The motivation for the next few visits to the elementary school is
that the kids are going to help design the playground for their new
school site, so I'm going to show them a bit about how things work, ie
classical mechanics. One thing I love about this school is that the
teachers frame things this way. Instead of just hearing that "today
we're going to be learning Newton's laws of motion" students have this
wonderful backdrop to keep them motivated and (perhaps more important)
foster creativity. The laws of mechanics will be a springboard to
creating something wonderful, not a straitjacket of rules we have to
memorize.
We set the foundation last time with
Newton's laws of motion exemplified in the simplest possible situations,
to make them as clear as possible. This time, we added complications to
show how interesting it can be when forces interact. I concocted three
different examples of interacting forces and set up three
stations. Each group of 6-8 kids split into 3 groups of 2-3 and spent
5 minutes at each station, with 5 minutes left at the end for group
discussion.
Station 1: I repeated the pulley activity from last week at Primaria.
I rigged up different pulley arrangements to lift identical 20-pound
weights. One arrangement was just a single pulley at the top as you
might expect, reversing the direction of the rope so that the kids
could stand on the ground and pull down on the rope to make the block
go up. The second arrangement had the end of the rope tied at the
top, running down to an "upside down" pulley attached to the block,
and then back up to a pulley at the top which acted much like the
single pulley, just reversing the direction of the rope. The kids
tried both setups and compared the difficulty of lifting the block.
The second arrangement is much easier, but why? I challenged the kids
to go beyond simple explanations like "two pulleys are better than
one" and "there are two ropes pulling up the weight so it's twice as
strong." The latter statement starts to get to the answer, but is by
no means a complete answer. If I have to drag something with a rope,
tying two ropes to it doesn't make it any easier.
The trick is to observe closely what happens when you pull. The
moving pulley makes it so that if I pull my end of the rope one foot,
the weight moves up half a foot. This means that you only need half
the muscle that you need with the fixed pulley. (This is called
"mechanical advantage" but I did not use that term.) This was not too
easy for the elementary kids; in fact I think last week the pre-K/K
kids did better, possibly because the three-station setup this week
was very distracting. They were able to extrapolate how to make it
even easier to lift (add more pulleys) but we didn't have time to
discuss how we would connect those extra pulleys, which would really
probe understanding. This could be a good home activity for
interested parents and kids: set up a 4-pulley system so that it's 4
times easier to lift a given weight. How do you set it up, and how
much rope will you have to pull to lift the weight 1 foot? (Advice:
don't try to connect 4 separate pulleys, because the ropes will easily
get twisted and tangled. Buy two "double parallel pulleys" so that
everything stays more or less aligned.)
Also note that in each case, one pulley exists only to reverse the
direction of the pull. You could simplify the comparison by thinking
about standing on a deck and pulling a weight straight up (no pulleys)
vs. tying one end of the rope to the deck, running it around a pulley
attached to the weight, and then pulling up on the other end. Here it
is clear that to get the weight up to the deck, you will need to pull
a length of rope which is twice the height of the deck. But the
benefit is that you need only half the strength to pull the rope.
Station 2: an overhead pulley with an adjustable amount of weight
attached to the rope on each side. This can be used to emphasize a
few different concepts. First, balance: when the weight on each side
is the same, neither side moves. This might seem boring, but it is
actually an easy way to move weight up and down. In balance, it takes
only a tiny amount of strength to move one side up or down, because
you are not moving any net weight up or down. This is how elevators
work: there is a counterweight so the motor doesn't have to work so
hard. This also provides safety in case the motor breaks: the
counterweight is always there and needs no power to function.
Wouldn't it be fun to have some kind of human-powered elevator on the
playground?
Second, this station can serve to reinforce ideas about force and
acceleration (Newton's laws of motion). When there is only slightly
more weight on one side, the net force due to gravity is small, and
that side accelerates downward quite slowly. But with a relatively
small counterweight, the the net force due to gravity is large, and
the heavy side accelerates downward quite rapidly. It's kind of like
a seesaw with rope, which makes it relevant to the playground.
