Unit 4 -- Balanced Forces Are Balanced (& Diagrammed)

We started out with a video & discussion on class discussion & its goals.  The hardest part, really, is for the teacher to let go the reins & trust students to have ideas.  & of course the kids have to know how to discuss things, rather than arguing or letting other people do all the talking.  Building that into the classroom culture will also be a bit of a challenge, at least the first few times.  (My notes say "code switching", which I know Laura talked about, so that'll be another place to introduce that.)  Classroom discussion can be broken into 3 main parts: giving students time to think, asking them to expand on their initial (& probably unformed) ideas, & having the other students repeat (& build on) ideas.  A reading in Unit 5 (sorry, I'm jumping the gun), the Talk Science Primer, reinforced these ideas & introduced a variety of "talk moves".  (Both the video & the reading came from this organization: http://inquiryproject.terc.edu/, altho I don't know who TERC is.)  I've seen these talk moves in action during this workshop & in some of my grad classes (but not in my undergrad classes) & I've tried them -- rather ineffectually, I'm afraid -- last year.  So, like Laura suggested, I'll have a copy of the talk moves on my clipboard & will give all of my students the bookmark version that was passed around in class.  (One of the other modeling workshops is using the bookmarks too, at least according to a picture on Twitter.)  Improving my classroom discussion skills is actually something that was in my end-of-year evaluation so it'll be nice to say "Hey look, not only did I improve my content knowledge, I improved my discussion leading knowledge."  Now hopefully it works in real life!

Closely tied with classroom discussion are student misconceptions, better called preconceptions.  Again, we had a couple of readings & videos -- Minstrell in particular seems to be an early proponent of uncovering & changing student preconceptions with classroom discussion.  Lots of these "common sense ideas" were held by folks like Aristotle, way back before Newton figured stuff out -- These are not dumb ideas.  Don also regaled us with first-person stories that he blatantly stole from other sources (he admitted it, & we had one of the stories in our readings).  I'm not such a good storyteller but maybe I've got the increasing popularity of sci fi on my side -- Will students still believe gravity is caused by air pressure?  Will anyone say that astronauts on the moon had no gravity but didn't float off because they wore heavy boots?  I'm probably luckier than some of my workshop classmates -- I've only got a single physics class next year & it's, like, 15 kids.  (The class list isn't posted yet so I'm not 100% sure of the numbers.)  I also get to try stuff out in Physical Science in the fall before I've got Physics in the winter & spring.

This unit, unlike the others, didn't start out with an experiment -- It started out with a statement.  The 1st rule of forces is that all forces must be applied by a real physical object made of matter.  After a brief discussion where we listed all sorts of potential forces on the board (& yes, the Jedi mind trick was one of them), we whittled down the list of forces to a push or pull.  (We're going to come back to gravity, magnetism, & electricity -- You can't hit people with these things or buy "a magnetism" in the store so...)  This is the start of our model so far -- We added statements over the course of the unit (& added a bonus one in Unit 5).

The completed Model So Far

Laura introduced us to schema, a tool for figuring out which forces are acting on whatever our object is.  (It looks a lot like a concept map, with words in circles connected by either solid or dotted lines.)  So for a book in her hand, the items on the schema might be book, hand, air, & entire earth.  We had a big discussion about if the air was exerting a force on the book & if so, in what direction.  We calculated that the air pressure on the surface of a standard book (about the same size as standard paper) was as much as an elephant standing on it ... only Laura picked up that elephant with ease.  So we decided that air pressure had to be coming from all sides equally & so cancelled itself out.  (The exceptions would be really strong winds, like when you have your hand out a car window, or suction cups, where there's no air underneath.)  This left us with the force of the hand on the book, a solid line, & the force of the entire earth on the book, a dotted line.  If there are 2 lines in the schema, there are 2 lines in the force diagram.  So from the dot in the middle of the book, there's one line up, representing the force of the hand, & one line down, representing the force of the entire earth.  We did not use the word gravity here.  In fact, we didn't really use gravity the whole entire unit.  ADD TO MODEL: System schema are a good tool for force diagrams

