Today I worked with the 1-2 graders to extend their concepts of force
and motion to include work and energy, and then, after the break,
fluid dynamics.
While waiting for the kids to come back from chorus to start science,
I sat with one child who hates chorus, and we interleaved the pages of
two phone books. When science started, we talked about friction and I
used the phone books as a demo. The friction of 200 pages trying to
slide past 200 other pages is so much that two strong adults cannot
bull the books apart. Mythbusters had a great episode on this, in
which they used bigger (800 page?) phone books and couldn't pull them
apart even with cars. They finally resorted to military tanks, and
found that it took a force of 8,000 pounds to separate the books!
We then talked about work, which is applying a force over some
distance. Sitting in your chair, you are applying a force (your
weight) to the seat of the chair, but you are not doing work.
Exerting a large force (eg lifting a heavy weight) over a large
distance makes for a lot of work. We related this to irrigation
because the kids are studying the community, and are about to learn
that farming really took off around here when large pumps became
available to move the water.
Energy is the ability to do work, and we spent a looong time talking
about different forms of (mostly stored) energy: food, chemicals,
light, heat, electricity, etc. We spent a loooong time figuring out
what makes the electricity that comes to our houses!
Then came break. After break we finished up a few more forms of
storing energy: magnets, rubber bands, springs, etc. But mostly we
moved on to discussing how water moves (fluid dynamics). I did the
"three-hole can" demo (see paragraphs 3-4 of this post) to introduce
pressure and the relationship between pressure and water height. Then
I did the finger-on-the-straw demo (paragraph 6 of that post) to show
that the air also exerts pressure. Next was a siphon tank demo, to
show that air pressure can sometimes help quite a bit in moving water.
This demo did not work well, possibly because of a leak, so see this
video. Finally, I did the balloon in a bottle demo (paragraphs 6-8 of
the post linked to above) which is very analogous to the
finger-on-the-straw demo but far more dramatic....I could see Teacher
Ethan do a double-take when he first saw it.
Then I led the kids through designing different water systems on the
whiteboard. I supplied basic ideas such as water flowing into a
shovel on a pivot, and asked them to predict what would happen (when
the shovel fills with water, that end pivots down, dumping the water
out). We went through a bunch of these ideas, and I made sure to lead
them to realize the need for a pump to cycle the water back from the
bottom to the top. By this point they were very eager to start
drawing their own ideas, which played right into my plan. We had a
great time making posters of our ideas. In the last five minutes, I
unveiled the hydrodynamics kit which they will use in free-choice time
(or whenever Teacher Pa deems fit) to actually implement their ideas.
Overall, I think it went really well. We discussed a lot of ideas,
without overwhelming the kids, and the poster-drawing session was both
fun and educational.
Showing posts with label machines. Show all posts
Showing posts with label machines. Show all posts
Friday, October 19, 2012
Friday, December 2, 2011
Turn! Turn! Turn!
At the elementary school, we continued our theme of learning more
about how things move, in preparation for designing the playground at
the new school site. Tomorrow, we have an optional field trip to the
Berkeley Adventure Playground to see what other kids have designed and
built. Today, we focused on spinning things.
We started with a spinnable chair. A volunteer sits in it and holds
two weights close to his/her chest while I spin up the chair. Then I
ask the volunteer to extend his/her arms as far as possible. The
chair then spins much more slowly. Arms in: the chair speeds up
again. Arms out: slows down again.
I ask the kids what else they have seen which is like this.
Surprisingly, no one said figure skating. I had to nudge them a bit
to realize it is just like the figure skater who brings her arms in to
spin rapidly. A lot of them did refer to playground equipment,
though. There is a public playground near the school (to which they
sometimes walk for lunch/PE) which has something like that, and I
think now they will have a new appreciation for it. But why does
pulling in your arms speed you up?
We had talked four weeks ago about how more massive things are more
difficult to accelerate. And to decelerate. In short, they have more
inertia. Rotational motion has an added complication. Rotational
inertia involves not only how much mass there is, but how far it is
from the center of rotation: the further from the center, the greater
the inertia. So it is much easier to spin up something whose mass is
concentrated near the center, compared to something of equal mass
whose mass is far-flung. The property of being spun up, which
physicists call angular momentum, is conserved so that a slowly
spinning far-flung object can easily be transformed into a rapidly
spinning concentrated object. Here's an analogy: I can have a certain
volume of water, but it results in a taller water level if it is put
in a skinny glass than if it is put in a wide glass. Here the volume
of water is analogous to the angular momentum (both are conserved),
and the height of the water level is analogous to the rate of
rotation.