See the Wikipedia article on the Atwood machine for a nice diagram,
and this video demonstrating the small acceleration when the weight is nearly the same on each side.
Third station: this was very much like a small seesaw, with a meter
stick balanced on a pivot at the center. The kids could hang weights
of various sizes at various distances from the center. They were
supposed to figure out that a small weight placed far from the center
could balance a much heavier weight placed close to the center.
However, five minutes was not enough time to absorb this. In many
cases it took them just a few minutes to figure out that if one side
of the balance beam is down, piling more weight on that side doesn't
help balance it! And others were not cognizant that the weights came
in different amounts, from 5 to 50 grams, and just counted the number
of weights rather than the total amount of weight. (OK, I know the
gram is not technically a unit of weight, but we have to keep things
simple!) So in the future I would structure the balance beam as a
complete activity in itself, and define a series of goals starting
from a very basic level. This time, I can forgive myself because I
only had one setup, which wouldn't have worked for 6-8 kids. Anyway,
with the balance beam station I also brought the discussion back to
the playground. What fun things could they design which might involve
balancing big things on one side and small things on the other? Maybe
a balance beam for kids to hang from and balance each other?
After the stations, we had a 5-minute wrapup for each group of 6-8
kids, discussing some of the nuances I wrote about above, which were
missed in the quick 5-minute rotations. This is the first time I
tried having small groups work on different things, and I have to say
it was hectic. Thank goodness the school is well staffed! I had at
least one teacher or or aide or intern rotate in with each group,
which saved the whole thing from being a complete organizational
disaster.
After all the groups rotated through, the kids reassembled in one big
group for circle time, and I asked for 5-10 minutes to do a few demos. I
did these in the big group because (1) there was no time to do it
during the rotations; and (2) the kids would have fought over these
things if it had been a hands-on activity. First, I showed a rod with
a heavy ball on one end and a light ball on the other end, and I asked
how I should place the rod so that it balances on my finger. Not
everyone answered near the heavy ball! So it was worth demonstrating.
But the really cool part is that if something is well balanced, it
will rotate nicely. So I showed how it spins about its balance
point very smoothly and for a long time, whereas it clearly would not
spin nicely about the center of the rod. Here's a video: (apologies for
the appalling quality of the video. I figured it was more important
to help parents see what their kids saw than to worry about looking
good.)
Second, I demonstrated Newton's cradle. This again relates to forces,
and a large version would make a really cool addition to a playground.
(Note: if your kids have studied pendulums, Newton's cradle may be best
understood as a kind of pendulum.)
To wrap up, I asked for their ideas on the playground. After taking a
few, we ran out of time, and we agreed that kids would draw their
concepts during free-choice time. In two weeks, I'll return to the
elementary for some activities involving rotation, and the next day
we'll take an optional family field trip to the Berkeley Adventure
Playground which has "many unusual kid designed and built forts,
boats, and towers." Then we'll get to work more seriously on
designing our own playground!
Friday, November 18, 2011
Saturday, November 12, 2011
Gearheads
The Primaria kids continue to be fascinated by contraptions,
factories, and the like. Thursday, the day before my visit, they
built contraptions using empty cardboard boxes, egg cartons, steel
cans, etc, plus a lot of imagination. So I explored pulleys and gears
with them on Friday.
In my previous visit we built an elevator; that was more about the
principle of balance than about pulleys, but it did give them a basic
intro to pulleys. This time, I rigged up different pulley arrangements
to lift identical concrete blocks, using the monkey bars to hang the
pulleys. One arrangement was just a single pulley at the top as you
might expect. The second arrangement had the end of the rope tied at
the top, running down to an "upside down" pulley attached to the
block, and then back up to a pulley at the top which acted much like
the single pulley, just reversing the direction of the rope so that
the kids could stand on the ground and pull down on the rope to make
the block go up. The kids tried both setups and compared the
difficulty of lifting the block.
The second arrangement is much easier. I didn't expect the kids to
figure out why, but I did expect them to see that it had two pulleys
instead of one, or that it had a moving pulley rather than just a
fixed one. Two of the four groups did not see this and required some
coaxing. But I made a kind of game out of it, telling them that in
science we have to be very observant, asking them to watch carefully
as I pull each one slowly, etc. I was happy to be able to frame it
such that they could gradually work toward the answer rather than just
have me give them the answer.