sample of a schema from worksheet 1

 Our next schemas involved a bowling ball on the table, then a tennis ball on the table.  The big question here was how did the table know how much force to push up with.  A brave volunteer from the audience went up & Laura put items into his outstretched hands -- He wobbled a lot more with the heavy book than with the buggy, & he wobbled a lot less 2nd & 3rd times the book was put in his hands.  People can learn but inanimate objects can't, so Laura continued the demonstration with a bed spring & a big sponge -- They all adjusted to the equilibrium.  She also had the floating magnets, which was really neat because the space between the bottom magnets got smaller & smaller as more magnets were added.  So we talked about how the molecules in the table compress & rebound, like the spring or the sponge.  ADD TO MODEL: at velocity = 0, forces are balanced

We also had a huge discussion over ground vs entire earth.  We'll see if that comes up in my class.

Our next schema introduced the force sensor, in this case a spring scale calibrated in Newtons.  Newtons were introduced as the unit of force with no definition provided, in keeping with the "vague enough to get started" theme.  So on the block, there was the downward force of the entire earth & the upward force of the string.  But it's the next example, the "hover car", that threw a monkey wrench in the works -- When it's sitting still, it's being acted on by the air pushing up & the entire earth pulling down, but what about when it's moving?  Not when it's being pushed & set in motion, but when it's floating serenely across the table at a constant velocity?  Surprise, it's still just the upwards air & the downwards earth.  The video of the person on a horse dropping a cannonball (& the cannonball continuing forward if the horse was galloping along) goes here, but I can't find a link.  ADD TO MODEL: when change in velocity = 0, forces are balanced (in vertical or horizontal directions)

Our next schema was pushing a book across a table.  Now the schema has 2 lines between the book & the table -- 1 for the upwards force & 1 for the sideways force.  (Just like we aren't saying gravity, we aren't saying normal force or friction.  Laura says we can use nicknames once we know the forces better.  That's a really good way to say that.)  She had us put 2 dry-erase erasers together & watch how the fibers stuck together & made it hard to slide the erasers.  She also had 2 hair brushes to show the same effect.  Since we don't have electron-microscope eyes, this is our analogy.  When to include the anti-sliding force of the table?  That depends on how the object is moving.  ADD TO MODEL: acceleration is in the direction of the unbalanced force

This problem has both the anti-sliding force (note the 2 lines between desk & floor in the schema) & an angled force.

We're building the idea of inertia here.  The hover cars are really good for this, actually.  We goofed around a little (Don started it) & tried to get the hover car to go all the way from the lunch area to the glass wall separating the offices, down the longest hallway in the building.  We never managed to get it thru the door but it certainly went the whole way with very little loss of speed.

After solidifying our ideas with worksheet #1 (symmetry is our friend & angled forces can be broken into "shadow forces"), we finally got to do a hands-on activity!  (This has been a much more "ideas only" sort of unit.)  In our inquiry lab, we found the mass of a bunch of objects then used the Vernier force sensor to find the downward force of the entire planet.  My group was a little rushed in finishing the whiteboard -- I got the slope upside down -- but it turns out that for every kilogram of mass, the entire earth exerts a downward pull of 10 newtons.  Hmm...  But we're still not calling it gravity.  Instead, we're saying it's the strength of the gravitational field of the Earth.  Specific is terrific.  ADD TO MODEL: forces at an angle have horizontal & vertical components (the "shadow parts")  ADD TO MODEL: 10 N/kg -- gravitational field strength

We also had a lot of discussion about the middle string, so Don put together a static demo during lunch.

Here is the static demonstration.

Here is the whiteboard with the problem.

