High School Mathematics-Physics SMILE Meeting
1997-2006 Academic Years
Mechanics: Dynamics
16 September 1997: Presentation of Bill Blunk [Joliet Central]
He took a long thin balloon and showed that in throwing it laterally, it would not go very far, but throwing it oriented along its axis (because of reduced air resistance) it would go for some distance.

Sold at 3 for $2.50 by

Amazing Toys
319 Central Ave
Great Falls MT 59401
[406] 727-5557 [Bob Pechlin]

28 October 1997: Karlene Joseph [Lane Tech]

          -apparatus  Push and Go Toy [Dinosaur Cars; etc]
car found in Toddler

It is hard to find cars that work and don't disappear or break into sections (TOMY ) Toys R Us $5.00 [http://store.yahoo.com/iqkids1/pungodutr.html].

Causes of errors by students

When students work in lab groups here in (4). There must be something to unite the experience of the group, and it is the Lab summary.

A way of using ticker tape - the push car --review-

She used the 60 cycle sparker, carbon paper, and a strip of tape. The tape can provide more feeling and information to the student than a graphing calculator and a sonar sensor. The student lets the car make a pass and has a tape with 6 dots per 0.1 sec. He then labels the tape and cuts it into 6 dot sections (1/10 sec) and then attaches the paper strips to form a chart showing the distances traveled in each 0.1 sec. At the start the lengths are ascending and then level, and afterwards fall back to 0. Using the tape to make the graph, one may then determine the slopes and calculate the acceleration and thus the forces. [Mass of Car 0.264 Kg] Also, the area under the curve gives the corresponding change in displacement.

Porter commented that the friction is always present. If on frictionless ice the cart will never accelerate. Friction is always present and is the "cause" of acceleration.

28 October 1997: Jamie Chichester [Lincoln Way HS]
He showed the Bandit--A cross-bow device
Try Meijers or Sportmart; $20.00
6-pack of darts approx $6-9

Put face on board with a apple on it. Then he used a laser pointer to show where it was aimed and then shot a dart, of course it landed below the apple, and then moved back with a lower position, and further back what would happen? ("Ask your neighbor") and of course it struck lower. (another version of the "dartmong dart" gun, but with seemingly better sticking darts, and laying a laser pointer in the trough gave a way of aiming the system.)

11 November 1997: Betty Roombos [Gordon Tech]
Inertia

  1. Chalk and Embroidery Hoop over Pop Bottle

    Hit the hoop so that the circle compresses vertically; then the chalk will fall down and into the bottle.
  2. Place a coin in someone's palm. To take it, hit the palm so that the coin stays up and grasp it.

Using hot wheels and track show-calculate minimum release height for the car to complete the loop-the-loop successfully. br>

 

11 November 1997: Lee Slick [Morgan Park HS]
Finished the day with several building projects:

  1. glue to cups so it would roll up a hill

25 November 1997: Lee Slick [Morgan Park HS]

He had a project using a coat hanger where one balanced a dime on the end and swung the hanger around
The coin would stay on the coat hanger end.

25 November 1997: Debbie Lojkutz [Joliet West HS]
She had us go into the hallway to pull a cart constructed with 2 skate boards as the wheels. The idea is to change the pulling force and then to change the mass (2 people). This is set-up to show relationships between force, mass, and acceleration, and not a quantitative study of Newton's Second Law.

Table Force masses Time Distance Acceleration
* * (# people) (seconds) (meters) (m/sec2)
Part I 16 Nt 1 11.0 6.0 0.10
* 32 Nt 1 7.3 6.0 0.23
Part II 40 Nt 1 5.0 6.0 0.48
* 40 Nt 2 9.0 6.0 0.15

We discussed the effect of changing the variables, and that we needed to only change one at a time. Otherwise our conclusions and predictions may be flawed.

10 February 1998 Ann Brandon [Joliet West HS]

Demos of Gravity

Comments from the floor: A horse shoe magnet was attached with a metal plate just below, and far enough not to be engaged by the magnet is placed on a shelf just below the magnet. Now the system is dropped, and the magnet "without gravity" can pull up the plate with an audible "clink".

24 March 1998  Ann Brandon [Joliet West High School]
She noted that the back of the hand possesses less "rubbing friction" than the palms. If you rub the back of your hands there is less friction and less warming.

She showed the waves on a slinky and the reflection by putting cups on the table and then producing a wave, noting the excitation distance that was swung was much less than that of the wave in the spring [resonance?].

She also showed a slinky held up at one end and dropped. She noted that the top would fall to the level of the bottom before the slinky would fall. She commented that the spring stretched out would pull up the bottom even though the bottom was pulled by gravity. The net result was that the bottom was stationary until there was no spring pulling up. Isn't that amazing?

07 April 1998  Richard Goberville [Joliet Central High School]
He showed very small balancing birds, which are available at about 12 per dollar from the following source:

Oriental Trading
4206 S 108th Street
Omaha NE 68137-1215
Tel: 1 - 800 - 875-8480
http://www.orientaltrading.net

In addition, he showed a Centripetal Force Puller which consists of two masses attached by a string, with a collar around the string for "twirling" the lighter mass about a horizontal plane. The light mass is about 20 grams, whereas the heavier one at the base is about 120 grams.

The light mass was rotated in a circle of about one meter, with the time for 10 complete revolutions being 6.1 seconds. Thus the period of revolution is T = 0.61 seconds. Using the formula

T = 2 p /w,

we determine the angular velocity to be

10.3 radians/second
.

The net [centripetal] force on the 20 gram mass is

F = m w 2 r = 1.1 Newtons.

This force of 1.1 Newtons balances the 120 gram weight hanging at the bottom, so that the numbers are consistent.

10 November 1998: Arlyn Vanek [Iliana Christian HS]
Students like to do things with weapons in physics labs, so he developed experiments with his bow. (His dad thought this was safer than a b-b gun, for some reason!) Hang a weight from the bow and measure the stretch.

W = f d    ;    PE = mgh  ;   KE = 1/2 mv2 = PE
Work is the area under the curve of force (F) versus displacement (X):

If shot straight up, what is its speed and how high it will rise? [Ans ? 27 m/s and 35 m].

Ann Brandon [Joliet West HS] remarked that the fit is not exact and any anomalies that arise could be discussed by asking the question What are the sources of error?

08 December 1998: Carol Zimmerman [Lane Tech HS]
Setup: 2 photo-gates and a cart with a mass to equal 2kg total, and twine connected through a pulley and a weight to accelerate the system. The times through the photo-gate with just enough mass to accelerate the system. Starting the acceleration as close as possible to the first photo-gate to effectively have it at 0 velocity. for 32cm distance times of 0.988 for 2kg, .682 for 3Kg, .599 for 4Kg cart masses would produce a slope of 1.4 where 2.0 was expected. Why?

In the discussion a point was brought up as the system mass was the Cart + Hanging mass therefore should the mass suspended be subtracted from the cart so that the total mass was 2kg. Since it was "physics" there were problems with the apparatus, and when it was fixed we ran out of time for discussion.

04 May 1999: Earl Zwicker [IIT Professor Emeritus]
Earl showed a device with two disks of different mass between springs. The device has a timer that when the springs were compressed it would stay for about 10 seconds and release the spring. If the lower mass disk was down at the table and the spring accelerated the higher mass, thus the assembly would jump, and the next trial the larger mass was on top-being accelerated; which condition would the assembly jump higher?

It was hard to tell, but seemed that with the the larger mass on top it would jump a little higher???

28 September 1999: Ann Brandon (Joliet West HS)
set up an experiment to detect differences in air resistance for 2 objects of equal mass. The objects were solid wood blocks, each suspended - in turn - as a bifilar pendulum of the same length (about 1.2 meters). Ann handed out stopwatches to some of us (available at K-Mart), and we observed (and Ann wrote on the board for all to see) the time (in seconds) for 5 swings of wood block 1. This was done both for large amplitude (about 15 deg) and small amplitude swings.