So why does the moving-pulley system make it easier? I took lots of
very entertaining guesses on this one before having them observe the
motion again. The moving pulley makes it so that if I pull my end of
the rope one foot, the weight moves up half a foot. This means that
you only need half the muscle that you need with the fixed pulley.
(This is called "mechanical advantage" but I did not use that term.)
Then I asked how they could imagine making it even easier to pull.
Some of the groups digressed at first ("add a motor", "get a lighter
block") but we generally concluded that even more pulleys would be
better. Kids love big numbers, and instead of suggesting four pulleys
some went straight to "a thousand pulleys!" I had tried setting up
four pulleys, but the ropes got too twisted. If you want to go to
four pulleys, I recommend buying sets of two pulleys already bolted
together side-by-side to avoid this twisting (parallel pulleys). I
can't imagine how twisted the ropes would get with a thousand pulleys!
Next, we did gears. They had already played a lot with
Gears!Gears!Gears! sets, but those are limited in terms of gear
concepts. I ordered some bags of gears of very different sizes and
had hoped to mount them in some way which allowed for exploration, but
I ran out of time drilling holes at 8:45 Friday morning. So this was
more of a demonstration than a hands-on activity, but that was ok
because it allowed me to use something I had only one copy of: the
book Get in Gear by Sholly Fisch, which is a really nice book. Each
page describes a new gear concept and gives you the framework for
assembling it and seeing it work for yourself.
Before going to the book, I wanted to make sure they understood gear
ratios (although I didn't use that term). I showed a little gear
turning a big gear in one of my homemade setups, and we counted how
many times we had to turn the little gear all the way around before
the big gear went around once. In this case, it was about 3, because
the big gear had about 3 times as many teeth. Conversely, turning the
big gear once makes the little gear go around about 3 times. So if
you need to build a high-speed machine, hook a motor up to a big gear
which turns a little gear, and the little gear will go crazy fast.
And if you need to build a low-speed machine, hook your motor up to
the little gear, and the big gear will trun slowly. We talked about
why people might need to build a low-speed machine. This connects
back to the pulleys: when moving a heavy weight, low-speed is
better. (I left it at that without talking about forces; I think the
low-speed motion of the concrete block in the easy-to-pull setup was
the most effective and appropriate "proof" for this age group.)
On to the book. I had noticed that the kids are paying attention to
clocks and starting to learn about time, so I started with the clock.
This was a natural segue from the gear ratio demo. We want to make
the hour hand go slowly, so how do we do that with gears? Attach the
hand to a big gear which is driven by a small gear! And we want to
make the minute hand go fast, so how do we do that with gears? Attach
it to a small gear which is driven by a big gear! I was pleased that
the kids were able to guess these answers most of the time. So here's
the clock in action:
Next, I showed them that gears are not limited to circular motion. Here is a rack gear in action:
Rack gears are used for turning circular motion into linear motion. In addition to all kinds of machines, rack gears are used in steep mountain railways, where the track contains the rack gear and the engine carries and pushes on the circular gear. (It's also used for rack-and-pinion steering; the pinion is the circular gear which meshes with the rack.) We talked about what kinds of machines might need to do this kind of motion. Maybe squeezing grapes for grape juice, or printing presses.
And we can also set up gears to do a sweeping motion, by attaching something off-center:
The last thing we had time for was planetary gears, so called because little gears go around a bigger gear like the planets around the sun:
This is cool and could just be a work of art, but there are applications. Note that around the outside is what is basically a really big inside-out gear (difficult to see in the video because it's made of clear plastic). I went back to the homemade big+small gear setup and asked why it would be useful to put the small gear inside the big gear. Answer: to save space, if you need to make a small machine, like a pencil sharpener, a kitchen mixer, maybe an electric toothbrush.
