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!