This was repeated for wood block 2, which had a different shape and which presented a different area (than wood block 1) normal to its motion through the air. Intuitively, one might expect the block with greater area to encounter greater air resistance to its motion, which might produce a difference in swing times. Upon looking at the data for both blocks, we concluded that there is no significant difference, and therefore air resistance is not a significant factor in their motion. However, there was an obvious difference in times between large and small amplitude swings for each block. Why? Any ideas? Thanks, Ann!

09 November 1999:  Carol Zimmerman (Lane Tech HS)
showed us several experiments - which she gets her students involved with before studying Newton's laws. The table cloth yank (slippery table cloth, glasses or other objects on top, yank the table cloth out from under, leaving the objects at rest on the table!). Next - bottle on table, balance circular flexible hoop on top at bottle's opening, place chalk vertically on top of hoop, lined up with opening of bottle below - then sweep your hand horizontally, grabbing the hoop away, so the chalk falls down into the bottle! Then Carol placed a stack of wooden blocks on the table, and swept a meter stick horizontally over the table top, knocking the bottom block out from under those above, leaving them still stacked! This was repeated, depleting entire stack. (We call these Betty's blocks, after Betty Roombos who first showed us this at a 1970s meeting. Good ideas don't die!) Carol then held up a spring scales, attached a weight to its end, and we could see what the scales read. But then she accelerated the scales upward - and we saw the pointer indicate greater weight! Finally, Carol covered the table with a pretty green felt cloth, improvising a pool table. Using chalk, she drew a circle on the cloth (about 37 cm diameter), placed a pool ball at the center of the circle and put a penny on top of the ball. Offering a cue stick, she challenged us to strike the ball with the cue (held parallel to the table) so that the penny would land outside the circle. Several of us tried, one after the other, without success. Carol finally told us that under Newton's laws, it was not possible for anyone to do this! These demonstrations of inertia prompted others of us to do the "grab the coin" from a person's hand (Betty R); "Where will the string break?" (Arlyn VanEk - who may do this for us next meeting.)

09 November 1999:  Fred Farnell (Lane Tech HS)
showed us a new twist on inertia. He placed an inverted glass on the table, then a flat card on top the glass, and then a circular roll of tape on top the card. When he snapped the card horizontally, the card flew out from under the roll, which then dropped down around the glass to rest on the table. Nice! Then he tried it with the glass placed open end up. Harder to do, because of the now greater diameter which the tape roll had to clear. But it finally worked!

23 November 1999: Arlyn van Ek [Illiana Christian HS]

02 May 2000: Fred Farnell (Lane Tech HS)
asks his students to estimate how fast an egg can be thrown into a vertically-held blanket without breaking the egg. He also asks from what height h could an egg be dropped onto a hard surface (about 5 cm) or a cushion (about 2 m) without breaking. What is the speed of the egg when it strikes the surface?

v = Ö(2gh)
gives an answer. What force is required to break an egg? To answer this last question, Fred showed us his egg tester. A flat piece of wood (about 4" X 6") with bolts sticking vertically up from its corners was placed on the table. An identical piece of wood had holes in its corners so it could move up-and-down freely, guided by the bolts. Fred placed an egg into a plastic bag and sealed it, then placed it between the wood pieces. With a set of weights handy, he asked us,"How much force will it take to break this egg?" Lee Slick thought about 10 Newtons, but others guessed lower. So - Fred stacked weights onto the top board; we were entranced as he added each 0.50 kg mass. The egg finally broke at 2.5 kg, or about 25 Newtons. Using Newton's second law, F = ma = m (dv/dt), Fred re-wrote it in the form Fdt = mdv, which led to the idea of "impulse," (Fdt), and showed that when the momentum of the egg is changed by mdv when being brought to rest, whether or not it would break would depend on how long (dt) it takes to bring it to rest. The longer dt, the smaller F, for a given change in momentum (mdv) (ie, dropping the egg from a given height h). By bringing it to rest relatively slowly, F would not exceed the F needed to break the egg! A great way to involve students with the concept of impulse. Nice, Fred!

24 October 2000 Betty Roombos (Gordon Tech HS)
held up some Mr Coffee™ paper coffee filters. She picked one, held it out, then released it. It fell to the floor at what appeared to be a constant speed. (It turns out that terminal velocity is reached in a negligibly short time, so that it is indeed a good assumption that coffee filters fall with constant velocity.) So - Betty did a Drop Contest.  As viewed by us, she held up two coffee filters - nested together - on the left, and a single coffee filter on the right, both at the same height - one meter - above the floor. Which will reach the floor first? was her question to us. After we made our guesses, Betty released them simultaneously; the two nested filters reached the floor first. So that we all would have no doubts, Betty repeated the experiment twice more; same result.

Next, Betty asked, "How high above the floor must I hold the nested two, so that when I simultaneously release them and the single filter - still held one meter above the floor - they will reach the floor at the same time?"

(In what follows, we changed Betty's direct proportion notation into equalities following after Porter Johnson's notation, since it is easier to write up that way.) Betty used the relationship F = kv2, for an object acted upon by a constant force F, and falling through air with a constant speed v. For the coffee filter,

F   =   filter weight   =  mg,
so,
mg   =   kv2.
From this one may solve for v and construct the ratio,
v2/v1   =   (m2/m1)0.5.
Then the ratio of the mass of the nested 2 filters (m2) to the mass of the single filter (m1) is 2, Thus
v2/v1  =   20.5   =   1.41.
Since v  =  d / t, it follows that
d2/d1 =   v2/v1  =   1.41.
With d1 = 1 m, the distance d2 must be 1.41 m. With assistance from some of us to hold meter sticks at those heights, Betty held the single filter at 1 m above the floor, and the nested two at 1.41 m. Counting down - 3, 2, 1, blast off! --- Betty released them simultaneously, and they fell, reaching the floor exactly at the same time! Beautiful! She repeated this twice more, and we were convinced that it worked - and very well!

Someone pointed out that if a nested 3 filters were used, they would need to be released from a height above the floor of 

30.5 m = 1.73 m.
So - she did this - and again, it worked perfectly. [Porter Johnson pointed out that these filters are very useful for dropping experiments, since they are flat on the bottom, but that cone-shaped filters are better for the purpose of filtering coffee!]

Great stuff, Betty!

24 October 2000 Larry Alofs (Kenwood HS)
asks his students, How high does a ping pong ball bounce? Students usually respond with, That depends on how high up you drop it. Larry's students then would find that beyond a certain height, no matter how much higher the point of drop was, a ping pong ball would not bounce any higher than about 3 meters! Similarly to a coffee filter, a ping pong ball reaches its terminal velocity fairly quickly (compared, say, to a baseball). Thus, no matter how much greater the drop height (beyond a certain height), the velocity at impact with the floor is the same terminal velocity, so the bounce height is the same.

21 November 2000 Bill Blunk [Joliet Central HS]
He used the mini-camera first presented at the ISPP Meeting a year ago and shown at a SMILE class last year [ph102699].  He cut a circular piece of plywood and attached it to a lazy susan, attached the camera to the plywood to the table, and ran the cable up to the ceiling so that the system could rotate freely for several turns.  Then, he set various objects on the rotating table, and we saw their motion [as seen from the table] on the big TV screen. Specifically, he used these objects:

The effects shown in this live demonstration were nicely presented in the PSSC Movie entitled Frames of Reference.

11 September 2001: Ann Brandon (Joliet West HS, Physics)
took a transparent plastic tennis ball tube, and attached washers from its inside bottom end with rubber bands.  The rubber bands were then stretched so that the washers lay outside the open top end.  She stood on the lab table and dropped the system. Surprise!  As it fell, we saw that the stretched rubber bands pulled the washers back inside and went limp.  She dropped it several times, so that we could be certain of what we were seeing.

06 November 2001: Ann Brandon (Joliet West HS, Physics) Newton's Third Law

Ann  brought in a pair heavy duty spring scales [up to 30 pounds], and hooked them together.  One victim/volunteer was told to pull one scale with a force of 10 pounds, and another one of us was told to pull on the other scale with a force of 30 poundsThey just couldn't do it, because of Newton's Third Law.Bill Shanks indicated that, as an important point, Newton's Third Law is still valid when the objects in question are being accelerated.