Finally, we didn't get time to build the piece de resistance, but here is a machine which combs your hair and brushes your teeth at the same time:
The whole activity worked well. I learned something about organizing kids, too. Because there weren't enough pulley setups, kids had to wait, but there wasn't really a line because it was just a few kids waiting. This led to a lot of confusion until Teacher Jessica brought "waiting chairs." When the kids have to sit in chairs to wait, it is 100% clear who is next!
If you want to see more, I recommend the video Gear Basics.
factories, and the like. Thursday, the day before my visit, they
built contraptions using empty cardboard boxes, egg cartons, steel
cans, etc, plus a lot of imagination. So I explored pulleys and gears
with them on Friday.
In my previous visit we built an elevator; that was more about the
principle of balance than about pulleys, but it did give them a basic
intro to pulleys. This time, I rigged up different pulley arrangements
to lift identical concrete blocks, using the monkey bars to hang the
pulleys. One arrangement was just a single pulley at the top as you
might expect. The second arrangement had the end of the rope tied at
the top, running down to an "upside down" pulley attached to the
block, and then back up to a pulley at the top which acted much like
the single pulley, just reversing the direction of the rope so that
the kids could stand on the ground and pull down on the rope to make
the block go up. The kids tried both setups and compared the
difficulty of lifting the block.
The second arrangement is much easier. I didn't expect the kids to
figure out why, but I did expect them to see that it had two pulleys
instead of one, or that it had a moving pulley rather than just a
fixed one. Two of the four groups did not see this and required some
coaxing. But I made a kind of game out of it, telling them that in
science we have to be very observant, asking them to watch carefully
as I pull each one slowly, etc. I was happy to be able to frame it
such that they could gradually work toward the answer rather than just
have me give them the answer.
So why does the moving-pulley system make it easier? I took lots of
very entertaining guesses on this one before having them observe the
motion again. The moving pulley makes it so that if I pull my end of
the rope one foot, the weight moves up half a foot. This means that
you only need half the muscle that you need with the fixed pulley.
(This is called "mechanical advantage" but I did not use that term.)
Then I asked how they could imagine making it even easier to pull.
Some of the groups digressed at first ("add a motor", "get a lighter
block") but we generally concluded that even more pulleys would be
better. Kids love big numbers, and instead of suggesting four pulleys
some went straight to "a thousand pulleys!" I had tried setting up
four pulleys, but the ropes got too twisted. If you want to go to
four pulleys, I recommend buying sets of two pulleys already bolted
together side-by-side to avoid this twisting (parallel pulleys). I
can't imagine how twisted the ropes would get with a thousand pulleys!
Next, we did gears. They had already played a lot with
Gears!Gears!Gears! sets, but those are limited in terms of gear
concepts. I ordered some bags of gears of very different sizes and
had hoped to mount them in some way which allowed for exploration, but
I ran out of time drilling holes at 8:45 Friday morning. So this was
more of a demonstration than a hands-on activity, but that was ok
because it allowed me to use something I had only one copy of: the
book Get in Gear by Sholly Fisch, which is a really nice book. Each
page describes a new gear concept and gives you the framework for
assembling it and seeing it work for yourself.
Before going to the book, I wanted to make sure they understood gear
ratios (although I didn't use that term). I showed a little gear
turning a big gear in one of my homemade setups, and we counted how
many times we had to turn the little gear all the way around before
the big gear went around once. In this case, it was about 3, because
the big gear had about 3 times as many teeth. Conversely, turning the
big gear once makes the little gear go around about 3 times. So if
you need to build a high-speed machine, hook a motor up to a big gear
which turns a little gear, and the little gear will go crazy fast.
And if you need to build a low-speed machine, hook your motor up to
the little gear, and the big gear will trun slowly. We talked about
why people might need to build a low-speed machine. This connects
back to the pulleys: when moving a heavy weight, low-speed is
better. (I left it at that without talking about forces; I think the
low-speed motion of the concrete block in the easy-to-pull setup was
the most effective and appropriate "proof" for this age group.)
On to the book. I had noticed that the kids are paying attention to
clocks and starting to learn about time, so I started with the clock.
