Unit 8 - Circular Motion

Blog Post – Circular Motion

To introduce the topic of circular motion, a rubber stopper was swung around in a vertical circle at “a constant speed”.  We were asked if the stopper was accelerating, and then we discussed ways to interpret this question.  Using a schema and FBD’s created at the extreme right and left endpoints, it became clear that there was an unbalanced force acting always toward the center of the motion.  From this, we used our knowledge of unbalanced forces to state that it must be accelerating. 

Demonstration:  Throwing the stopper.   In a wide area, Don practiced throwing the rubber stopper at a participant and it was observed that the stopper traveled along a tangent line of the circular motion.  From this, we drew a motion map showing the velocity and acceleration of an object moving through uniform circular motion; we then wrote our first two rules:

1)       Velocity arrows always point tangent to the circular path.

2)      Acceleration arrows always point toward the center of the circular path.

Other Demonstrations:  A clever way of showing how velocity is related to the distance an object is from the center of rotation involved 4 people walking shoulder to shoulder around a central object.  The 1^st person walks slowly near the central object, and then a person is added one at a time.  By the time the 4^th person is added, that person needs to run in order to keep up.  It was discussed why the person on the outside leans inward and then it was demonstrated how an object hung from a string also “leans inward” when moving in a circle. 

Worksheets:  We then worked on a few problems on a worksheet.  These problems are always tricky for students!  After white boarding three examples (merry go round, graviton, and roller coaster), it was demonstrated how an object resting on a plate can be swung in a vertical circle without falling off, provided the speed is high enough.

Practicum:   Our final practicum involved using a pendulum made of sewing thread (low tensile strength);  We could choose our own weight and angle of release.  We needed to allow the weight to pass through equilibrium without breaking the string, and then by increasing the angle by 10 degrees, the string was to break.  A very good, but difficult practicum! 

How I feel about it:    Very fun topic with lots of interesting and engaging demonstrations.  However, this topic is often difficult for students to fully understand.  I’m interested in seeing if student understanding improves with a modeling approach.  I’ve done most of the demonstrations before, but haven’t always done a thorough job of developing how we know the object is accelerating.  I really liked the demonstration of the 4 people walking shoulder to shoulder!

How I plan to implement:  I see myself following this unit design pretty much as it is written.  Very powerful demonstrations and the discussion techniques employed seem to do a good job explaining centripetal acceleration.  I expect I will need to show numerous examples of solving problems with circular motion.

Difficulties I see coming:  I imagine students will have difficulty applying Newton’s 2^nd law to cars going over hills and cresting the bottom of a hill.  However, with numerous examples and the white boarding discussion techniques, I believe students will overcome these difficulties.  I am excited to try the practicum with my students to see if they figure it out! 

Unit 7 – Blog Post (Energy)

What is Energy?  A significant amount of time spent discussing the fact that no one really knows what energy is, but that we are all familiar with its use in everyday language as well as in science class.  It is a pervasive topic central to many aspects of science, yet is elusive in developing a pure definition that all can agree upon.  In typical fashion, we started by generating a broad list of ideas related to energy and then attempted to narrow down.  Since energy is not “tangible”, we used an analogy to help describe it.  Energy could be like “currency”; $100 could be represented as a bill, as a balance in a bank account, as an IOU, etc.  All of these are different representations of a particular amount of something, but what is most useful as an analogy are the examples in which there is nothing material (a balance in a bank account, IOU, etc) as energy itself is immaterial.  In all, we spent a lot of time discussing energy, but not really sure how it helped build the concept of energy in terms of a model.  This is something I will need to develop more. 

1^st rule:  All energy is STORED energy, you must name where it is stored (or how it is stored)

Visual Representation:  Pie charts were utilized to help provide a visual representation of energy, especially related to conservation of energy; a well documented and often discussed topic that is pervasive in all of science.   

