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.

## 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.

## Crocodile Chronicles

September 3, 2011

By : Jill Brown

Each year I purchase the growing alligators from Educational Innovations for my Fourth Grade class.  These growing alligators start at about three inches long and grow to over a foot long when placed in water!  From this one item, I have developed lesson plans that incorporate Math, Science, Reading, Social Studies, Writing, Technology, and Language Arts!

Observation is the first action taken by learners to acquire new information about an organism; therefore, the first thing my students do is observe their polymer alligator.  The students in the picture below are in the process of measuring the length, weight, circumference, and area of their polymer alligators. Students in my class also trace their alligators on graph paper then they calculate the area of each and eventually compare the area of their small (dehydrated) alligator to that of their fully grown alligator. (Math & Writing & Language).  These measurements are compiled into a line graph for each student’s crocodile which aids students in making predictions about the rate of future growth of their growing reptile.

Students also use the information found on the back of the alligator package that gives facts related to alligators and crocodiles to guide them in research of the various types of crocodiles and alligators found around the world.  Students then prepare a PowerPoint presentation they eventually present to the class, (Science, Social Studies, and Technology ) Students also incorporate that information into scientific reports on reptiles and amphibians.  Their particular research focuses on these two different animals which have structures that enable them to function in unique and specific ways an example being how they obtain food.  Students are also asked to give their “croc” a name then create a story about the life and times of their creature.

Finally, the data the students gather is then incorporated into their “Crocodile Chronicles”. We referred to the alligators as crocodiles for literary purposes, i.e. “Crocodile Chronicles” sounds better than Alligator Chronicles!  Students then re-create the habitats of reptiles and amphibians using the data they discover through their exploration of where each creature lives, how they live, and what each reptile eats.

Students also conduct a series of experiments where they place one polymer alligator in salt water and another in pond water.  They then create a class Venn diagram that visually depicts the similarities and differences between how the alligators grow and develop in salt water vs. pond water.  The data collected from these experiments are also entered into each students’ Crocodile Chronicles.

Each year we invite our special needs friends to join us in this lesson so this gives my students an opportunity to mentor children that otherwise might have some challenges in working on this project.  Let me tell you this, there is not a single student who does not LOVE  this project!  They enjoy it and learn so much at the same time!

I have created a booklet, Crocodile Chronicles, where students keep all of their measurement recordings, drawings, and stories about their crocodile. This booklet has a crocodile on the cover and its mouth is the closure of the booklet and Velcro is attached right at its mouth so each time the student opens their booklet it sounds as if the crocodile is taking a big bite! Oh, it is just a thrill for me to teach this unit and I appreciate Educational Innovations offering such tremendous tools for my students!  It’s a gift for a teacher to come across materials that can be incorporated into cross-curricular lesson plans!  That makes the job of teaching just that much easier!  Thanks, Educational Innovations!

## 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.

## Soil Porosity, Permeability and Retention Experiments

August 8, 2011

by: Cynthia House

Demonstration Materials:

• 125 ml graduated cylinder or similar item
• ~100 ml of pea gravel or small marbles
• kitchen sponge
• tap  water

Experiment Materials:

• preforms and racks (three preforms/student or group)
• fine gravel  such as aquarium gravel (~ 30 ml/student or group)
• coarse sand* (~ 30 ml/student or group)
• fine sand* (~ 30 ml/student or group)
• small plastic cups ~ 100 ml capacity
• squares of tulle (“bridal illusion”) and organza, ~ 10 cm x 10 cm
• rubber bands
• electronic balance (capacity at least 100 gm)
• one pound margarine tub or similarly sized plastic cup per balance**
• stopwatch or count-up timer (MyChron Student Timer)
• 125 ml graduated cylinder or similar item
• calculators
• tap water

* Home centers sell sand for sand boxes, landscaping, paving, mortar etc.  Beaches are another source, although you may encounter undesirable contamination. Sifting non-homogeneous sand with a fine kitchen strainer may yield two usable grades of sand.

** secondary containment to prevent accidental spillage of water onto the balance

Background Vocabulary:

Porosity is the measure of how much groundwater a soil can hold, permeability is the measure of how quickly water passes through a soil, while retention is the measure of how much water stays behind.  Even elementary students can relate these concepts to their everyday lives. They observe that some areas in their yards or school grounds form puddles while others drain quickly after a rainstorm. They may wonder why one neighbor’s garden and yard remains lush and green although a sprinkler is rarely used. Children in communities dependent upon well water can understand the importance of replenishing the water table. In most rural and many suburban areas, homes use septic tanks and drain fields to process household wastewater. The “water cycle” is a topic in elementary science curricula. There are many excellent age-appropriate online sources for information on these topics including the United States Geological Survey (USGS) and the GLOBE program.

The commercially available kits I investigated for porosity/permeability/retention experiments were designed for high school students, requiring a level of dexterity not yet developed in many younger students. They also required much larger quantities of test material. One can expect larger samples to provide more accurate results, however, we achieved acceptable accuracy and precision with the method described here.

Procedure:

Set-up: Using the 125 ml graduated cylinder, measure 25 ml of gravel or sand into each preform tube.  Prepare one sample of each material for each student or team of students.  If you have enough material and preforms, prepare some extra samples in the event a group spoils a test and has time to repeat it. The caps that come with the preforms are particularly useful in that filled tubes need not be stored upright for convenient storage or transport. Provide each student or team of students with their samples placed in racks, one piece of tulle and one piece of damp organza fabric, a small cup, several rubber bands, a timer, pencil, and copies of “Procedure” and “Data Table” sheets.

Demonstration:

Model the procedure by following the instructions on the “Procedure” sheet as the students follow along.  Use the 125 ml graduated cylinder in place of a preform tube, and ~100 ml of pea gravel or small marbles. The students will be able to visualize the concepts of “voids” within the sample, and how measuring the water that fills those voids allows one to determine their overall volume.  Although it will move very quickly, point out the movement of the waterfront, and when to start and stop the timer. In particular, point out when to stop adding water, and that adding water very slowly is important with the finer materials so as not to overshoot the mark. I believe that overfilling the tube was the cause of most errors.

Students can easily visualize the concept of retention. Let the students handle a dry kitchen sponge. Soak the sponge in a container of water until it is saturated.  Wring out the sponge, then allow the students to handle the still-damp sponge.

Experiment:

I allowed the students to proceed at their own pace. I work with first through fifth grade students in a science club; for the purposes of this experiment I paired first and second grade students with older children, primarily because of the reading, and the math involved later on. Adults manned the balances both to speed up the weighing process and to reduce spillage. I used two balances for twelve teams of students; if you have more balances available, and somewhat older students, the students could handle the weighing process themselves. They may need to be taught how to tare the balance using an empty cup.

Analysis:

Students fill in the remaining columns in the data table, rounding porosity and retention values to the nearest five percent. They should calculate permeability to two significant figures.  Plot porosity and retention results as histograms, one for each material type.  This experiment lends itself to elementary statistical analysis, i.e. mean, mode, and average. I have included histograms from one of my sessions. The presence of a few errant results, both too high and too low, sparked conversation among the students as to possible sources of error in the experiment.

Clean-up:

The sand and gravel can be rinsed out of the preforms, filtered, then spread out on layers of newspaper to dry for reuse.

Cynthia House is the Science Club Adviser at Olive-Mary Stitt Elementary School

## 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!

## 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.

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.