This was a natural segue from the gear ratio demo. We want to make
the hour hand go slowly, so how do we do that with gears? Attach the
hand to a big gear which is driven by a small gear! And we want to
make the minute hand go fast, so how do we do that with gears? Attach
it to a small gear which is driven by a big gear! I was pleased that
the kids were able to guess these answers most of the time. So here's
the clock in action:
Next, I showed them that gears are not limited to circular motion. Here is a rack gear in action:
Rack gears are used for turning circular motion into linear motion. In addition to all kinds of machines, rack gears are used in steep mountain railways, where the track contains the rack gear and the engine carries and pushes on the circular gear. (It's also used for rack-and-pinion steering; the pinion is the circular gear which meshes with the rack.) We talked about what kinds of machines might need to do this kind of motion. Maybe squeezing grapes for grape juice, or printing presses.
And we can also set up gears to do a sweeping motion, by attaching something off-center:
The last thing we had time for was planetary gears, so called because little gears go around a bigger gear like the planets around the sun:
This is cool and could just be a work of art, but there are applications. Note that around the outside is what is basically a really big inside-out gear (difficult to see in the video because it's made of clear plastic). I went back to the homemade big+small gear setup and asked why it would be useful to put the small gear inside the big gear. Answer: to save space, if you need to make a small machine, like a pencil sharpener, a kitchen mixer, maybe an electric toothbrush.
Finally, we didn't get time to build the piece de resistance, but here is a machine which combs your hair and brushes your teeth at the same time:
The whole activity worked well. I learned something about organizing kids, too. Because there weren't enough pulley setups, kids had to wait, but there wasn't really a line because it was just a few kids waiting. This led to a lot of confusion until Teacher Jessica brought "waiting chairs." When the kids have to sit in chairs to wait, it is 100% clear who is next!
If you want to see more, I recommend the video Gear Basics.
Saturday, November 5, 2011
An object in motion...
So it's time for the elementary kids to learn Newton's laws of motion.
The key for good demos and hands-on activities is getting rid of
friction, so we can see how objects behave in the absence of forces.
I usually use hover pucks, devices that look like very big hockey
pucks but have a fan inside so they float on a cushion of air, like
air hockey without the table. (They are also sold under the brand
name Kick Dis.) But I decided we would have more fun and soap up a
table so that we could slide anything without friction. The night
before, I started soaping tables to see how frictionless I could get
them. The result was a lot of frustration. I could never really get
them frictionless, not close enough to make convincing demos. I even
tried soaping a large sheet of glass (one of the mirrored sliding
doors on my closet) and that was better, but still not good enough.
It seems that no table or mirror is quite flat enough; objects will
glide along a bit, but then hit a high point and stop. So I ended up
going to bed late and frustrated, with some mess still to clean up in
the morning. Such is the life of an educator.
So Friday morning quick I went to work and picked up a bunch of
hoverpucks. (I also bought some donuts for the donutapult; see
below.) I had already picked up some carts which looked like very
large skateboards. On a smooth floor or sidewalk, these are
reasonably frictionless and safe to kneel on.
After scouting the school to find the smooth surfaces, I set up a
three-stage plan for each group. We started at the long, smooth table
with the hoverpucks. I asked the kids what they knew about friction,
and then I asked them to rub their hands together to feel friction.
Then I slid a switched-off hoverpuck on the table (it went a very
short distance) to show that friction is why it's hard to slide
things, and I asked them for ideas to get rid of friction. After
entertaining various ideas, I asked them to make predictions for how
the hoverpuck would move after I switched it on and pushed it toward
the other end of the table. Then I did just that, and it went in a
perfectly smooth straight line. So this makes it clear that, in the
absence of forces, objects in motion continue their motion (in a
straight line at constant speed). This is Newton's first law of
motion, but I didn't ask them to remember that. We had too many cool
experiments to do, and I can count on the regular teachers to review
the terminology several times!
So I seamlessly continued with the hoverpuck. I asked a child seated
along the middle of the table to give the puck a sideways tap as it
passed her down the long axis of the table. First time with a small
tap, then with a larger one, and each time I asked the kids to predict
the subsequent motion. This sequence shows a few things. First, that
a bigger force (or tap, or push) causes a bigger acceleration (change
in motion, whether it be a change in speed or direction...mostly
direction in this case), which is part of Newton's second law.