Next, I gave them a chance to apply this new principle. I had a set
of two rods of the same size and mass, one of which secretly had most
of its mass concentrated near the middle, and the other of which
secretly had most of its mass concentrated near the ends. You grasp
the center of each rod in either hand, and rotate them back and forth.
There is a startling difference in the resistance to rotation! Once
each child had a chance to feel it, I asked them to come up with
hypotheses as to why one is easier to rotate. Surprisingly, the
connection was not instant. (I wonder how often words are a dead
giveaway. I used the word "rotation" here, but in class I just said,
"go like this." I bet if I had said "rotate the rods" something would
have clicked. But this something would not have been understanding of
physics! Asking questions with familiar terminology leads students to
"solve" problems they don't really understand, and make both teachers
and students overconfident in how much understanding has been gained.)
Many students insisted that the rods did not weigh the same, despite
my assurances. Next time, I should bring a scale to prove it!
Some students were able to guess that it had something to do with how
the weight was distributed (at least that's how I rephrased what they
said), or that something inside the hard-to-turn rod moved (which it
didn't, but I think they were on the right track in thinking that a
similar effect would be produced by some of the weight moving from the
middle toward the ends). I had to give quite a few hints, in one case
sitting on the demo chair and stretching my arms back and forth. We
finally established that we could explain the behavior by supposing
that one rod had most of its mass on the end and the other had most in
the middle. I pointed out that we had just used what we could see to
figure out something about what we couldn't see directly. That's
pretty cool, and that's what science is about.
Next, we took a bicycle wheel and I passed it around. Each student
felt that it is easy to change the orientation of the wheel (in other
words, change where its axis pointed) when the wheel is not spinning,
but quite difficult to do the same thing when the wheel is spinning.
This is another manifestation of conservation of angular momentum.
The rotating wheel seems to fight back; you have to do a lot of work
to change its direction. I asked in what real-life situations they
might have noticed the same thing. "Bicycle wheel" was a very popular
answer, but they couldn't pin down what about a bicycle wheel was
relevant. I had to hint a bit before they realized that this is why
it's easier to stay up on a bike when you're moving faster. When
you're not moving, the wheels can just fall over. When you're moving
fast, changing the axis of the wheels is not so easy, so you find it
easier to balance.
The same bicycle wheel can be used for a really neat demo. Sit on the
spinnable chair, hold the bicycle wheel so it's vertical, and have
someone spin the wheel. Now, when you turn the wheel so it is
sideways, the change in angular momentum gets transferred to the
chair, which begins to spin. Now flip the wheel over, and the chair
begins to spin the other way! This is the rotational equivalent of
two ice skaters pushing off each other and sliding off in opposite
directions.
Finally, I showed them a model of a merry-go-round, to the center of
which I had attached a spring with a small mass on the end. They
predicted that upon spinning the turntable, the mass would go toward
the outside (which it did), but they were not able to articulate
precisely why. I reminded them of the donutapult experiment four
weeks earlier: objects travel in straight lines unless acted upon by a
force. If an object is on a merry-go-round and does not hold on,
travel on a straight line means sliding off the merry-go-round. The
spring was there to prevent losing the mass, and when the turntable
slowed, the spring pulled the mass back toward the center, as the kids
predicted.
We talked about how to apply these ideas in designing a
playground. Some of the ideas were far-fetched, but that's ok! I
didn't want to discourage creativity. We also talked about space and
astronauts. Muscle and bone become very weak after extended periods
in space, and one way to provide artificial gravity to counteract this
is to spin a space station. Because everything inside "wants" to
stick to the rim of a spinning space station, the people inside will
feel like the outside edge of the station is "down", and that there is
gravity pulling things that way. And one child remarked that if you
still need some zero-g environment in the space station, you can put
it inside the axis of the spinning part. One child also asked about
stars, and I explained how some stars which are much more compact than
the Sun (neutron stars) rotate much more rapidly, as often as 30 times
per second! We know that because we can see a hot spot for a brief
period during each revolution.
about how things move, in preparation for designing the playground at
the new school site. Tomorrow, we have an optional field trip to the
Berkeley Adventure Playground to see what other kids have designed and
built. Today, we focused on spinning things.
We started with a spinnable chair. A volunteer sits in it and holds
two weights close to his/her chest while I spin up the chair. Then I
ask the volunteer to extend his/her arms as far as possible. The
chair then spins much more slowly. Arms in: the chair speeds up
again. Arms out: slows down again.
I ask the kids what else they have seen which is like this.