How do we know energy is stored in a spring?  After a quick demonstration, we discussed how the spring can cause an object to be propelled when it returns to its original shape.  We then performed an experiment in which we determined the relationship between the force acting on a spring and the resulting displacement.  After graphing the relationship, we took “a broad leap” and said that the area under the force-displacement graph must be the energy stored in the spring.  I honestly had difficulty with this approach as there wasn’t any clear understanding presented as to why the area under the F-D curve represented anything.  Personally, I feel this is a huge issue as energy is central to all of physics and a major factor in most all other sciences.  I felt a bit let down here, and feel I will need to spend much more time trying to justify this with my students.  We found that the force could be represented as F = kx and that energy could be easily found as the area under the curve; EPE = ½ k x^2. 

Development of Kinetic Energy and Gravitational Field Energy:  Using our relationship for energy stored in a spring, we then set about determining how the speed of an object depends on the energy stored in the spring, as well as how the height an object acquires depends on the energy stored in the spring.  These activities led to relationships from which we could develop the equations for Kinetic Energy and Gravitational Field Energy.  Although our groups worked very accurately and efficiently, it was clear that errors were too great to accurately develop these relationships.  This is a bit troubling, as students will likely be less accurate then the physics teachers performing these activities.  Nonetheless, we developed that KE = ½ mv^2, and GFE = mgh. 

  

We also attempted to incorporate friction into our energy model by looking at how the distance an object slides was related to the energy stored in the spring.  This one yielded even more inaccuracies then the others.  No relationship was able to be derived that matched the actual models.  From a practical standpoint, it appears there are just too many variables that must be controlled in order to obtain meaningful data.  L 

Worksheets:  We spent lots of time working on worksheets that used the visual representation of energy to help guide students through problem solving.  I found these problems, and the use of visual representations to solve them, to be time well spent! 

Practicum:  We attempted to drop an object attached to a spring so that it just touched a tin foil cap placed over a cup on the floor below.  This proved to be a rather challenging practical, but did a nice job of connecting the different energy topics developed through this unit. 

How I feel about it:  Personally, I think the energy unit needs to be developed a bit more for the workshop experience.   This is not to say the unit is not developed enough for student delivery, but we appeared to rush through this topic a bit too quickly in the workshop.  I was uneasy, at first, about the loose use of vocabulary in the beginning stages, and began to question whether or not modeling strategy was the best way to go.  Over time, I began to understand, and at least partially accept, the reasons for loose vocabulary.  I feel that I will need to spend significant time developing how I will deliver this unit in order to have it be meaningful to my students.  I do feel, however, that the experiments used to develop kinetic energy and gravitational field energy were useful and insightful.  I question, however, how much they will help with student problem solving. 

How I intend to implement:  As stated above, I will need to work on the pacing and depth of coverage for this unit before I feel comfortable implementing it in a modeling format.  This is such an important topic in physics that I want to make sure its delivery provides the student with the full insight that this topic deserves

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Difficulties I see coming:  I think students will be able to handle the visual representations of energy without much difficulty, but will still struggle somewhat with the set up of the more challenging problems.  However, I am hopeful that, with repeated practice and white boarding, more and more students will begin to understand this powerful topic and how to apply it to everyday scenarios

Unit 6 Blog - 2D and Projectile Motion Unit

Blog Post – Unit 6 – 2 D motion with projectile motion

Revisit of Free Fall:  We started with revisiting the free fall acceleration model by recalling what we know about objects dropped from rest (v vs. t, displacement from graph, etc) and then considered what would happen when objects are thrown upward.  We tried a Wile E. Coyote problem from the book and drew a motion map showing velocity and acceleration at various times.  Don suggested (a good idea) that we have students draw these vectors approximately to scale, showing how the acceleration vector, when (“multiplied by time to change from acceleration to delta v”) could be added to the previous velocity so that the new velocity could be represented.  This is a challenging idea in straight vector mathematics, but is fairly easy to follow if done graphically.  (I’ve tried this approach previously when dealing with circular motion to show that when acc is multiplied by t we get a new quantity called delta v, which when added to the previous velocity yields the new velocity, which would be in a new direction.  In this way, what’s created is an isosceles triangle since there is no change in overall speed if uniform circular motion. 

  

How to connect new learning to old learning:  consider showing what it would look like if the person were on the ground and kicking the ball at an angle…this would show a full parabola as opposed to just half of a parabola

 

Worksheets:  We spent some time completing some worksheets related to projectile motion and then white-boarded some key results.  Specifically, we attempted to draw a horizontally launched projectile motion problem to scale. 