Second, a force changes the motion only while the force is being
applied. The tap changes the direction of the puck, but only while
the tap is applied. After the tap, the puck follows its new direction
in a straight line. A one-time tap cannot make it keep curving
around. This reinforces the first law: while there are no forces, it
goes in a straight line at constant speed.
To wrap up the hoverpuck activity (which was only the first of the
three stages I had planned), I gave each child a hoverpuck and asked
them to figure out how to make it travel in a circle (which is
distinct from spinning). They needed this bit of playing to relieve
the wiggles, because to this point it had been mostly demo, with some
assistance from 1-2 kids. After several minutes, we discussed how the
only way to make the puck go in a circle is to keep your hand on it
and move your hand in a circle. In other words, circular motion
requires a continuously changing direction of motion, and therefore a
continuous force. This bit isn't strictly necessary if we just wanted
to do Newton's laws, but it connects to the next stage and some other
interesting ideas in the next paragraph.
Second stage: we went outside and I made a bagel-on-a-string go around
in circles over my head. I asked them to imagine what would happen if
the string broke. If they really got Newton's first law, they would
answer that it would fly off in a straight line, but of course most
people don't grasp it that well after just the first demo. So some
said it would fall straight down, a few said it would fly off in a
circular motion, etc. So now comes the really fun part. It's not
practical to cut the string, so instead I tie a donut to a string, and
the string cuts its own way through the soft donut as I whip it around
over my head. I ask them to observe well, because once the donut
comes free there's only a split second before it hits the fence, or a
tree, or a person! Of course it flies off in a straight line:
Newton's first law strikes again. Then I ask them to think of
anything else that moves in a circle. Sometimes I have to hint "in
space", but they can guess Earth around the Sun, or the Moon around
the Earth. So that's the proof that there is a force keeping the Moon
around the Earth: if there were not, the Moon would fly off in a
straight line. (This comes as a revelation to many adults and college
students...they were never helped to make the connection between real
life and Newton's abstract laws of motion.) Then I ask them what the
name of that force is, and in each group at least one child knew it
was called gravity.
Third stage: we went to the sidewalk for the cart activity. First,
each child gave a push to an unloaded cart, and then the same size
push to a cart loaded with 40 pounds of weights. The heavier cart
accelerated much less. This is the other facet of Newton's second
law: acceleration is proportional to force, but inversely proportional
to the mass of the object being accelerated. The phrase "same size
push" is an attempt to make "same force" sound less technical. Some
kids initially seemed to interpret it as "make the cart accelerate the
same amount" so I made sure to counter this by continually repeating
phrases like "use all the same muscles" or "push just as hard as last
time." In cases where they still didn't quite get it, I asked if they
ever got so mad at their brother (or sister, or friend) that they
wanted to push them. Yes, you can admit it! Pretend the cart is your
brother, you are mad, and you push him. Now, for the other cart,
you're still just as mad, so push just the same!
Also, a common misconception is to look at how far the cart travels as
a measure of the effect of the push. We must not do this, because how
far it travels is a complicated function of how much friction there
is, whether it had to roll over a small stone or a crack, fight a gust
of wind, etc. No, we must observe how fast the cart was moving
immediately after the push.
Finally, we get to Newton's third law. I need two volunteers, one to
kneel on each cart. Alone, each child can't get his or her cart to
start moving. But they can if they push against each other, and this
results in equal and opposite accelerations if I wisely chose
volunteers of the similar mass. This shows that forces come in equal
and opposite pairs, which is Newton's third law. (The usual
formulation, "Every action has an equal and opposite reaction," is
very misleading because it gives the impression that the net result is
zero.)