Surprisingly, no one said figure skating. I had to nudge them a bit
to realize it is just like the figure skater who brings her arms in to
spin rapidly. A lot of them did refer to playground equipment,
though. There is a public playground near the school (to which they
sometimes walk for lunch/PE) which has something like that, and I
think now they will have a new appreciation for it. But why does
pulling in your arms speed you up?
We had talked four weeks ago about how more massive things are more
difficult to accelerate. And to decelerate. In short, they have more
inertia. Rotational motion has an added complication. Rotational
inertia involves not only how much mass there is, but how far it is
from the center of rotation: the further from the center, the greater
the inertia. So it is much easier to spin up something whose mass is
concentrated near the center, compared to something of equal mass
whose mass is far-flung. The property of being spun up, which
physicists call angular momentum, is conserved so that a slowly
spinning far-flung object can easily be transformed into a rapidly
spinning concentrated object. Here's an analogy: I can have a certain
volume of water, but it results in a taller water level if it is put
in a skinny glass than if it is put in a wide glass. Here the volume
of water is analogous to the angular momentum (both are conserved),
and the height of the water level is analogous to the rate of
rotation.
Next, I gave them a chance to apply this new principle. I had a set
of two rods of the same size and mass, one of which secretly had most
of its mass concentrated near the middle, and the other of which
secretly had most of its mass concentrated near the ends. You grasp
the center of each rod in either hand, and rotate them back and forth.
There is a startling difference in the resistance to rotation! Once
each child had a chance to feel it, I asked them to come up with
hypotheses as to why one is easier to rotate. Surprisingly, the
connection was not instant. (I wonder how often words are a dead
giveaway. I used the word "rotation" here, but in class I just said,
"go like this." I bet if I had said "rotate the rods" something would
have clicked. But this something would not have been understanding of
physics! Asking questions with familiar terminology leads students to
"solve" problems they don't really understand, and make both teachers
and students overconfident in how much understanding has been gained.)
Many students insisted that the rods did not weigh the same, despite
my assurances. Next time, I should bring a scale to prove it!
Some students were able to guess that it had something to do with how
the weight was distributed (at least that's how I rephrased what they
said), or that something inside the hard-to-turn rod moved (which it
didn't, but I think they were on the right track in thinking that a
similar effect would be produced by some of the weight moving from the
middle toward the ends). I had to give quite a few hints, in one case
sitting on the demo chair and stretching my arms back and forth. We
finally established that we could explain the behavior by supposing
that one rod had most of its mass on the end and the other had most in
the middle. I pointed out that we had just used what we could see to
figure out something about what we couldn't see directly. That's
pretty cool, and that's what science is about.
Next, we took a bicycle wheel and I passed it around. Each student
felt that it is easy to change the orientation of the wheel (in other
words, change where its axis pointed) when the wheel is not spinning,
but quite difficult to do the same thing when the wheel is spinning.
This is another manifestation of conservation of angular momentum.
The rotating wheel seems to fight back; you have to do a lot of work
to change its direction. I asked in what real-life situations they
might have noticed the same thing. "Bicycle wheel" was a very popular
answer, but they couldn't pin down what about a bicycle wheel was
relevant. I had to hint a bit before they realized that this is why
it's easier to stay up on a bike when you're moving faster. When
you're not moving, the wheels can just fall over. When you're moving
fast, changing the axis of the wheels is not so easy, so you find it
easier to balance.
The same bicycle wheel can be used for a really neat demo. Sit on the
spinnable chair, hold the bicycle wheel so it's vertical, and have
someone spin the wheel. Now, when you turn the wheel so it is
sideways, the change in angular momentum gets transferred to the
chair, which begins to spin. Now flip the wheel over, and the chair
begins to spin the other way! This is the rotational equivalent of
two ice skaters pushing off each other and sliding off in opposite
directions.
Finally, I showed them a model of a merry-go-round, to the center of
which I had attached a spring with a small mass on the end. They
predicted that upon spinning the turntable, the mass would go toward
the outside (which it did), but they were not able to articulate
precisely why. I reminded them of the donutapult experiment four
weeks earlier: objects travel in straight lines unless acted upon by a
force. If an object is on a merry-go-round and does not hold on,
travel on a straight line means sliding off the merry-go-round. The
spring was there to prevent losing the mass, and when the turntable
slowed, the spring pulled the mass back toward the center, as the kids
predicted.
