Unit 6 Two dimensional Motion

Unit 6 Two Dimensional Motion

Drawing of person on building dropping something

As the ball falls can we get a sense for how fast it is moving?

T	V	Dist fall
0	0	0
1	-10	5
2	-20	20
3	-30	45
4	-40	80
5

Can we make a distance time graph?  The best way would be to make a v-t graph?

If it fell for 5 seconds how far would it fall? 

You can also use the equations  

Freely accelerating a=-10m/s/s

Physicists, to confuse us more, will change the equation to  

If you want students to understand CAPM

1.       Start w/ v vs t graphs

2.       Make data tables

You can expect the assessments will look something like this then.

We then worked on Unit 6 worksheet 1 and then put it on the white boards.

With partners we watched a Video of steel ball on a computer and taped a transparency to screen and use marker to mark the different positions.  I could do this at school using the interactive white board.  It wouldn't be as active for the students though.

Ask question how do you think the spacing will be vertically and horizontally.

Afterwards—What did you notice about the spacing horizontally?  CVPM

What do you notice about the vertical?  CAPM

Drop ball and throw at the same time.

What do you think if it is thrown harder or softer.  If I throw it is more intriguing than using mechanism

What happens when you turn the gravity switch off? Going back to the dropping off the building

Skill set for worksheet 2  Making a motion map from the graph above.

Draw a right velocity and a down velocity.  Then draw a box and the diagonal is the

 

We then white boarded Unit 6 worksheet 2

 A white boarding tip:  Since everything is the same if you do a full class discussion you need to have questions ready, like,  "How would this be different if . . ." or give each group a different extension question.

How can we connect something we already know with something new.  What if we took the guy on the roof and extended it back (symmetry is your friend) So this isn’t very much different than the firing straight from the roof.

The bead activity.  Cut string 5 20 45 80

Find the angle where the first and last beads are at the same level.  Came up with about 53 degrees

A soccer player kicks a ball at 53 degrees.  Can we physics this up? 53 degrees is a 3-4-5 right triangle

T	X	Vx	Y	Vy
0	0	15	0	20
1	15	15	15	10
2	30	15	20	0
3	45	15	15	-10
4	60	15	0	-20

  Practicum

Roll ball down ramp and then figure out where to put the cup.

Now use the launcher Give each group an angle.  This falls into the category of really, really hard

There are a lot of different activities that we could use. But don’t spend too much time.

Summary

Horiz       Vert

CVPM    CAPM

I've always liked projectile motion and so I found that I liked this unit.  The bead thing was very nice and can illustrate things nicely for the students.  I wonder if it would be profitable to make a larger one with baseballs?  I have probably spent too much time on this in the past so I think I will have to be careful.  We did seem to jump into the problems with little instruction but Don mentioned that he usually goes through a sample with something falling from 80 meters with a horizontal velocity of 30 m/s which we didn't do to same time.  Not as much model building here, more model adapting to combine the CVPM and CAPM.  There are also not as many labs to write up in this unit.  There is a good variety of practicums to choose from with varying difficulty.

Implementation:  I do have one nice launcher that I can use for demonstrations and perhaps the practicum for the AP class.  I would also like to incorporate some rocket stuff more qualitatively than quantitatively.  If the students solidly understand the two 1D models then I don't think this will go too poorly.  They just have to get their mind around the idea that the vertical and horizontal can be done separately.

Unit 5 Constant Force Particle Model

Unit 5 transition lab

Talk about the max and the force for moving at a constant speed before

What are the factors you could change that might affect the friction between the block and the table?

Unit 5 Paradigm lab

What are the factors you can change that might affect the acceleration of the cart?

Force

Pull angle

Mass/weight

Ramp angle

We did the lab with mass vs acceleration and found it difficult to get accurate data with the spring scale.  There was a good interaction with the instructor as we thought it looked linear with a negative slope.  We were directed to think about the significance of the intercepts.  We ran another point and found a good inverse fit.

