guide, which includes experiments to conduct using the Newtown Apple, information about Sir Isaac Newton, and information about the Newton as a unit.

Experiments For Your Students:

Elementary/ Middle School Students

1.     Have students hold their hand straight out. Ask them to describe what they feel on their hand. Then place the Newton’s Apple on their hand. Ask them to describe what they feel on their hand now. Ask them what they think will happen if another apple is added to their hand.  Ask them to explain why this is the case.

2.     Take a Newton’s Apple and a pencil or another small object and weight each object so the students can see the difference in weights. Ask them to predict what would happen if you dropped the objects from the same height at the same time (i.e. which would hit the ground first?). Have a student release the objects at the same time from the same height. Ask the students to describe what happens. Try to relay the concept that the mass of the objects didn’t really matter because no matter what they weigh, the objects will still fall at the same speed and hit the ground at the same time.

3.     Repeat the same experiment as before but use something with a lot of air resistance, such as a piece of paper. Then crumble the paper up into a ball and drop both objects again. This time explain to the students that because the paper had a lot of air resistance before, it took longer, but then when it was made in a ball, the paper was still the same weight but now less air resistant.

High School Students

1.     Take a block of wood and tie it to a piece of string. Then tie the other end of the string to the Newton’s Apple. Put the block of wood on a table and then hang the Newton’s Apple over the edge. Make the table surface smooth enough that the block will slide, but not too fast. This experiment is to demonstrate friction between two surfaces and how it would affect the almost free falling object. Place the block on a table with a different surface (one that is less smooth).  Notice the difference.

2.     Attach a spring to a pole or hanger such that the spring can dangle freely. Then attach the Newton’s Apple to the other end of the spring. Pull down the Newton’s Apple so that when you release the Newton’s Apple it will move up and down in a continuous pendulum-like motion. Ask the students to describe the motion and to predict what would happen if you double the weight at the end of the spring. Add a second Newton’s Apple to the end of the spring and repeat the motion of the spring by pulling down the Newton’s Apples the same distance as before.

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Posted by Tami O'Connor

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