We talked about how to apply these ideas in designing a
playground. Some of the ideas were far-fetched, but that's ok! I
didn't want to discourage creativity. We also talked about space and
astronauts. Muscle and bone become very weak after extended periods
in space, and one way to provide artificial gravity to counteract this
is to spin a space station. Because everything inside "wants" to
stick to the rim of a spinning space station, the people inside will
feel like the outside edge of the station is "down", and that there is
gravity pulling things that way. And one child remarked that if you
still need some zero-g environment in the space station, you can put
it inside the axis of the spinning part. One child also asked about
stars, and I explained how some stars which are much more compact than
the Sun (neutron stars) rotate much more rapidly, as often as 30 times
per second! We know that because we can see a hot spot for a brief
period during each revolution.
Friday, November 18, 2011
Playground Design 101
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!
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!
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, October 29, 2011
Going up?
The pre-K/K kids have been really interested in machines for a few
weeks now. When I first heard about that interest, I (with Linus's
permission) brought our set of Gears!Gears!Gears! to the room for a
long-term loan. Since then, I have seen kids playing with the gears
every morning I drop Linus off. When we saw a slightly more advanced
set of Gears!Gears!Gears! in Costco one Sunday (with different size
gears and a loop gear, plus some non-gear bells and whistles), it was
a no-brainer to buy that and bring that for a long-term loan as well.
The kids seem to really be into it.
So I thought of building on that interest by doing something with
pulleys, and I settled on building a simple elevator as an activity
which seemed doable, but still challenging enough to be interesting.
I borrowed a big old pulley from the physics department, brought some
of my own ropes and weights, and counted on the school having some big
dairy cartons and a decent place to hang the pulley.
After some looking around and testing, I settled on a certain tree
branch as a good place to hang the pulley, and I found a dairy carton
big enough for a kid to climb into. With the first group, I started
from scratch, asking them what they thought would be necessary to
build an elevator, and they suggested a basket (they even found one)
and rope (which I supplied). They needed a bit of prodding to suggest
a pulley, but they got that too after I suggested looking above my
head. Most of them didn't really know what a pulley was, so we
discussed that. I strung a rope through it and we each verified that
pulling down on one end of the rope made the other end go up. The kid
were really excited at this point! It was difficult for some of them
not to grab the rope, jump up and down, etc. I pointed out that one
advantage of the pulley is that the puller (the kids in this case, a
motor in real life) need not be on the roof to make the elevator work.
Then I attached the large milk carton and put some heavy object in it
for a first test. The more excited kids volunteered to pull on the
other end of the rope. They were able to lift the elevator, but it
was quite difficult; they had to recruit help and I think it was
successful only with four boys pulling at once. I warned them that if
they let go suddenly, the elevator would crash to the ground and hurt
the (imaginary) people in the elevator.
So I asked them to think about what could make the pulling and the
letting down easier and safer. They thought of all kinds of crazy
ideas before they spotted my weights. So I attached the
counterweights (in a small basket so we would adjust the amount of
counterweight) and we saw that the elevator was much easier to lift
and also easier and safer to let down. So then we were ready to give
rides.
The problem was that the dairy carton tilted too easily when lifted
off the ground, threatening to dump the passenger out. I tried to
stabilize it with additional ropes and by telling the passenger to balance,
but it never really worked. So starting with the second group, I
forbade rides. Instead, we used three containers full of sand to
represent three people. This was actually nice for the lesson because
I was able to put in just enough sand to balance the particular
counterweight I had; with a human passenger, the counterweight was a
help, but never really made it super easy to ascend and descend. With the fake
passengers matched to the counterweight, ascents and descents were very easy,
and I could tell the "motor" to let go, simulating a broken motor. The elevator
did not crash to the ground because it was attached to the just-right
counterweight.
So, once we got it going smoothly, I repeated these steps for each
kid: remove the counterweight; ask them to lift the passengers to the
top floor and have them discover how difficult that is; have them feel
how tricky the descent (from whatever point they reached) is; after
finishing the descent, add the counterweight and ask them to lift the
passengers to the top floor and see how easy it is this time; ask them
to let the passengers descend safely and feel how easy that is; ask the
motor to "break" and see how the passengers do not crash to the ground
because of the counterweight; finish the descent and start over with
another kid. I repeated this whole cycle about a million times
because many kids wanted to do it over and over! I was exhausted by
the end.
This was a pretty simple activity and the kids had a lot of fun. This
is a good lesson for me because I'm often tempted to think that a
potential activity is too simple and that I have to add a lot to it.
Simple can be good! If I ever try rides again, I need to experiment
beforehand how to make the elevator "car" tip-proof. But I think the
rides may have been a distraction. Each child was quite happy in the
"motor" role, so much that they wanted turns over and over, and of
course the motor role is the instructive one.