Arlyn Van Ek initiated  a discussion concerning the difference in mass and weight, in that metric spring scales are conventionally calibrated in mass units [kilograms], rather than force units [Newtons].  Somehow this led naturally to a discussion of the history of the Denver Mint.  Ann said that the Denver assay office minted gold coins for regional usage that were slightly heavier than those from, say, the Philadelphia Mint, because "g" was lower in Denver.  These privately minted coins were legally allowed until 1864, since they did not "debase" the value of standard currency.

Announcements:

20 November 2001: Bill Blunk (Joliet Central HS, Physics) Air-driven Cart
Bill
showed a fan cart http://store.pasco.com/pascostore/showdetl.cfm?&DID=9&Product_ID=51492&Detail=1] that ran on a PASCO [http://www.pasco.com/] ramp [http://store.pasco.com/pascostore/showdetl.cfm?&DID=9&Product_ID=52911&Detail=1].  He turned the fan to the maximum setting, and tilted the ramp to determine the "stall angle". He used an electronic protractor to get an angle of 3.5°Lee Slick objected to the value, and determined the angle by measuring the "rise" and "run" of the ramp to be 7.5 cm and 120 cm, respectively. He then calculated the angle to be arcsin (7.5/120) = 3.58°, verifying the original result.  Bill then calculated the thrust produced by the air cart, which is equal to the component along the track of the weight of the cart, corresponding to F = 580 gram sin 3.5° = 35 "gram weights", or about 0.35 Newtons.  He then carefully leveled the track on the laboratory table, and set up a pulley system using a light string with a total of 3.5 grams suspended at the end of the track.  He released the air cart with the motor turned on, and showed that the forces were balanced. Great!

Bill next calculated that, if the cart of mass of 0.580 kg were released on the track with the fan running, it would accelerate at a » 0.35 nt / 0.58 kg = 0.6 m/s2.  In other words, it would travel 1 meter in a time of about Ö(2 d/a) = Ö(2.0/0.6) » 1.8 seconds.  As we watched, Bill set up the experiment, and we measured with a stopwatch to be 1.75 seconds.  Physics works!

Finally, Bill speculated that the air cart would go faster if he replaced the heavy batteries inside with a lead to an external battery pack.  However, he was only able to increase the stall angle to about .  How could he do it better, and where can he get better wires to conduct electricity into the fan?

04 December 2001: Bill Blunk (Joliet Central HS, Physics) Fan Car, Revisited
Bill
showed us a refinement of his presentation of the Fan Car on 20 November 2001 [see the write-up for the November 20 High School Math-Physics SMILE Meeting], in which he asked us whether we knew where to get flexible, braided wire with lower electrical resistance than his earphone cord.  He said that the answer is often right around us --- and especially around Christmas time!  He found that wire from burned-out Christmas tree lights worked very well.  Bill placed the fan car on an incline, and we observed a "stall angle" of 8° to 10°, as compared with a maximum of around obtained with smaller wires last time.  Thanks, Bill!  Persistence pays big dividends.

Bill also showed off his set of Choositz Decision Balls [which are also called "Happy" and "Sad" Balls], ordered from the Fall 2001 Educational Innovations Catalog.  You may call EI directly at the toll-free number 1 - 888 - 912-7474, or else visit their website, http://www.teachersource.com/.  Here is the information on this item that appears on their website:

 SS-3 Choositz Decision Balls

These are the largest "Happy-Sad" balls we have seen! They are over 1-1/4" in diameter! These two black rubber balls appear identical, but have extremely different physical properties. Dropped onto a hard surface, one ball bounces high while the other hits the floor and stops immediately. Show students that some properties cannot be observed without experimentation. Set includes two balls (one 'yes' and one 'no').

Qty Cost
1-10 $6.95
11 p $6.25

11 December 2001: Arlyn van Ek (Iliana Christian HS, Physics): 24 Hour Towing Service
The standard demonstration [Hewitt, Conceptual Physics] of how one person can get a car unstuck with only a rope is to tie one end of the rope tightly to the car, and the other end to a nearby tree.  [You may have to move a tree over, if none happen to be nearby.]  The person merely has to push sideways on the taut rope near its center, in order to move the car a little toward the tree.  Then, one must re-tighten the rope and push sideways again, repeating the process until the car is out of the mud.  Of course, in this safety-conscious age, one can no longer do such a demonstration in the school parking lot, because of the risk of injury.

Arlyn recommended an alternative.  Lay a large board [say, "2 ´ 12" lumber around ten feet long] flat on the floor in the hall, and tie a rope tautly to it and to a sturdy door knob.  Have a number of students sit on the board, and then ask one modest-sized student to push sideways at the middle of the rope.  The board, with all the students on it, will move.  As a variation, you might have two teams of students pulling on opposite ends of the rope.  Then ask a single student to  push on the rope, thus causing the teams to move together.  Mechanics at work!

Arlyn also recommended that teachers make a Design Template for students participating in the local bridge building contests [ http://www.iit.edu/~hsbridge/database/search.cgi/:/public/index], so that they can directly visualize what the size limitations on their bridges must be in order to be qualified.

05 February 2002: Fred Farnell (Lane Tech HS, Physics) Newton's Second Law; Momentum
Fred
passed around the new book The Grip of Gravity[The Quest to Understand Laws of Motion and Gravitation] by Prabhakar Gondalekar [Cambridge 2001]  ISBN 0-521-80316-0.  According to this book [p 94], Leonard Euler, [circa 1750] was the first person to write Newton's Second Law in the modern form, F = ma.  The same point is made on the former website "http://www.eng.vt.edu/fluids/msc/euler.htm" [as quoted below]:

"Euler was part of the continental school who adopted Leibniz's calculus and, along with d'Alembert and the Bernoulli brothers (Daniel and Nicolaus), clearly demonstrated its power. His treatise "The Theory of the Motions of Rigid Bodies" (1765) established the field of analytical dynamics. In fact, Euler was the first to write down Newton's Second Law in its current form (F = ma)."
Newton is also described as having a "flawed character" in Gonalekar's book [p 114], as well as elsewhere [http://www.worldscibooks.com/histsci/p299.html]. For details of Euler's life and his considerable accomplishments, see the website http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Euler.html.

Fred next illustrated the concept of momentum by dropping and catching two different masses 100 grams and 2 kilograms] from a fixed height about 2 meters. He took the precaution of putting heavy gloves on his hands, while catching the dropped masses. He caught the lighter weight while holding his hands still, whereas he began moving his hands just before catching the heavier weight.  He was able to stop the heavier weight by letting it fall a somewhat greater distance, so that the average force on his hands would remain modest in size.  Because the heavier mass acquires more momentum than the lighter one when falling through the same distance, it takes either a substantially greater force, or else a significantly greater time, to stop it.  A simple, direct way to show the relation between force, momentum, and impulse.  Thanks, Fred!
Earl and Porter
pointed out that a good fielder catches a baseball while moving the glove away from the ball to absorb the blow and to keep the ball from popping out of the glove, and then promptly puts the other hand over the glove to grab the ball. Arlyn Van Ek uses a blanket to catch a raw egg, and then breaks a water balloon by throwing it against the wall, to illustrate the effect of the "stopping time" in a collision.  Watch out for those falling masses and flying eggs!

05 February 2002: Larry Alofs (Kenwood HS, Physics) Pendula
Larry
set up a pendulum with a cylindrical bob that was supported by two strings [bifillar] for  better control, which passed on its swing through a photo-gate timer.  The cylindrical bob blocked out the light signal during the time of its passage, which is given in terms of its diameter, L = 0.028 meters, and its velocity v as T = L / v.  [Note:  a cylindrical bob is used because its cross section remains fixed, even if its orientation changes slightly.]  The bob was released at a height h = 0.20 meters above its lowest point, where the photo-gate was located.  Thus, the bob theoretically would have speed v = Ö (2 g h) = Ö (2 ´ 9.8 ´ 0.2) m/sec = 1.98 m/sec when passing through the gate. And the time T is predicted to be T = L / v = 0.028 / 1.98 sec = 0.014 sec.. The measured time was 0.013 sec, indicating reasonable agreement.