We then did a practicum in which we attempted to hit a cup with a ball rolled down a ramp and then along a horizontal track.  We then used a pasco launcher to launch at an angle to hit a target.  Having done this lab in the past, history shows that air resistance has a significant effect on the total range. The question is whether or not we should have the students try to take this into account???  This would tend to emphasize practical vs. theoretical. 

Summary of 2D motion:  Horizontal and Vertical Motion of a projectile can be understood by combining and using all previous models (horizontal is CVPM and Free Particle Model), (vertical is CAPM and CFPM)

How I feel about it:  I really like how studying projectile motion after basic forces helps the student understand this difficult topic.  Although students can be (and often are) taught how to solve projectile motion problems without an understanding of forces, incorporating specific aspects of all four previous models should help provide meaningful connections and lead not only to greater conceptual understanding, but I suspect, more concrete problem solving.   For example, the problem of air resistance affecting the path of a projectile can be more easily understood, and described quantitatively if desired, using the forces model. 

How I intend to implement:  I would need to change the order in which I cover topics if I were to cover topics in the same order we did in the workshop.  However, realizing that students really have a difficult time with projectile motion, there is some benefit to covering this topic after forces.  Having said that, it is difficult to do many outdoor activities with projectile motion if the topic is delayed too long in the school year.  At this point in time, I’m uncertain which approach I’ll take.

Difficulties I see coming:   I expect students will still have difficulty solving projectile motion problems as there is a fair amount of mathematical manipulation required, especially if we do angled launches in which vector resolution must also be done.  I am uncertain whether conceptual development (which is the backbone of modeling) will help with problem solving.   I know from experience that a practicum in which students attempt to hit a target from an elevated angled launch position is very difficult to perform; not only in calculation, but also in practice as air resistance can have a significant effect on the projectile’s motion. 

Unit 5 Blog - Unbalanced Forces

Blog Post – Unit 5: Unbalanced Forces

Friction Model:  We began this unit with an attempt to model the friction force.  By using a large dial spring scale and a block, it was evident that when pulling the block, the force acting on it grew to a maximum value and then reduced slightly once motion began.  We then posed the question:  What are the factors that you could change to that might affect the friction between the block and the table?   The list of factors we generated were:  surface area, mass (or weight) of block, surface texture, angle of pull, speed.  Different groups chose a different factor to test and then we white boarded the results. 

What we found is that friction was affect by the two surfaces in contact, and that there was a linear (direct) relationship between the force of friction and the force pushing the surfaces together. We then named the slope of the friction vs surface force the coefficient of friction. 

We then moved into our “paradigm lab” which explored the factors that might affect the acceleration of an object.  A question was asked:  “what factors could you adjust to affect the acceleration of the cart?”  The factors we determined were:   Applied force, mass (or weight) of cart, angle of pull, angle of ramp.  Each group was asked to pick two of the factors and run an experiment using logger pro, newton scales (or force sensors) and motion sensors.  We found that acceleration varied directly with applied force and inversely with mass (Newton’s 2^nd law).  

We went through a fairly confusing method of combining two generic relationships found experimentally and then determining the value of a new coefficient introduced to make the combined relationship an equality.

The coefficient was found to be “1”, which allowed us to write our equation as (a = f/m) which was verified on Google to be Newton’s 2^nd law.  

Elevator Ride:   After a brief discussion about what a bathroom scale reads (which was decided to be how hard the floor or scale pushes up on the person) each group determined the acceleration of the elevator as it traveled from 2^nd floor to 1^st floor, and then from 1^st floor to 2^nd floor.  This was done by recording the reading of a scale (or force sensor) that was measuring the “weight” (really apparent weight) of the object as the elevator moved between floors.  From these recorded “weight” changes, we used 2^nd law to compute the accelerations of the elevator.  