After giving each child a turn at this, we had a minute or two left in
some of the groups, so we did a more advanced third-law demo. I got
on a cart and held a bathroom scale, while I gave the child on the
other cart a bathroom scale. We pushed off each other's scales, and
her cart accelerated a lot while mine accelerated only a little. I
had asked them to predict the accelerations, and they invariably get
that right. But then I asked them what they thought the forces (the
readings on the scales as we pushed) were: more on my scale, more on
hers, or the same? They invariably think more on mine, because I'm
bigger and so they think I must exert more force. But the scale
readings are the same, which is just Newton's third law! The effect
of the force (the acceleration) is different because she has little
mass and I have a lot, but the amount of force is the same.
Similarly, in a car collision, where the massive vehicle decelerates
relatively little while the light vehicle decelerates a lot; this can
only happen if the forces are the same!
The kids seemed to really like these activities. In fact, Becca told
her mom so, and Becca is hard to impress. The only thing I would do
differently is not buy such cheap bathroom scales. They constantly
had to be re-zeroed, and were not very reliable or accurate. But stay
away from the digital ones too, which you have to step on, step off,
step on again, etc. These would be frustrating for kids in a pushing
experiment.
The key for good demos and hands-on activities is getting rid of
friction, so we can see how objects behave in the absence of forces.
I usually use hover pucks, devices that look like very big hockey
pucks but have a fan inside so they float on a cushion of air, like
air hockey without the table. (They are also sold under the brand
name Kick Dis.) But I decided we would have more fun and soap up a
table so that we could slide anything without friction. The night
before, I started soaping tables to see how frictionless I could get
them. The result was a lot of frustration. I could never really get
them frictionless, not close enough to make convincing demos. I even
tried soaping a large sheet of glass (one of the mirrored sliding
doors on my closet) and that was better, but still not good enough.
It seems that no table or mirror is quite flat enough; objects will
glide along a bit, but then hit a high point and stop. So I ended up
going to bed late and frustrated, with some mess still to clean up in
the morning. Such is the life of an educator.
So Friday morning quick I went to work and picked up a bunch of
hoverpucks. (I also bought some donuts for the donutapult; see
below.) I had already picked up some carts which looked like very
large skateboards. On a smooth floor or sidewalk, these are
reasonably frictionless and safe to kneel on.
After scouting the school to find the smooth surfaces, I set up a
three-stage plan for each group. We started at the long, smooth table
with the hoverpucks. I asked the kids what they knew about friction,
and then I asked them to rub their hands together to feel friction.
Then I slid a switched-off hoverpuck on the table (it went a very
short distance) to show that friction is why it's hard to slide
things, and I asked them for ideas to get rid of friction. After
entertaining various ideas, I asked them to make predictions for how
the hoverpuck would move after I switched it on and pushed it toward
the other end of the table. Then I did just that, and it went in a
perfectly smooth straight line. So this makes it clear that, in the
absence of forces, objects in motion continue their motion (in a
straight line at constant speed). This is Newton's first law of
motion, but I didn't ask them to remember that. We had too many cool
experiments to do, and I can count on the regular teachers to review
the terminology several times!
So I seamlessly continued with the hoverpuck. I asked a child seated
along the middle of the table to give the puck a sideways tap as it
passed her down the long axis of the table. First time with a small
tap, then with a larger one, and each time I asked the kids to predict
the subsequent motion. This sequence shows a few things. First, that
a bigger force (or tap, or push) causes a bigger acceleration (change
in motion, whether it be a change in speed or direction...mostly
direction in this case), which is part of Newton's second law.
Second, a force changes the motion only while the force is being
applied. The tap changes the direction of the puck, but only while
the tap is applied. After the tap, the puck follows its new direction
in a straight line. A one-time tap cannot make it keep curving
around. This reinforces the first law: while there are no forces, it
goes in a straight line at constant speed.
To wrap up the hoverpuck activity (which was only the first of the
three stages I had planned), I gave each child a hoverpuck and asked
them to figure out how to make it travel in a circle (which is
distinct from spinning). They needed this bit of playing to relieve
the wiggles, because to this point it had been mostly demo, with some
assistance from 1-2 kids. After several minutes, we discussed how the
only way to make the puck go in a circle is to keep your hand on it
and move your hand in a circle. In other words, circular motion
requires a continuously changing direction of motion, and therefore a
continuous force. This bit isn't strictly necessary if we just wanted
to do Newton's laws, but it connects to the next stage and some other
interesting ideas in the next paragraph.