Larry then set the photo-gate to measure the period of the pendulum.  He first measured the period for a small angle (about 5°), and found it to be T = 1.416 sec.  Then, he carefully held the bob so that the strings made a large angle of about  q0 = 57°  (around 1 radian) to the vertical direction, and released the pendulum.  He made several measurements of the period, obtaining 1.484 sec, 1.493 sec, and 1.501 sec, respectively, corresponding to an average To = 1.493 sec. Then he found the following formula [allegedly accurate for the period T at large angles q0, and expressed in this notation] in a somewhat older ***CRC Handbook of Chemistry  and Physics, under the category "simple pendulum":

To / T = 1 + (1/4) sin2(q0/2) = 1.0574
But, according to our observations, 
To / T = 1.493 / 1.416 = 1.0543
Not bad agreement between observation and formula, Larry!
*** The 40th Edition [1958-1959] of the CRC Handbook contains the following statement [p 3113, in the section on Definitions and Formulas]:  "If the period is T0 [in our notation] for maximum angle q0 [in our notation], the time of vibration in an infinitely small arc  is approximately To / T = 1 + (1/4) sin2(q0/2)  [in our notation]. But what does that statement actually mean?? 
Porter Johnson (Physics, IIT) pointed out that the correct expression for the period for the large amplitude simple pendulum of length L and maximum displacement q0 from equilibrium is expressed in terms of  K(k), the complete elliptic integral of the first kind.  Here are some details
T = [4Ö(L/g) ] ´ K(k)   ,   with k = sin(q0/2),

The function K(k) is defined as the (elliptic) integral:

K(k) = ò0p/2 dj /Ö (1 - k2 sin2j )

One may make either of the following expansions of the elliptic integral [See the web article Large Amplitude Period of a Physical Pendulumhttp://web.njit.edu/phys_lab/Laboratory%20Manual/laboratory231/labO/labO.html as well as the Java Applet http://hyperphysics.phy-astr.gsu.edu/hbase/pendl.html:

K(k) = p/2 ´ [ 1 + (1/2)2 sin2(q0/2) + (1 · 3 /2 · 4 )2 sin4(q0/2) + ... ]

or

K(k) = p/2 ´ [ 1 + (1 / 16) q02 + (11 / 3072 ) q04 + ... ]

Both expansions are viable if q0 is sufficiently small, but the first expansion is neither more accurate, nor more rapidly convergent, than the second one. Let us compare them

q0 2/p ´ K( sinq0  1 + (1/4) sin2(q0/2)   1 + (1 / 16) q02
 0° 1.0000 1.0000 1.0000
15° 1.0043 1.0043 1.0043
30° 1.0174 1.0167 1.0173
45° 1.0400 1.0366 1.0385
(1 radian)
57.3°
1.0663 1.0574 1.0625
60° 1.0731 1.0625 1.0685
75° 1.1190 1.0926 1.1070
90° 1.1803 1.1250 1.1542
105° 1.2622 1.1573 1.2099
120° 1.3728 1.1875 1.2741
150° 1.7622 1.2333 1.4284
180° ¥ 1.25 1.6168

If anything, the first expression is less accurate than the second, since the term of fourth order in q0  has the wrong sign in that expression, although neither one is correct at large q0.

Ann Brandon (Joliet West, Physics) Pendula, Continued
Ann
described an class exercise to study the dependence of a period T of a small amplitude pendulum upon its length L.  She tied cords to round metal washers and cut them to produce pendula of lengths from, say, 10 to 150 cm.  Each student took a pendulum, suspended it from a paper clip taped to the lab bench, and measured its period, averaging over ten complete oscillations.  She took each pendulum, taped it directly to the board along a ruled horizontal line at a point corresponding to the measured T. Thereby, she constructed a graph of length versus time, using each pendulum to mark its own length.  The graph was definitely not linear.  Then, she drew another ruled line indicating time-squared, and placed each pendulum at the appropriate point on that graph.  This time, the graph was straight.  Here are typical data:

 L( m)   T(sec)   T2 (sec2
0.10 0.6 0.4
0.25 1.0 1.0
0.50 1.4 2.0
0.75 1.7 3.0
1.00 2.0 4.0
1.25 2.2 5.0
1.50 2.4 6.0
[Do these numbers look contrived, perchance?]

The formula T = 2 p Ö (L/g) may also be written as L = g / 4 p2 T 2, so that the slope of the graph of L versus T2 is g / 4 p2 » 4 m/sec2. Very interesting, Ann!

05 March 2002: Walter McDonald (CPS Substitute) -- Centripetal Force
Walter
constructed a conical pendulum; for details see the references http://farside.ph.utexas.edu/teaching/301/lectures/node88.html and http://www.physics.purdue.edu/demo/1D/pendulum.html. He took a piece of string about 2 meters long, and  ran it through a section of a plastic drinking straw about 5 cm long.  Then he tied  washers of mass m on the upper end, and  washers of equal mass m on the lower end.  He held the plastic straw vertically and swung the upper mass m around in a circular orbit, so that the mass m on the lower end could move up and down, changing the radius of  the circular orbit of the mass m on the upper end until equilibrium was reached.  Equilibrium occurred at a circular radius of 0.50 meters, with the orbiting mass making 13 revolutions in 15 seconds.  We calculated the velocity of the orbit to be v = 2 p r / T = 2 p (0.5 m) /(1.15 sec) = 2.73 m/sec. By setting the force m g = m v2 / r, we get v = Ö(m g r /m) = 2.23 m/sec. Very interesting, Walter!

10 September 2002: Ann Brandon (Joliet West HS, Physics) "Running Dog"
Ann
announced the next ISPP
Ann showed the Running Dog" toy, which consisted of a little plastic dog supported on moveable legs, with a string attached to the front.  When a metal washer was tied on the other end of string, and hung over the edge of the table, the dog walked deliberately toward the edge.  Where do we get this little dog, Ann?  More later?

24 September 2002: Ann Brandon (Joliet West HS, Physics) Walking the Dog, continued; Graphs and More Graphs
Ann
brought in a different Walking the Dog Physics Toy, which she obtained last spring for all-important St Patrick's Day festivities.  She obtained the [green] toy from Oriental Trading Center; [Address: PO Box 2308; Omaha NE 68103-2308; Tel: 1 - 800 - 228-2269; website: http://www.orientaltrading.com].  When just the right amount of weight was attached to the dog [see the minutes of the last SMILE meeting], the Ersatz Animal walked slowly to the edge of the table and then stopped, although it was rumored that the back legs had been dragging.  Very good, Ann, is there an obedience school for plastic dogs?

Next Ann showed a graph based upon one of the favorite stories of her childhood, Ben and Me: Astonishing Life of Benjamin Franklin As written by His Good Mouse Amos by Robert Lawson [Little, Brown & Company; 1988; ISBN: 0-3165-1730-5] recommended for ages 8 to 12.  Publisher's description:  "The true story of Ben Franklin, as told by his closest friend and advisor, Amos the mouse. According to Amos, it was really he who was  responsible for Ben Franklin's inventions and discoveries." Others seem to like this book; for example, see Ben and Us: Sparking the Standards: http://teachersnetwork.org/impactII/profiles00_01/block.htm. and Ben and Me: http://www.amazon.com/Ben-Me-Astonishing-Benjamin-Franklin/dp/0316517305Ann related this to graphing by showing a rather unusual-looking distance versus time graph, and explaining that it described Amos's first departure from his home, in which, over a 20 second period, he went from just in front of his mouse-hole toward the middle of the room, then came some closer to home,  saw the cat, rushed back into the hole, and peeked out to see if the cat was still there.  The graph represents  a visual summary of these events, and serves to re-enforce the connection between the graph and Amos's travels. 