Here is some of the questions during board meeting

• ·         Lets start with varying force
• ·         How did you do it—we put extra mass on the car and it made it easier to keep up with the car
• ·         Make sure you write down the things that were kept constant—do it on your boards now.
• ·         Why did you load the car up with a bunch of mass?
• ·         Do we see a proportional increase?
• ·         Do the data tables bear that out?  Looking at different intervals in the data table comparing with different models
• ·         You have to convince us, does your data table help with that?
• ·         Where is your intercept?  What does 0, 0 mean in your graph.
• ·         If we say its linear then if we multiply the x by 2 what happens to the y.
• ·         If it is linear we should have a for every statement, what is your for every statement.
• ·         Why do you have different slopes?
• ·         Write on the board—graph of accel and force as a straight line. a=( ) F
• ·         Let’s look at the mass vs acceleration board someone points out that one group had added mass instead of total mass.
• I don’t want to write on the board unless you are confident.
• Just because I’m writing on the board doesn't mean its correct. We may need to adjust it. (Teacher mode Sometimes I leave something hanging, keep track of what you leave and when you need to circle back) There is a procedure for that.
• ·         Look at the angle of pull—questions focus on the unbalanced force and the force causing the acceleration.  Draw a force diagram for a 60 degree pole.  Discuss.  Then draw a critical competitor.  How does that compare to what we saw from the acceleration – force plot.

A general rule is not to put units in the equation but when you are naming the coefficient.  

Relate these together.

Assignment try to find coeff3.  The assumption is the pulling force is the unbalanced force.  This is a big moment.  We used “the google” to verify our response

The force is the cause and the acceleration is the result.  a=F/m  The process is what is important.

So if we are given the forces, we can find the unbalanced force and then find the acceleration.

Also note that the unbalanced force and the acceleration are in the same direction.

We work on Unit 5 worksheet 1 and then practicum of elevator work.

Is there a value for a freely accelerating object.

We have dealt with being careful of terms quite a bit like "Falling faster?  Seems to denote velocity. Analyzing graphs from dropping a ball.

Get away from freefall acceleration because it denotes going down.

Bathroom scale measures the force between you and the scale.

Elevator activity

Discussion of when you feel heavy and light.  Does your weight change?  What is true of the acceleration?

Lead to weightless discussion.  What if the floor doesn't push you up anymore?

Block sitting on the table name two forces acting on the object.  Are they Newton’s third law force pairs?

Extras Make a list of questions and misconceptions Give seeds and prompts as you walk around

Aron’s article chapter 3  Operational definition of mass

Day 10

Begin talking about Arons 3.10-3.20.  Got into a discussion of newton’s 3^rd law equal but opposite terms

Cart on track with small weight

You have the tools to find the acceleration of the cart.

1^st step draw the system schema

How many interactions are there on the mass?  2  so the force diagram should have 2 arrows

Is the earth force bigger or smaller than the force of the earth.

Can we predict the acceleration of the cart mathematically

Let’s look at the system.  What stuff matters. 

Greg asked a question.  It was becoming a dialog between Don and Greg and so then he had us discuss it among ourselves to try and get into Greg’s head and describe what he is saying.  A chance to bring it back to the whole class instead of a 2 person discussion

System—stuff that matters  Draw a dotty line around the stuff that matters.

The intuitive leap—What does the pulley do it rotates the string 90 degrees clockwise  What if we undid that  Can the two string forces be the same?  Can the earth then be the unbalanced force

The unbalanced force is the weight of the object but it accelerates the whole thing mass and cart.

White board and find the acceleration of the cart

Now do the atwoods machine (named after mr. machine)

New system box being pulled by a person .  What forces are acting there is some friction but he is accelerating to the right.  How do you know where to hold the flashlight?

Kates rule the flash lights are oriented perpendicular and parallel to the surface.

Block on a ramp—only do this for advanced classes.Drawing horizontal and vertical doesn’t help because we need a force in the direction of a and funbal.  Should I put the flashlight on the surface force?  Doesn’t cast a shadow.  So shadow the earth force.

I felt pretty good about this unit and I think it will go well.  There were a lot of aspects about force that I haven't been spending time on that I will focus on more and I think as I get into more complex problems some of those early preconceptions will be dealt with and so things will go smoother.  I think the schema will be very effective in helping the students identify what to put in their force diagrams.  As before I think limited lab stations could pose a problem that I will have to attempt to find a solution for.  One way that I will probably implement this that is a little different is that I think I will use F's for forces but subscript them with the object applying the force.