So now the entire class tired to come up with an operational definition for "mass", without using the terms "matter" & "stuff".  Which was really hard.  Some groups used google but the definitions they found didn't help much.  (My favorite was "how much an object weighs when there's no gravity", which Don didn't like at all.)  Don had a demo with rolly carts, one with a heavy book & one without, & the one with more mass was harder to start and harder to stop ... but that was left to simmer.  Instead, we did this:  ADD TO MODEL:  an object in motion stays in motion in a straight line at a constant velocity if the forces are balanced; an object at rest stays at rest if forces are balanced (Newton's 1st law)

"We're not done" is the nature of science & we'll be coming back to the issue of mass & weight.  (The other noncontact forces -- magnetism, electrostatic, & strong -- are not in this workshop.)  We've actually circled back to the "force field" idea of gravity -- the gravitational field of the planet -- which is pretty neat.

Before we tried worksheets 2 & 3, Laura wrote out the 5 steps for solving problems, of which "Follow the schema" is the most important.  There were a lot more diagonal forces &  I'm definitely stealing Laura's "shadow forces" demo.  I haven't done enough math lately so I wrote SOH CAH TOA for pretty much every problem.  What math will my Physical Science kids have compared to my Physics kids?

This group used a property of a 30-60-90 triangle instead.

1) Write out the schema
2) Draw the force diagram
3) Figure out the "shadow components" of a diagonal force
4) Figure out where (or if) the forces are unbalanced, vertically & horizontally
5) Solve!

Talking over the problems on the whiteboards is pretty helpful.  Choosing the right problems is also a skill I need to learn, or at least sharpen.

This sets the stage for force pairs!

Then Don had a force demo & we got to do some hands-on stuff again.  When I do this with my students, I'm sure I'll get complaints that suddenly the class is much more "notes"-y.  Anyways, Don had somebody come up & hop on a force plate, which essentially acted just like a bathroom scale only read things in newtons & was connected to the computer.  Then they did push ups.  We talked a little about how the force line changed, & when.  Then Don had 2 people, one big & one little, come up & do battle!  Actually, they just banged the force plates together & pushed each other around.  No matter what they did, the forces recorded by the force plates were the same.  (There's a really cool video about equal forces but unequal effects, the cars with the band saw blades on them, but again I can't find the link.)  So then each group tested this out, colliding carts equipped with force sensors in various ways.  It didn't matter if we collided the carts head-on, while they were at different velocities, when they had different masses, on an incline ... Whatever we tried, the force on each car was exactly the same.  ADD TO MODEL: all forces come in pairs that are equal in strength, opposite in direction, & act on the other object (Newton's 3rd law)

 

No matter what these guys did, the forces registering on their plates were always equal.

The discussion about force pairs was kind of interesting.  Don put a block on a table & draw the force diagram.  Then he asked if the diagram showed a force pair.  Half the class moved to the yes side, half to the no side.  I said yes, because the forces were equal & opposite.  However, I wasn't thinking about the definition (they affect different objects) & the force diagram (which are the forces on a single object).  The schema shows a single line between the block & the table & that represents a force pair but you'd have to draw 2 different force diagrams to show the same thing.  This is something I'll try in class -- The whole "convince the other side to join you" was really useful.  I'll have to be very careful about saying "action reaction" when I really mean "force pair".

At this point we've got 3 possibilities for what "weight" is: the force of the entire earth on the object, the force the the object on the surface, or the force of the surface on the object.  We're leaving this until later -- O the suspense! :-)

We did a problem from worksheet #4 & measured out the forces & angles with a ruler & protractor.  We came pretty close to the correct trig answer & I learned a new term -- fatty marker error.  It will be helpful to know the "special" triangles when I assign students problems.  Don had us set up an angled track with a cart on a string & measure the force on the string.  As the angle gets closer to vertical, the force on the string gets closer to the "weight" of the cart.  What goes from 0 at 0 degrees & reaches its maximum at 90 degrees (& then goes down again)?  Sine!  So the force on the string is represented by a sine function, which is pretty cool.  (Again, what math level am I dealing with in my students?)