Ann then showed a set of 4 graphs of d versus t , along with 4 graphs of velocity versus time, as well as 4 graphs of acceleration versus time, as in the SMILE meeting of 25 September 2001:  mp092501.htm. We then began to try to match the graphs with one another.  She made the following chart to formalize the matching process:


Quantity to Determine
Plot
Given  
a
d - t Read Graph Slope:
D d / D t
"smile": a > 0
"frown": a < 0  
"line": a = 0
v - t Area Read Graph   Slope:
D v / D t
a - t (calculus--ugh)   Area Read Graph
The entry in the upper right corner means that, if the d-t curve is a "smile" [convex upward] the acceleration is positive; when it is a "frown" [concave downward] the acceleration is negative, and when the d-t graph is a straight line [up, down, or sideways] the acceleration is zero.  A wealth of good  ideas, Ann, and keep smiling!

07 November 2002: Ann Brandon [Joliet West HS, Physics]     Collisions and Momentum
Ann
applied the Bigger is Better philosophy to a freely moving, 7 kg cart. Along its path, a 25 pound [11 kg] bag of kitty litter was dropped onto the cart, slowing it down perceptibly. By pulling ticker tape with the cart, and using a spark timer to put marks on the tape every 1/60 second, she was able to determine the speed of the cart just before and just after the bag was dropped onto it.  The class verified that momentum was conserved, to a precision of a few percent.

We performed a modified experiment, in which a Pasco® cart [mass about 500 grams] with ticker tape attached to it was set into motion across the lab table.  A sealed sandbag [mass 394 grams] was dropped onto it, and it slowed down perceptibly.  The velocities just before and just after dropping were determined by measuring the length of the tape for 6 marks [0.1 second].  We obtained v1 = 13.5 cm / 0.1 sec = 135 cm/sec before dropping, and v2 = 6.9 cm / 0.1 sec = 69 cm/sec after dropping. The initial momentum was p1 = 0.500 ´ 1.35 kg m/sec = 0.675 kg m/sec, whereas the final momentum was p2 = 0.894 ´ 0.69 kg m/sec = 0.617 kg m/sec.  Momentum was thus conserved, with a precision of about 8%.  The standard PSSC experiment involves repeating this experiment with various initial masses. 

Ann also mentioned launching a tennis ball using a little lighter fluid in a tennis ball cannon.  The cannon is made from two steel cans welded together.  She warns her students against using Aluminum cans, which may burst to produce dangerous shrapnel.  For additional details see, for example, the University of Texas website, http://www.ph.utexas.edu/~phy-demo/demo-txt/1h11-20.html. Her speed record for such a launch is 107 mph, or 45 meters/second.  If you put too much lighter fluid inside the can, a flaming tennis ball is ejected.  Porter Johnson mentioned some interesting theories as to what caused the ignition of the von Hindenberg Airship at Lakehurst NJ on May 6, 1937.  For interesting theories on this matter, see the website http://americanhistory.about.com/library/weekly/aa042101b.htm.

19 November 2002: Betty Roombos [Gordon Tech HS, Mathematics]     The Ballistic Cart Put on Television 
Betty
presented a 21st century adaptation of the standard ballistics car demonstration, for which apparatus is available from, say, Sargent-Welch: http://www.sargentwelch.com/ [for a description of their ballistics car, see http://sargentwelch.com/search.asp?ss=ballistics+car&x=15&y=9]. The idea is that, when a ball is shot straight up from the cart while the cart is in uniform motion, it lands back in the cart, just where it came from.

As a modern variant of this standard demonstration, Betty used her digital camera, a Sony Mavica Model FD-88 with an 8X lens. It records 5, 10, or 15 second video images directly onto the 1.44 MB diskette that serves as the "film".  She recorded the video sequence before class, and then played it back on her MacIntosh computer, using the "freeze frame" option to show that the ball left the cart, went up, "stopped" in mid-air, and returned to the cart.  She used a grid on a transparency sheet to obtain quantitative information on the position of the cart at various time intervals.  To show us how simple this is, she played her recorded image back to us on our large TV Monitor, with impressive results. It was suggested that she could relate the "frame rep rate" to real time by recording the image of the second hand of a clock with her camera, either separately or as part of the apparatus.  You showed us how it really should be done,  Betty!

03 December 2002: Bill Blunk [Joliet Central HS, Physics]     Jumping off the Table 
Bill
began by climbing onto the laboratory table in front of the room, standing on it, and saying, with a SMILE on his face ... "I do this so that students can look up to me!"  He then asked why ballet dancers, gymnasts, and especially paratroopers always flex their legs as they land upon the ground.  To illustrate this, Bill stepped off the table, landing on the floor feet first, and flexing his body into a crouch as he came to rest. He then wrote down the following relation involving the (average) force F acting on a body over a time interval Dt, expressed in terms of the mass m of the body and its change in velocity Dv:

F Dt = m Dv

This relation, a direct consequence of Newton's Second Law, relates the Impulse (on the left side) to the change in momentum (on the right side). Bill pointed out that if he is the body, the mass m is constant. And since he falls through a given distance - the height of the table - his velocity, v, at contact with the floor is always the same. So Dv must  always be the same, since it is the reduction of v to zero while coming to rest on the floor. Thus, for Bill stepping off the given table and coming to rest on the floor, m Dv must be the same each time. And the change in momentum of Bill, the right side of the equation, is constant.

Using the notation popularized by Paul Hewitt [Conceptual Physics], a smaller force F acting over a longer time interval Dt produces the same impulse as a larger force F acting over a shorter time Dt :

F Dt = F Dt = m Dv = constant

By going into a crouch as he landed and slowed himself to rest, Bill increased the "landing time," and so lowered the average force on his body to a smaller value, F. If he had kept his legs stiff as he landed, he would have slowed to rest rather abruptly, greatly decreasing the time interval to Dt, and resulting in a much larger average force on his body, F!

To make this point in a more dramatic fashion, Bill said he would fall backwards off the table. But first he set up team of six of us (potential pall bearers?!) to catch him. The team was arranged into three pairs. Within a pair, each person faced the other. Each held his upper arm vertically at his sides, and forearms held forward and parallel to each other and the floor. Then - with hands facing down - each person grasped his own right wrist with his own left hand, and with his right hand he grasped the left wrist of his partner. The "people platform" thus formed by each pair can support much weight. (If you were a Scout, you probably know this!)

The three pairs then lined up in a row, perpendicular to the table, and Bill stood at the edge of the table, with his back to the row of these three "people platforms." Then he slowly tipped over backwards, keeping his body rigid, and falling right onto the "people platforms" - who were able to catch him before he might experience certain calamity! Everybody breathed sigh of relief, and Bill gave us the following pointers when attempting this feat:

It was suggested that one could practice the "rigid falling" component off the side of a swimming pool, preferably when the lifeguard wasn't looking directly at you. Bill pointed out that paratroopers make practice jumps from a height of about  3 meters [10 feet], corresponding to the speed at which they hit the ground during an actual jump [8 meters/sec or 15 mi/hour].  You really do have a jump on things, Bill.  Very nice!

03 December 2002: Ann Brandon [Joliet West HS, Physics]    Energy of A Pendulum
Ann
 led us through the following experiment: Is mechanical energy conserved when a pendulum swings?