Extras covered during this unit

Video on math Dan Meyer  “Patient problem solvers”

1. lack of initiative

2. lack of perseverance

3. Lack of retention . . .

Impatient with irresolution—the math serves the conversation not the conversation the math.

Video on Kahn academy by veritasium videos will only reinforce what you believe unless misconceptions are dealt with

Video  by xted frank Noschese on modeling

Unit 4 Free Particle Model

This unit differs from the others in that instead of starting with an actual experiment you start with a thought experiment.  From the reading it is really clear that this is an important concept  and some time needs to be spent on the at rest condition.  Some things to discuss during this initial conversation.

·         Are there forces on the book sitting on a desk?

·         Come up with a list of what a force is

·         Come up with an operational definition.  Make sure the students know that it may be refined

·         A force must be from an object so cross off anything that is not an object.  An object is something I can hit you with or buy in a store.

First rule of forces—You must name the physical object applying the forces.  I think it is going to be really helpful to have students label the forces with the object that is acting on the object in question.

Types of forces

Contact forces	Non contact forces (spooky)
Everything else  The key is contact	Gravity
	Magnetism
	Electrostatic
	Nuclear forces (strong and weak)

We then developed a graphical representation for forces, a force scheme as a way to keep track of the forces that are present solid line for contact forces dashed line for non-contact forces. Then transition to force diagrams (free body diagrams) use a dot to represent the object.  Use arrows and the name of the object exerting the force.  Introduce the metric unit of force the newton.

I’m a little unclear as to how to introduce the idea that if the velocity is zero then the forces are balanced without just giving them that on authority (use spring scales to measure forces).  This is also where the idea of the surface force is developed using the springs and the sagging white board.  “How does the table know how much force to exert?”

Inquiry lab—What is the relationship between the force the earth pulls and the mass of the object?  Come up with a relations ship between kg and N.

 The concept of the surface exerting a force is a very important concept to cover so that some very common preconceptions can be over come.  To deal with this we used springs and sagging surfaces.

Force rules (these will be different because the students will be coming up with operational definitions but this is what I’m shooting for)

1.       When naming forces you must use the name of the object (and they must be made of matter)

2.       If the Dv =0 then the forces balance

3.       Surfaces push with a force perpendicular to themselves

4.       Strings pull in the direction parallel to the string

5.       Acceleration and unbalanced force are always in the same direction

6.       Surface forces will compensate to balance the forces (like a spring)

Use a hover disk to answer the question what is the force that keeps the disk moving   This is really important to counter the preconception that a force is needed to keep an object moving (impetus) So now the rule can be change from v=0 to delta v=0) A related question that can be asked is why do you need to keep pedaling on a bike?  What gives you a clue that the wind is exerting  a force in this case?

The idea of components is then introduced but we used ‘shadow arrows’ which I think will be a little clearer when forces are not inline.  Having taught pre-calculus I think that I will definitely relate things to components to help those student who will take pre-calculus.  Depending on the level of the class we can delve into the trigonometry if needed otherwise just focus on the qualitative concept of the forces balancing.

Some other concepts that were explored to help overcome some preconceptions dealing with Newton’s 3^rd law force pairs.

2N block on 4N block which block pushes more?

A critical competitor 4N on 2N

All forces come in pairs that are equal in strength opposite in direction and act on the other object.

Ask the students to tell you how to walk (or some other simple task involving an equal force in the opposite direction.

Come up with Newton’s Third Law force pairs.

Bike swimming canoe helicopter bullet in gun

What do you notice about each pair?

Force of bike on ground—Force of ground on bike

We also used the force probes and looked at the relation between the forces between two carts in various situations.

Some Extras that we covered during this unit

·         Praise the effort not the intelligence growth mindset verses fixed mindset.

·         Use demos for entertainment and as discrepant events.

Some Problems I can forsee

After 8 weeks or so of me doing little talking there might be some rebellion at the first part of this unit which involves a lot of discussion.  Hopefully the students can be brought into the discussions to be active participants.