A small improvement would be to use two pulleys, to give some
horizontal space between the elevator car and the counterweight. One
thing which would take this to the next level would be to crank the
whole thing with some gears attached to a drum which winds up the
rope. I'll keep my eye out for surplus equipment which might be used
for this. And for a toy gear set with these kinds of pieces, which I
will then have to buy and put on long-term loan!
weeks now. When I first heard about that interest, I (with Linus's
permission) brought our set of Gears!Gears!Gears! to the room for a
long-term loan. Since then, I have seen kids playing with the gears
every morning I drop Linus off. When we saw a slightly more advanced
set of Gears!Gears!Gears! in Costco one Sunday (with different size
gears and a loop gear, plus some non-gear bells and whistles), it was
a no-brainer to buy that and bring that for a long-term loan as well.
The kids seem to really be into it.
So I thought of building on that interest by doing something with
pulleys, and I settled on building a simple elevator as an activity
which seemed doable, but still challenging enough to be interesting.
I borrowed a big old pulley from the physics department, brought some
of my own ropes and weights, and counted on the school having some big
dairy cartons and a decent place to hang the pulley.
After some looking around and testing, I settled on a certain tree
branch as a good place to hang the pulley, and I found a dairy carton
big enough for a kid to climb into. With the first group, I started
from scratch, asking them what they thought would be necessary to
build an elevator, and they suggested a basket (they even found one)
and rope (which I supplied). They needed a bit of prodding to suggest
a pulley, but they got that too after I suggested looking above my
head. Most of them didn't really know what a pulley was, so we
discussed that. I strung a rope through it and we each verified that
pulling down on one end of the rope made the other end go up. The kid
were really excited at this point! It was difficult for some of them
not to grab the rope, jump up and down, etc. I pointed out that one
advantage of the pulley is that the puller (the kids in this case, a
motor in real life) need not be on the roof to make the elevator work.
Then I attached the large milk carton and put some heavy object in it
for a first test. The more excited kids volunteered to pull on the
other end of the rope. They were able to lift the elevator, but it
was quite difficult; they had to recruit help and I think it was
successful only with four boys pulling at once. I warned them that if
they let go suddenly, the elevator would crash to the ground and hurt
the (imaginary) people in the elevator.
So I asked them to think about what could make the pulling and the
letting down easier and safer. They thought of all kinds of crazy
ideas before they spotted my weights. So I attached the
counterweights (in a small basket so we would adjust the amount of
counterweight) and we saw that the elevator was much easier to lift
and also easier and safer to let down. So then we were ready to give
rides.
The problem was that the dairy carton tilted too easily when lifted
off the ground, threatening to dump the passenger out. I tried to
stabilize it with additional ropes and by telling the passenger to balance,
but it never really worked. So starting with the second group, I
forbade rides. Instead, we used three containers full of sand to
represent three people. This was actually nice for the lesson because
I was able to put in just enough sand to balance the particular
counterweight I had; with a human passenger, the counterweight was a
help, but never really made it super easy to ascend and descend. With the fake
passengers matched to the counterweight, ascents and descents were very easy,
and I could tell the "motor" to let go, simulating a broken motor. The elevator
did not crash to the ground because it was attached to the just-right
counterweight.
So, once we got it going smoothly, I repeated these steps for each
kid: remove the counterweight; ask them to lift the passengers to the
top floor and have them discover how difficult that is; have them feel
how tricky the descent (from whatever point they reached) is; after
finishing the descent, add the counterweight and ask them to lift the
passengers to the top floor and see how easy it is this time; ask them
to let the passengers descend safely and feel how easy that is; ask the
motor to "break" and see how the passengers do not crash to the ground
because of the counterweight; finish the descent and start over with
another kid. I repeated this whole cycle about a million times
because many kids wanted to do it over and over! I was exhausted by
the end.
This was a pretty simple activity and the kids had a lot of fun. This
is a good lesson for me because I'm often tempted to think that a
potential activity is too simple and that I have to add a lot to it.
Simple can be good! If I ever try rides again, I need to experiment
beforehand how to make the elevator "car" tip-proof. But I think the
rides may have been a distraction. Each child was quite happy in the
"motor" role, so much that they wanted turns over and over, and of
course the motor role is the instructive one.
A small improvement would be to use two pulleys, to give some
horizontal space between the elevator car and the counterweight. One
thing which would take this to the next level would be to crank the
whole thing with some gears attached to a drum which winds up the
rope. I'll keep my eye out for surplus equipment which might be used
for this. And for a toy gear set with these kinds of pieces, which I
will then have to buy and put on long-term loan!
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