    Procedure:
  1. Hang a pendulum (wood block with two eye hooks at the top edge) from two strong strings, so that it will swing in a vertical plane.
  2. Measure the distance h2 from the floor to the center of the pendulum mass, as it hangs straight down.
  3. Set up the photo-timer so that the pendulum will break the beam at the bottom of its swing.
  4. Measure the thickness DD of the pendulum, front to back, and record it.
  5. Lift the pendulum to one side, and measure the distance up to the center of mass h1.
  6. Zero the timer.
  7. Let the pendulum swing ONCE through the beam.
  8. Record the time Dt on the timer.
    Analysis:
  1. Determine the mass m of your pendulum.
  2. Calculate the Initial Gravitational Potential Energy.
  3. Calculate the Gravitational Potential Energy at the bottom of the swing.
  4. Calculate the Velocity at the bottom of the swing.
  5. Calculate the Kinetic Energy at the bottom of the swing.
    Questions:
  1. What was the Total Mechanical Energy before the swing?
  2. What was the Total Mechanical Energy at the bottom of the swing?
  3. Was the Total Mechanical Energy conserved during one swing of the pendulum?
  4. What forces are acting on the pendulum during its swing?  Draw a picture of these forces.
  5. We know that any pendulum will eventually stop swinging.  Which force causes this to happen?
  6. What happens to the missing energy?
The experiment was done with the following photo-gate / light source, and timer: Thornton / DEC 102 APC 100 Power Supply, which records the beam interruption time in milliseconds on a digital display. We made measurements to determine: m =0.300 kg, h1 = 0.10 m, h2 = 0.86 m, Dt = 0.025 sec, and DD = 0.08 m.  We calculated the velocity at the bottom of the swing to be v = 0.08 m / 0.025 sec = 3.2 m / sec. The kinetic energy at the bottom is thus 1/2 mv2 = 1/2´0.3 ´ (3.2)2 = 1.54 Joules, and the change in potential energy is m g (h2 - h1) = 0.300 ´ 9.8 ´ (0.76) = 2.23 Joules.  We conclude that about 30% of the energy is lost in the swing, either through air resistance or other frictional losses, or flexing of the bar, which has one end attached on the table and the other tied to the strings. With a lighter, smaller steel ball or brass cylinder, the results are obtained in closer agreement with energy conservation.  A nice, swinging experiment, Ann!

28 January 2003: Ann Brandon  [Joliet West HS, Physics]        Tennis Ball Collisions
Ann showed us how to attach two tennis balls of roughly equal mass (old ones are readily available at her school).  Simply cut a small gash in a ball, and insert a knotted end of a ribbon inside the ball.  She then set up a horizontal bar above the lab table, draped the ribbon over the bar, and taped it in place so that the balls were just touching and at the same height when at rest.  First, Ann [and trusty assistant Fred Schaal] pulled each ball an equal distance [d0, about 15 cm] in opposite directions, and released them from rest.   They bounced nicely off one another when reaching the bottom at the same time, and recoiled by about the same distance [d1, about 10.5 cm]. We concluded that the collision was slightly inelastic, in that some of the mechanical energy had been converted into heat, or thermal energy.  However, the net momentum remained the same before and after the collision: i.e., 0 = 0.  She next pulled the balls back by different distances, and we saw quite clearly that the bounce distances were different.  Finally, she used one ordinary tennis ball, and one ball that had been made twice as heavy because it had been partially filled with sand.  Ann said that it was simple to get some sand inside one of the balls; she just stuck a small funnel through the slit and poured sand into it. Tres simple!  We saw that, when the balls had been released from equal distances, d0, as before, the heavier ball hardly moved at all after the collision, whereas the lighter ball recoiled by quite a bit.  It was suggested in group discussion that the "small angle" approximation should be pretty good out to an angle of about 15°.  The information sheet that Ann distributed to the class can be seen by clicking here.

You made it look easy, as well as fun! Thanks, Ann!

06 May 2003: Peter Smagacz [Lane Tech HS, Physics]       Isolating Rotational Kinetic Energy
Peter
discussed using a YoYo to describe various forms of mechanical energygravitational potential energy, kinetic energy of translation, and kinetic energy of rotation::

E = PEg + KEr + KEt = m g h + ½ I v2 + ½ m v2
Unfortunately, his designated Yoyo expert (his son) was unable to attend the class, so that he could not demonstrate the effects.  The idea is that, when the YoYo leaves your hand and falls, gravitational potential energy is converted into kinetic energy, and when the YoYo is "sleeping" at the bottom of its path, it has only rotational kinetic energy.  When the expert gently tugs on the cord, the string wraps around the YoYo shaft and the YoYo rises almost to its original position.  Very interesting discussion -- but can you "walk the dog"?

Interesting ideas, Peter!

18 November 2003: Richard Goberville  [Joliet Central HS, physics]        Newton's Third Law
Richard
showed us the video of a failed jump from a ladder resting against the top edge of a fence, in which the jumper missed landing into a swimming pool, but ended up falling straight down onto the ground, instead.  The ladder was nearly twice as tall as the fence, so when the jumper pushed off from a rung well above the fence top, the ladder went one way and the jumper the other, but not as far as he had expected.  The video had appeared on a Canadian Cable TV Channel called Captain Video, and Maximum Exposure.  Good physics at the heart of this sad outcome, Richard!  He also passed out plastic jumping frogs, as well as flying pencil whirligigs, which he had obtained in large quantities from Oriental Trading Center: http://www.orientaltrading.com/.

Thanks for sharing your physics toys, Richard!

09 December 2003: Arlyn VanEk [Illiana Christian HS, physics]        Air Resistance of Swinging Block
Arlyn VanEk
set up a bifilar pendulum in front of us. He explained that he had done this in his classroom. He used a wooden block (with two eye screws) on its top edge for its bob, and suspended it from the ceiling using light, inelastic cord tied to the eyes screws. He then swung the bob back in an arc, keeping the cord taut to make angle to the vertical. Then he released the bob from rest, and measured the time for it to pass through a Pasco® (http://www.pasco.com) timing gate at the bottom of its swing. Knowing the width of the block, its speed could be calculated. From this kinetic energy could be calculated at the bottom of its swing, and its gravitational potential energy could be calculated by measuring the decrease in altitude from the beginning to the bottom of its swing.

Assuming air friction is nil and noting that the motion of the block should not depend upon its mass, when he did careful measurements, he found that energy was not being conserved! Thinking that this might be due to air friction, Arlyn made a second block with a streamlined shape, resembling the head of a doubled-bladed axe. Repeating the experiment with this bob, he found this time that it had more energy at the bottom of its swing than it had potential energy at the beginning! How could this be?!

Ann Brandon and Larry Alofs remarked that the separation of kinetic energy of a moving body into rotational and translational motion can be made only corresponding to a translation of the center of mass, and rotation with respect to the center of mass.  One may thus apply the principle of conservation of energy using that principle.  Correspondingly, it is crucial to be certain that the center of mass of the pendulum moves through a circular arc, and that translational speeds are measured for the motion of that center mass.  The standard arrangement for a ballistic pendulum is to suspend  a wooden block by four strings, attached on the top side on locations symmetric with respect to the front, back, left, and right edges.  One thereby makes a bifilar pendulum, with the desired properties.   PJ also mentioned that an aerodynamic shape should more properly represent an aircraft wing --- sharp in the front and smooth in the back, rather than being front-back symmetric.  He pointed out that the winning athletes in the platform ski jumps in the 2002 Winter Olympics (in addition to being anorexic) held their skis- cross-pointed at the front, to reduce air resistance, rather than in the standard railroad track position,  to reduce air resistance. 

As a sequel, Arlyn showed that two steel balls collide almost elastically when one rolls into the other at rest on a smooth table.  However, if the balls smash against one another in mid-flight and stay together, all the mechanical energy must be converted into heat.  How do we know this?  Arlyn took two solid steel balls [mass of about 500 grams each; about 5 cm in diameter], and smashed them together while a sheet of ordinary paper was held between them.   It was quite plain to see that a small hole had been burned through the paper with each encounter.  Furthermore, when the experiment was repeated in a darkened room, we could see flashes of light with each collision.  Also, the smell of burnt paper was unmistakable  Remarkable!

Finally, on a non-destructive note, Arlyn held up a Thumb Drive Flash Memory Stick with a capacity of 64 MB that can be inserted into the USB plug on his fairly new computer.  He is using this small memory stick  (normally used for a digital camera) to transfer data from the school computer to his computer at home -- the hard drive recognizes it as a formatted [ROM] disc, so that files can be moved to and froNeato!

Arlyn, you showed us how it really is!  Thanks!