Modified Atwood’s Machine Analysis:  We spent considerable time analyzing the modified atwood’s machine and learned an interesting and, I think, powerful method of analyzing this as a “system” as opposed to treating objects separately and writing a system of equations to solve.  One difficulty I had with this system when I first studied it in college was how to determine whether the tension force was greater than, less than, or equal to the weight of the hanging object when the system accelerates.   Conceptually, this proved very challenging to me as I had a poor conceptual understanding of mechanics at this time.  I visualized replacing the hanging mass with my hand and pulling on the cart.  This led me to think that the force of tension would be greater than the weight of the object, which is opposite of the correct interpretation.  I could see having students place a force sensor on the cart and comparing the tension force with the weight of the object when accelerating.  This would cement, once and for all, that the net force and acceleration are in the same direction…so the tension force must be less than the weight! 

How I feel about it:  I like how the relationships that we typically use in the classroom can be developed by the student through experiment.  However, I’m uncertain whether or not the development of the relationships experimentally will have much impact on their ability to interpret and use them in real life (or classroom story problem) situations.  If nothing else, however, this would allow the student some concrete experience on which to draw upon when solving problems later on.  I really like the elevator ride scenario and have done this numerous times in my own classroom.  The difficulty I’ve always had was obtaining accurate results, but the use technology as demonstrated in this modeling session seems to ease this concern.

How I intend to implement:  I can envision doing all these activities in my classroom, however, I’m not sure of the order at this time.  In the past, I have covered friction models near the end of the forces unit, and in the modeling class, friction came first. 

Difficulties I see:  As I mentioned, I’m not sure that experimental development will aid in problem solving ability, so I envision students will still struggle with apply the 2^nd law to classroom problems.  I also am not certain that students will understand (or appreciate) how the two relationships for acceleration were merged into one relationship, nor will they appreciate the meaning or interpretation of the 3^rd coefficient being a value of one.  

Blog Post – Unit 4 on Balanced Forces Model (aka Inertia and Interactions – Free Particle Model)

Force – Operational Definition:  We started this unit by attempting to develop an operational definition for the term FORCE. In contrast to other topics, we started with the vocabulary term and then attempted to define what it meant.  This seemed to go against the suggested method of concept before term, but because of the ubiquitous use of the term force in both everyday language and in the classroom, we chose to violate the rule.  I liked the way Don introduced the topic…”since this is not your first day as a human, you’ve heard of this term before…”   A long list of terms (or phrases) associated with the term “force” was written on the board and then Don attempted to narrow the list down by “combining ideas”, eliminating if the word did not correspond to a “process used to determine its existence, duration, quantity” (from Wikipedia definition of “operational definition”).  The list of words eventually was reduced to “push or pull, or rubbing”.  I’m still a bit confused about how to eliminate the words that don’t fit…that is, how to determine if the word belongs in or can be used for an operational definition.

Force – What is it exerted BY?  We then attempted to refine our concept of force by looking at ONLY THE OBJECT that exerts a force.   So the question posed “what forces are acting on a block” (a person holding a block stationary) was reduced to only the objects that exert a force, not the force itself.  Our list was reduced to “Hand” and “Earth”, and temporary included the term “air”.  Words eliminated were “light”, “mass”, “inertia”, “moon”, “sun”, “magnetism”, etc. 

Don was careful to list all words thrown out by the class, but then narrowed it down to just the two objects.   This is to ensure that the list is generated by the class so it’s not just the list we use in physics class and it is something else outside of class…it is THEIR list.    Our first general rule was established:

1:   “When naming forces, you must name the physical object doing the “pulling/pushing/rubbing” – objects must be made of MATTER”

Force – System Schema:  A representational strategy (new to me) was shown called a system schema.  In this representation, the object under study and the object(s) that exert force on it are shown in circles and connecting lines are shown representing the interaction (force).  This was very effective in showing that objects exert force, and that if you can’t identify the object, there is no force.  I felt that this will go a long way in helping students realize there is no impetus force.  The forces of interaction represented by connecting lines are drawn either as solid lines or dashed lines, which help illustrate the difference between “contact” forces and “non contact” forces.   A list was made of “non-contact forces” and “contact forces” and under the “non-contact forces” was listed three of the four fundamental forces (gravitation, magnetism, electrostatic, and strong nuclear) and under the “contact forces” was listed the phrase – “everything else”.

