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1997-2006 Academic Years Mechanics: Dynamics |
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1997-2006 Academic Years Mechanics: Dynamics |
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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
Bad data
Misconceptions
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
11 November 1997: Lee Slick [Morgan Park HS]
Finished the day with several building projects:
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:
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
we determine the angular velocity to be
The net [centripetal] force on the 20 gram mass is
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.
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]
Suspend a heavy weight [1 kg] with a string above it attaching it to the ceiling, and a string below it.
Suppose that you are stuck in the mud, with no means of assistance. How do you get out? One answer is to take a rope, tie it tautly to the car and to a conveniently located nearby tree, and then push transversely at the middle of the rope. You should generate enough force to pull the car a little bit toward the tree. They, tighten the rope and do it again, repeating until you get out.
This principle is easy to speak about, but impractical to demonstrate directly for reasons of safety. Instead, get a bunch of students to stand n a 2" x 12" board [promise them anytheeng!], and attach the board as well as a "fixed object" with a steel cable. Tighten the cable and apply a transverse force to demonstrate the effect. It works beautifully, and is a good example of practicing "safe science".
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?
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,
Someone pointed out that if a nested 3 filters were used, they would need to be released from a height above the floor of
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 pounds. They
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 5°. 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 5° 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":
*** 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
The function K(k) is defined as the (elliptic) integral:
One may make either of the following expansions of the elliptic integral [See the web article Large Amplitude Period of a Physical Pendulum: http://webphysics.davidson.edu/alumni/BeKinneman/pendulum/report.htmas well as the Java Applet http://hyperphysics.phy-astr.gsu.edu/hbase/pendl.html:
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 |
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://www.teachnet.org/impactii/profiles00_01/block.htm. and Ben and Me: http://www.lessonplanspage.com/Ben/BenandMe.html. Ann 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 |
d | v | 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 |
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:
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
:
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:
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?
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
energy: gravitational potential energy, kinetic
energy of
translation, and
kinetic energy of rotation::
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.orientaltc.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 fro. Neato!
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 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-seconds. Babatunde
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 |
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 |
Lab 2.3: Motion of a PendulumDebbie 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!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:
Analysis:
- Set up the pendulum with a length of about 2 meters, so that it just misses the ground as it swings.
- You will need about 2 meters of ticker tape.
- Thread the ticker tape through the timer.
- Place the timer on the ground, about 1 meter from the bottom of the swing.
- Pull the mass over to the timer, and attach the ticker tape to the mass.
- 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.
Questions:
- Mark every 6th dot on the tape.
- Measure the distance from the start of the tape to each 6th dot mark, and record in your data table.
- Calculate DD, DT, and V, recording in your data table.
- Graph D vs T, and V vs T.
- On the D vs T graph, mark the positions of Zero Velocity and the Maximum Velocity.
Conclusion:
- What is the average velocity of the pendulum for the one-way swing?
- What is the average acceleration of the pendulum for the one-way swing?
- What is the period of a complete cycle of the pendulum?
- What is the maximum velocity of the pendulum?
- What is the acceleration of the pendulum at the beginning of the swing?
- What is the acceleration of the pendulum at the end of the swing?
- Look at the graphs. Describe each of them.
- 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?
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:
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 pieces! Porter 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 |
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
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.An oldie but a goodie! Thanks, fellows.
Q: What will the cart do with the sail in place and the fan operating?(a) move in the direction of the air,A: It will remain at rest."
(b) move opposite to the direction of the air, ... or ...
(c) remain at rest.