27 January 2004: Arlyn VanEk [Illiana Christian HS, physics]        Rotational Mechanics
Arlyn
first set up a race between a solid metal disk and a hollow ring (masses and diameters approximately equal), which were released from rest and rolled down the same inclined plane.  The solid disk won the race because it has a smaller rotational intertia than the hollow ring.  [Equivalently, it requires less energy for the solid disk to produce a given rotational speed than for the hollow ring.]  Arlyn explained that the distribution of mass, as well as the amount of mass, is relevant for rotational dynamics.  Arlyn pointed out that the moment of inertia of the ring (mass m; radius R) about its center is Ic= mR2, whereas for a disk of the same mass and radius the corresponding moment of inertia is Ic = 1/2 mR2.  At this point Earl Zwicker scurried out of the room, and he came back shortly with two meter sticks, each having two 100g masses taped to them.  For the stick with masses taped at its ends, it is more difficult to twist the stick back and forth about its center, than  for the stick with masses taped at its center. Very convincing, Earl!  Arlyn then rolled a small, light disk down the plane along with a large, heavy disk --- they rolled down at about the same rate.  He concluded from this and other experiments that the mass and radius of the object are unimportant, whereas the distribution of mass is crucial for winning the race. Arlyn then showed that a solid (metal) sphere is faster than a disk, whereas a hollow sphere (tennis ball) is slower than the disk, but faster than the ring.  These conclusions are consistent with the following table of moments of inertia (mass m, radius R) about the symmetry axis:

Moments of Inertia: Ic  

Ring       mR2
Hollow Sphere   2/3 mR2
Disk  1/2 mR2
Solid Sphere  2/5 mR2
Arlyn then illustrated that a hard-boiled egg spins nicely on the table, whereas a raw egg quickly stops spinning, because of internal dissipation of the rotational energy.  That's certainly one way to tell if your eggs have been cooked! 

Arlyn then balanced a (uniform) meter stick of weight W with a weight W0 attached to an end.  He showed that balance occurred at a distance x from the center of the stick, the weight at the end being a distance y = (0.5 m)  - x from the balance point.  Since the net torque about the balance point must be zero, W x = W0 y = W0 (0.5 - x), or x = 0.5 W0 / (W0 + W).  Note that the total weight to the left of the balance point, (0.5 +x ) W = 0.5W (2W0 + W) / (W0 + W), is not equal to the total weight to the right, W0 + (0.5 - x) W = W0  + 0.5 W2 / (W0 + W).  Balance occurs because torques balance at left and right, and not because there are equal amounts of weights on the right and left sides.  Arlyn also pointed out that, in "pumping" a swing, a person is putting energy into the system by systematically adjusting his/her center of mass

Arlyn, you showed some good stuff!  Thanks!

20 April 2004: Babatunde Taiwo [Dunbar HS, Physics]         Vernier Force Plate with Graphing Calculator
Babatunde
had recently obtained the Force Plate from Vernier Corporation: [http://www.vernier.com/probes/probes.html?fp-bta&template-standard.html].  He had used this apparatus to do various experiments involving impulses generated by jumping onto the plates, as well as the distribution of weight when one stands on two plates.  He illustrated the operations by having Bill Shanks stand on the force plate, and then jump into the air, and then land on the plate again.  Babatunde showed the recorded images of force on the plate versus time.  When Bill stood on the plate, the force on the plate had a steady value of about 800 Newtons.  As he jumped the force spiked upward. and then went quickly down to zero.  It remained at zero while he was in the air, for about 0.2 seconds.  When he returned to the table there was another spike, similar to the first one.  Babatunde then determined the total impulse over the jump period from data by numerical integration, and obtained about 700 Newton-secondsBabatunde then investigated how the force and impulse would change from these values (natural lant here were more oscillations in the force in these two cases.  In addition, the net impulse was less for the crouch landing (500 N-s) and the rigid landing (300 N-s) than for the natural landing (700 N-s).  Also, Don Kanner, the rigid jumper, could feel the difference in his bones!

A very nice display of impacts, there for all to see! Thanks, Babatunde!!

28 September 2004: Larry Alofs  [Kenwood HS, Physics]           The First Motion Graph
Larry brought in a small battery operated car that he obtained some time ago at  American Science & Surplus [http://www.sciplus.com/], but which is no longer available.  The car operated at two speeds  -- we tested it on the table at the lower speed.  Taking averages with two trials and four stopwatches provided by Larry, we obtained the following set of data for distance traveled versus time.

Distance (cm) Time (sec)
0 0.0
25 1.20
50 2.40
75 3.56
Larry plotted the graph of Distance vs Time on a sheet on the overhead projector, and used a translucent ruler to show that the data lay along a fairly good straight line passing through the origin, corresponding to an average speed of  about 21 cm/sec.   The students learned that the speed is equal to the rise/ run (slope) of the graph, and that a second plot with the car at higher speed yields a greater slopeVery slick, Larry!

28 September 2004: Debbie Lojkutz   [Joliet West HS, Physics]           Studying Straight Line Motion with a Ticker Tape Timer
Debbie described the following experiments that  involve linear motion:

Number Experiment Category
1 Stomper Car Speed 1 ---> Speed 2
2 Car Rolling down Ramp Uniform Acceleration (slow)
3 Free Fall Uniform Acceleration (fast)
4 Chain Sliding off Table Variable Acceleration
5 Pendulum Simple Harmonic Motion
She passed out a handout with data table on the last experiment.  Debbie and Ann Brandon set up the pendulum apparatus, running the ticker tape through the timer and attaching it to the pendulum bob. After several false starts, they got a good set of  dots for a half-period on the ticker tape, produced every 1/60 second by the spark timer. They gave us a handout that contained the following information:
Lab 2.3: Motion of a Pendulum

Purpose: To Investigate the relationships among Distance and Time, and Velocity and Time for a one-way swing (1/2 period) of a Pendulum.

Procedure:

  1. Set up the pendulum with a length of about 2 meters, so that it just misses the ground as it swings.
  2. You will need about 2 meters of ticker tape.
  3. Thread the ticker tape through the timer.
  4. Place the timer on the ground, about 1 meter from the bottom of the swing.
  5. Pull the mass over to the timer, and attach the ticker tape to the mass.
  6. Turn on the timer.  Let go of the mass. Have your partner catch it on the other side, JUST as it starts to swing back.
Analysis:
  1. Mark every 6th dot on the tape.
  2. Measure the distance from the start of the tape to each 6th dot mark, and record in your data table.
  3. Calculate DD, DT, and V, recording in your data table.
  4. Graph D vs T, and V vs T.
  5. On the D vs T graph, mark the positions of Zero Velocity and the Maximum Velocity.
Questions:
  1. What is the average velocity of the pendulum for the one-way swing? 
  2. What is the average acceleration of the pendulum for the one-way swing?
  3. What is the period of a complete cycle of the pendulum?
  4. What is the maximum velocity of the pendulum?
  5. What is the acceleration of the pendulum at the beginning of the swing?
  6. What is the acceleration of the pendulum at the end of the swing?
  7. Look at the graphs. Describe each of them.
  8. Is the V vs T graph symmetrical?
    What does this indicate about the velocities at either end of the swing?
    What does this indicate about the accelerations at either end of the swing?
Conclusion:
Debbie also reminded us of the chart she and Ann Brandon have long used to describe determining the Displacement, Velocity, and Acceleration, from graphs of Displacement vs Time, Velocity vs Time, and Acceleration vs Time; respectively. That chart is described in detail in the HS Mathematics-Physics SMILE lesson of 24 September 2002: mp092402.html.  Very nice, Debbie!

23 November 2004: Charlotte Wood-Harrington [Brooks College Preparatory School,  physics]           Newton's Third Law -- a 'Tom Senior' Demo 
Charlotte placed some dowel rods (each about 30 cm long) on the table, and on top of them placed a sheet of pink foam insulating board, which was about 30 cm wide, 100 cm long, and 2 cm thick. Then she put a small self-propelled toy car on the top of the foam board, which served as a racetrack for the car.  When the car was turned on and then placed on the foam board to travel in the long direction, it went forward, the dowel rods rotated, and the foam board went backwards --- as required by Newton's Third Law.  The arrangement worked very well, except that Charlotte had inadvertently gotten a 'hot' car, which traveled only at top speed. The car went so fast that the foam board almost immediately shot off the table in the opposite direction.  We need to find a car that isn't such a speed demon!