 

(Personal notes:  This appears to be the opportune time to address the fact that there are only 4 fundamental forces and although for convenience we can talk about “contact forces”, in reality, nothing ever actually touches anything else.   Granted, this is not the time to delve into details or mathematical descriptions of these forces.  The premise of “modeling” is that nature behaves in patterns that can be understood through some basic models… these models serve as the foundation upon which one can understand more complex processes as they can be described through simultaneous application of the basic models.   Narrowing the list of forces to the 4 fundamentals may help strengthen the foundations of these models as they are being built and reinforce the notion that nature can be described by only a handful of basic laws applied in a myriad of ways.   

Our second rule was established:  2:  If vel = 0 then forces are balanced (will be replaced later with if change in velocity = 0 then forces are balanced, and then ultimately if acceleration = 0 then forces are balanced)

A demonstration was shown, but not explored, in which boards bend or change shape to provide the supportive force necessary to maintain equilibrium.  A lot of discussion took place about how this could be used to answer the question…”how does the table know to push up with 4 N on the board and by 20 N on the book?”  In our reading, there was discussion about how a spring behaves as an “automatic force adjuster”, but I’m honestly not sure where this is going or how it’s helping students build a model just yet.  A suggestion was made that a series of magnets around a dowel rod can be used to show the compressibility of matter.

 

A demonstration using a “Kick Disc” was used to illustrate the fact that there is no “impetus” force.  This helped provide the visualization for students that there is “no contact force” that remains acting on the disc after it is set in motion.  A list of objects was generated that could be exerting forces to keep it moving, but then subsequently they were removed from the list as they weren’t making contact.  It was concluded that there is no force acting in the direction it is moving, and after describing the motion of the disc after set in motion, we changed our #2 rule to the “no change in velocity means balanced forces”. 

Activity:  Relationship between mass of an object and the force that earth exerts on it:  Using spring scales we measured the “weight” of a variety of masses and plotted on graph paper in our usual method.  From this activity, we determined the relationship that “W = (0.01 N/g) * M”  or “W = (10 N/kg) * M which experimentally confirms our fundamental equation relating mass to weight (W = mg).  This relationship was summarized in words as “for every 1 kg of mass the earth pulls on the object with a force of 10 N”.  Although the mathematical representation of this relationship was not utilized in our classroom setting, I see this as a good opportunity to show how the equation W = mg describes this relationship and discuss with my students the meaning/interpretation of the value of “g”. 

 

Atwood’s machine demo – balanced and unbalanced:  A demonstration was done to see how well we understand balanced forces.  An atwood’s machine with equal weights was shown, Don then lifted one higher than the other and asked what would happen when released (system stayed put), then he said he would throw one downward giving it a slow but steady speed.  What would the system do?  (It continued at a constant velocity)

Worksheets were done to practice drawing force diagrams and schemas for a variety of different scenarios.  During discussion period, Don nicely led us to see that direction of an unbalanced force and the direction of acceleration are always the same.  Following one of the more challenging worksheets (dealing with 3^rd Law) we used force sensors attached to dynamics cars to study forces of interaction between two objects that are in contact while one is pushed, and then also studied forces of interaction between objects as they collide.

 

This was all done PRIOR to any discussion of the 3^rd law.  Prior to 3^rd law worksheets, Don shared a story about “confrontational Stu” to help introduce the idea that forces always come in pairs.  We were all asked to think of a situation in which an object can be propelled and discuss how the 3rd law can explain the propulsion.  Drawings were created as well....

 

How I feel about all of this?  I really like how the activities allow students to learn these conceptually difficult concepts through kinesthetic experience.   However, it is very apparent that true learning will take place only if the instructor does a thorough job of questioning and guiding student thinking through the common misconceptions (or preconceptions).  That is to say, the teacher cannot sit idly by and hope that students make sense of the material or that they will perform the necessary reflections on their own.  

How I intend to implement:  At this point, I can see myself implementing most or all of these activities in my classroom.  I am inclined, at this point, to introduce more mathematical representations as we go along, however.    This is not to emphasize any particular form of representation, but rather to reinforce that all representations have their own merit, and that best practice may necessitate using more than one representation in order to convey a particular idea or provide additional insight.      