Second stage: we went outside and I made a bagel-on-a-string go around
in circles over my head. I asked them to imagine what would happen if
the string broke. If they really got Newton's first law, they would
answer that it would fly off in a straight line, but of course most
people don't grasp it that well after just the first demo. So some
said it would fall straight down, a few said it would fly off in a
circular motion, etc. So now comes the really fun part. It's not
practical to cut the string, so instead I tie a donut to a string, and
the string cuts its own way through the soft donut as I whip it around
over my head. I ask them to observe well, because once the donut
comes free there's only a split second before it hits the fence, or a
tree, or a person! Of course it flies off in a straight line:
Newton's first law strikes again. Then I ask them to think of
anything else that moves in a circle. Sometimes I have to hint "in
space", but they can guess Earth around the Sun, or the Moon around
the Earth. So that's the proof that there is a force keeping the Moon
around the Earth: if there were not, the Moon would fly off in a
straight line. (This comes as a revelation to many adults and college
students...they were never helped to make the connection between real
life and Newton's abstract laws of motion.) Then I ask them what the
name of that force is, and in each group at least one child knew it
was called gravity.
Third stage: we went to the sidewalk for the cart activity. First,
each child gave a push to an unloaded cart, and then the same size
push to a cart loaded with 40 pounds of weights. The heavier cart
accelerated much less. This is the other facet of Newton's second
law: acceleration is proportional to force, but inversely proportional
to the mass of the object being accelerated. The phrase "same size
push" is an attempt to make "same force" sound less technical. Some
kids initially seemed to interpret it as "make the cart accelerate the
same amount" so I made sure to counter this by continually repeating
phrases like "use all the same muscles" or "push just as hard as last
time." In cases where they still didn't quite get it, I asked if they
ever got so mad at their brother (or sister, or friend) that they
wanted to push them. Yes, you can admit it! Pretend the cart is your
brother, you are mad, and you push him. Now, for the other cart,
you're still just as mad, so push just the same!
Also, a common misconception is to look at how far the cart travels as
a measure of the effect of the push. We must not do this, because how
far it travels is a complicated function of how much friction there
is, whether it had to roll over a small stone or a crack, fight a gust
of wind, etc. No, we must observe how fast the cart was moving
immediately after the push.
Finally, we get to Newton's third law. I need two volunteers, one to
kneel on each cart. Alone, each child can't get his or her cart to
start moving. But they can if they push against each other, and this
results in equal and opposite accelerations if I wisely chose
volunteers of the similar mass. This shows that forces come in equal
and opposite pairs, which is Newton's third law. (The usual
formulation, "Every action has an equal and opposite reaction," is
very misleading because it gives the impression that the net result is
zero.)
After giving each child a turn at this, we had a minute or two left in
some of the groups, so we did a more advanced third-law demo. I got
on a cart and held a bathroom scale, while I gave the child on the
other cart a bathroom scale. We pushed off each other's scales, and
her cart accelerated a lot while mine accelerated only a little. I
had asked them to predict the accelerations, and they invariably get
that right. But then I asked them what they thought the forces (the
readings on the scales as we pushed) were: more on my scale, more on
hers, or the same? They invariably think more on mine, because I'm
bigger and so they think I must exert more force. But the scale
readings are the same, which is just Newton's third law! The effect
of the force (the acceleration) is different because she has little
mass and I have a lot, but the amount of force is the same.
Similarly, in a car collision, where the massive vehicle decelerates
relatively little while the light vehicle decelerates a lot; this can
only happen if the forces are the same!
The kids seemed to really like these activities. In fact, Becca told
her mom so, and Becca is hard to impress. The only thing I would do
differently is not buy such cheap bathroom scales. They constantly
had to be re-zeroed, and were not very reliable or accurate. But stay
away from the digital ones too, which you have to step on, step off,
step on again, etc. These would be frustrating for kids in a pushing
experiment.
Subscribe to:
Posts (Atom)