A very nice illustration of physics in action, Charlotte!

07 December 2004: Karlene Joseph [Lane Tech HS  physics]           The Physics of Hopper Poppers
Karlene showed us a flexible rubber spherical segment (popper) about 3 cm in width and 1 cm high, which she had obtained recently as a party favor.  She pressed on the top of the popper so as to turn it "inside out", thus elastically "priming" it into a state of higher potential energy.  She then placed it on the table. After a few seconds, the popper spontaneously and suddenly relaxed to its original shape, jumping several meters into the air.  Then she primed it again, and placed it on the table upside down.  This time when it "jumped", it achieved a height of less than one meter.  Why the difference? There was some talk in the group about "needing a good push" off the launch pad.  To illustrate the effect, Bill Blunk primed the popper and put it on the edge of a film canister --- which was just the right size!  The launch fizzled ... Why?  These "hopper poppers" may be obtained in bulk from either the American Science and Surplus [http://www.sciplus.com/] or Oriental Trading Company [http://www.orientaltrading.com/].

Good launch for a serious discussion of impulse, Karlene!

07 December 2004: Ann Brandon  and Debby Lojkutz [Joliet West HS, physics]           Non-scrambled Eggs 
Ann and Debbie  held opposite ends of a fitted bed sheet so it was open and mostly spread out in a vertical plane.  From two meters away, Fred S, Benson U, and visiting student Nicole each threw a raw egg at the sheet.  None of the eggs were broken in the process.  Why not?

The answer lies in the Impulse-Momentum Theorem, which is a direct consequence of Newton's Second Law:

F = DP / Dt
... or ...
I = F Dt = m Dv
For a given mass (m) and stopping speed (Dv), a small average force results when the stopping time is large (soft landing: egg survives intact). For a small stopping time the average force must be large (hard landing: egg breaks).  In the notation of Conceptual Physics by Paul Hewitt :
F D t = F Dt = m Dv
Arlyn van Ek described a variation of this experiment, in which students throw a water balloon (a balloon filled with water) at a bed sheet.  According to Arlyn, at least one person in every class manages to break the balloon.  Now, why does that happen?

Porter Johnson described an Egg Crush video demonstration, in which an egg is placed with its long axis vertical into a crushing apparatus with heavy, strong rubber padding on the top and bottom against the egg.  The egg was easily able to stand a steady load of 10 - 20 - 30 - 40 -50 kilograms.  For visual impact, that egg was then dropped into a frying pan from a height of 30 cm --- and its shell broke into piecesPorter mentioned the Diamond Anvil [ http://scienceworld.wolfram.com/chemistry/DiamondAnvilCell.html] as a tool for achieving high pressures (up to 106 atmospheres), to study the properties of materials such as solid Helium at room temperature. John Scavo called attention to the production of industrial diamonds that are of the same quality as the best natural diamonds. It is believed that natural diamonds were created over eons of time under conditions of high pressure and high temperature, deep within the earth.

Thanks, Ann and Debbie.

26 April 2005: Don Kanner and Bill Blunk [Joliet West HS, physics]              You Can't Win at Tug-of-War just by Pulling Harder
Don and Bill
stood  facing each other, each holding one end of his own spring scales.  The other ends of the scales were then hooked together between them.  They pulled in opposite directions, Don attempting to get and maintain a scale reading of 50 Newtons (about 12 pounds) and Bill tried to maintain 100 Newtons (about 24 pounds).  Don merely chased Bill across the room with increasing speed -- or did Bill pull Don! They always had about the same scale reading, despite their efforts.  It may have been an exercise in frustration for them, but it was quite entertaining for us.  Why did they fail?  Isaac Newton and his laws of motion have something to say about this. Don't they?

It was an excellent Katzenjammer Kinderen comedy routine, which served  to illustrate the consequences of  Newton's Laws. 

By chance, are you twins? Thanks, Don and Bill.

26 April 2005: Fred Farnell [Lane Tech HS, physics]              Rolling, Falling, Rolling
Fred
brought in a defunct classroom white board (about 1 meter by 1.5 meter in size), which he carefully clamped  to the desk in front of us, so that it formed a broad inclined plane sloping slightly down toward us.  He then brought out a plastic ruler of length about 30 cm with a groove down the center, which he attached to near the top  right edge of the white board, with the groove on the top side; the ruler tilted upward from the board about 10°. He carefully attached the ruler so that a marble released from rest at a point on its groove would roll down it, and then go smoothly onto the white board.  He was able to adjust the initial direction of  motion of the marble on the white board to be horizontal and parallel to its top edge.  We watched as it rolled on the white board along a parabolic path, till falling off the bottom of the board.  Fred had thus created a system for studying two dimensional motion.  He varied the release height H of the marble above the ruler's lowest end, and we took several measurements of the time T required for the marble to roll off the bottom edge of the board.  Here are the data:

H
Release Height
T
Average Rolling Time
05 cm 2.25 sec
10 cm 2.36 sec
15 cm 2.18 sec
18 cm 2.18 sec
Surpr-i-i-i-se, surpr-i-i-i-se! The times are all the same, to within experimental uncertainty. How come? Perhaps the horizontal and vertical motions are independent of one another in this case. Shouldn't they be?

So far, so trivial!  Fred assumed that the marble was perfectly round, and that it rolled without slipping down the inclined plane. Under these conditions, the component of acceleration down the plane, which is inclined at angle q above the horizontal, is

ay = 5 / 7 g sin q 
Using this formula, Fred obtained a "roll time" of 1.90 seconds ---- which is significantly smaller than the measured value. Now, just why do things happen this way? One possible explanation is that the connection between rotational angular velocity and translational speed is different for a marble riding along a groove from what it would be on a planar surface. Thus, the marble would slip somewhat when it goes onto the plane. At first it would slide across the plane, losing mechanical energy through friction --- like a bowling ball going down the lane! Maybe that is the reason!

An related question posed by Porter Johnson:

Q: What happens when a tire is rolled without slipping at an oblique angle down an inclined plane?"
A excellent experiment to challenge physics understanding. Thanks, Fred!

10 May 2005: Porter Johnson and Earl Zwicker [IIT, physics]              Newton's Third Law
Porter found an old fan cart (propeller-driven, four-wheel cart) with a very corroded battery case, which he rejuvenated through liberal application of WD-40™ solvent, toothpicks, Q-tips, and elbow grease to remove the corrosion.  Roy Coleman mentioned that WD-40 was developed in the Atlas Missile Program http://www.au.af.mil/au/awc/awcgate/au-18/au18004f.htm, from which the following has been excerpted:

"As a sidelight, during development, designers determined that the Atlas needed corrosion protection from the salt-laden Cape Canaveral air. Convair chemists worked on many formulas to provide a wipe-on protection. This endeavor led to the development of WD-40, (water displacement formula, trail number 40) which now has worldwide applications."
The rejuvenated fan cart worked very well at the SMILE meeting. It had ball-bearing wheels attached to the base, and the battery pack had six 1.5 Volt C-Batteries.  In addition there was a switch to activate the small motor, which drives a  propeller (fan) with two plastic blades about 10 cm long.  Earl put the cart through its motions, using it to show basic concepts in mechanics:

For additional details, including a picture, see the SUNY Stony Brook website http://naples.cc.sunysb.edu/CAS/pdemos.nsf/By+Course+Number/C.+Kinematics+And+DynamicsC5.+Third+Law+Of+MotionC5-18Fan+Cart, from which the following has been excerpted:

"With the sail unmounted, turn on the fan and release the cart; it moves in the direction opposite to that of the blowing air. Mount the sail and blow into it with your breath; it moves in the direction which you are blowing. Finally, with the sail in place turn on the fan and release the cart.
Q
: What will the cart do with the sail in place and the fan operating?
(a)  move in the direction of the air,
(b)  move opposite to the direction of the air, ... or ...
(c)  remain at rest.
A: It will remain at rest."
An oldie but a goodie! Thanks, fellows.