Don's demo of the set up

Force vs angle, 0-90*

Our results

Don also reinforced that the upward force of a surface, like the track, is perpendicular to that surface no matter what angle the surface is at.  So if the track is angled, the upward force is also angled, at least with reference to the ground & downwards force of the entire earth.  Heck, even walls have a perpendicular force.  Sometimes it's better to have the surface be the "horizontal" & break the downwards force of the entire earth into its components.

This was also the "measured" & "fat marker error" whiteboard.

The other videos we saw during the unit were more about how people learn.  The effectiveness of science videos (https://www.youtube.com/watch?v=eVtCO84MDj8) was called into question (especially considering that Khan Academy is now the official provider of SAT prep videos) -- Unless the video starts with misconceptions, students don't listen because they think they already know.  I've shown this video (bowling ball & feathers falling in a vacuum, https://www.youtube.com/watch?v=E43-CfukEgs) to my Physical Science kids; next time maybe I'll have before & after discussion to see how their ideas change.  (Don only shows videos for engagement, & that might be the way to go.)

The format of school was considered in a video by a guy with a PhD about skateboarding & how he struggled for years to master a particular trick (https://www.youtube.com/watch?v=lHfo17ikSpY).  (For some reason, I had never put "skateboarder" & "PhD" together in my head.)  This ties right in with Laura's motto "There's no comfort in the learning zone & no learning in your comfort zone", only with bruises, cussing, & no real way to issue grades.

& then the format of math class, in particular math questions (& you could just as easily say physics questions), was examined (https://www.youtube.com/watch?v=NWUFjb8w9Ps).  Most questions are way artificial & contain exactly what you need to know, rather than being grounded in real life & having not enough info & unnecessary details.  The take-away from that video was "Be less helpful", which really is the theme of this whole workshop.  I can certainly be less helpful but will it be in a way that helps people learn?  Time will tell. :-)

"But wait," you say, "what about Newton's 2nd law?  That's totally missing!"  Watch this spot!  Acceleration coming soon!



Equipment List

Vernier Force Plate, for measuring the force of humans rather than little carts, $245
http://www.vernier.com/products/sensors/force-sensors/fp-bta/

Vernier Force Sensor, for measuring the force of the carts & small hanging things, $109
http://www.vernier.com/products/sensors/force-sensors/dfs-bta/

Double-ended Spring Scale, to measure both pushes & pulls, $10
http://www.teachersource.com/product/pushpull-spring-scales/lab-equipment

Big-faced Spring Scale, for classroom demos (we only have small ones), $45
https://www.enasco.com/product/SB21390M

Triple-beam Balance (we don't seem to have one, just electronic scales), $80
http://www.teachersource.com/product/adam-triple-beam/lab-equipment-balances

Big Protractor, for use by students (more accurate than clinometer apps?), $16
http://www.amazon.com/Westcott-School-Chalkboard-Protractor-Handles/dp/B001AZ65F8

Air Zooka, to hit kids with air, $20
http://www.teachersource.com/product/air-zooka/air-pressure

Hoover Car (OK, Hoover Soccer Disk), for balanced-forces-while-moving demo,
http://www.teachersource.com/product/air-soccer-disk-2014/air-pressure-general

Suction Cup Demo (it's just air pressure!), set of 3, $10
http://www.teachersource.com/product/lilsuctioner-package-of-3/air-pressure-general

Newton's Apple (it weighs a newton), $7 (or $30 for 6)
http://www.teachersource.com/product/newtons-apple/physics

"Force Pear", or at least the pear, $3
http://www.amazon.com/Pear-Artificial-Fruit-Kitchen-Decoration/dp/B000J56HLW

Helicopter Toys for Don's painful demo, $2 for 12
http://www.amazon.com/Fettipop-Plastic-Dragonfly-Assortement-Yellow/dp/B0035RRPJE/ref=sr_1_7?s=toys-and-games&ie=UTF8&qid=1436108776&sr=1-7&keywords=whirligig