Difficulties I see coming:    What I will struggle with is the pacing and depth of the material to keep the students (especially at the higher end) from getting bored and “zoning out”.  Unfortunately, many introductory physics students believe they already understand this material and that they don’t really need to pay attention as it may appear (at least to them) that this material is “below them”.  In reality, this material is rife with student mis and preconceptions that, if not fixed, will continue to plague their problem solving abilities as the rest of the course unfolds.  I can see myself performing a balancing act for a lot of this unit, attempting to balance the necessary focus on “basics” with the students’ desire to be challenged with meaningful learning activities that stretch them a bit.  

Unit 3 - Constant Acceleration Particle Model (CAPM)

Ahhhh... let the fun begin!  Lots of really cool activities to help students fully grasp the difficult concept of acceleration.  After many years of trying to teach this concept by telling, I'm excited to try out the modeling method to help my students master this topic.  The motion of a dynamics car along an incline was studied with a motion sensor and logger pro.  Lots of different variations of motion were sampled (cart released from rest, car pushed up the incline, sensor at top, sensor at bottom) with different groups performing different activities and boarding the results.  Discussions and questioning followed.  We developed an operational definition for acceleration being the "slope of the velocity curve" on a velocity - time graph.  We learned a "up up down down" song to help our students understand directional nature of acceleration and velocity and finally showed how the typical kinematic equations (I call them the Fab 4) could be written directly from the graphical data obtained from an experiment in which the car's motion was sampled moving and accelerating down the ramp with the motion sensor starting after the car was in motion (so that we had a non-zero initial velocity and starting position).  I found this portion of the unit particularly satisfying as it allows the student an opportunity to see how these equations (a staple of basic kinematics) are "derived" from (or at least accurately model) motion that students created simply by having a car accelerate along a ramp.  Seems like it will help take away the mystery, though I'm not sure it will be that meaningful to all students.  I think students that either dislike math, or have trouble with it (or both) will not find it all that useful or insightful, but for the "traditional" physics student, I think it will be very useful.  We culminated this unit with another practicum whereby we attempted to hit a constant velocity car by rolling a ball down a ramp.  A recommendation I have for improving this practicum (something I will do in my class) is to make sure the angle of the ramp is fairly small so that there is a significant time interval for the rolling ball (providing less margin of error).  With a steep ramp, the ball will travel the ramp distance in less than 1 second and is fairly easy to hit a moving car.  Something  even better might be to have the ball travel down the ramp and then along a horizontal section of ground before colliding with the car.  This might be too challenging for general classes, but would definitely work with honors or AP classes.

Again, loved this unit and think there are lots of great ways to help students truly learn acceleration.  I plan on implementing every one of these activities and am excited to see how well it works!

Unit 2 - Constant Velocity Particle Model

Unit 2 focused on numerous methods to analyze, interpret and represent constant (or uniform) velocity.  The models explored were graphical, motion mapping, and equations, including "area under the curve" or "area bounded between the relationship curve and the horizontal axis" representing the displacement of the object.  We used constant velocity "buggy" cars and motion sensors connected to logger pro in order to obtain the graphical data, and then used logger pro to develop the equations that fit the curves.  From this we discovered that the slope of the position time graph represents the velocity of the obj
ect.  We culminated the unit with a "practicum" whereby we attempted to collide two different constant velocity cars at an "X" placed in the center of the room.  Though most groups were not successful (only 1 in 4 collided), it was decided that most failures were attributed to the "curvature" of the cars.

Similar to unit 1, I liked how this unit included relatively straight forward experiments that provided meaningful and useful graphical representations from which basic physics relationships are derived.  Questioning techniques helped bring forward the relationships that were developed by the students.

Unfortunately, I missed a day of this unit due to illness.  So, although I found the unit useful, I know there is quite a bit of material I missed which I'll need to review in the provided literature.

I can see real value in performing these activities in my own classroom.  Unfortunately, I have been having hardware (and software) issues with my "datastudio" equipment and will need to get it fixed in order to fully employ the modeling method.