We started with a demonstration of a flying pig on a string. We were asked to draw a schema and a force diagram and answer the following questions: If the speed is constant, then is the velocity constant and is the acceleration constant? We noticed through much discussion that the force was always towards the center and if there is an unbalanced force inward toward the center of the circle, then the acceleration is pointing toward the center of the circle as well. Centrifugal is not a physics term. The correct term is centripetal. What we think of as centrifugal is just inertia.
We then did some Worksheet examples where a cart was going up a hill and another problem where the cart was going down a hill. We had to draw velocity and acceleration arrows on the motion map for the cart. We noticed that as it went down and then back up this was like the elevator going down and slowing to a stop, and when you went to the top of the hill this was like the elevator going up and slowing to a stop at the top.
This was discussed the final day of class and so there was not much class time given to this unit.
Saturday, July 11, 2015
Unit 7 -- Energy (With Less Work)
We started the Energy unit by being posed the question "What is energy?" We came up with some basic answers, and it led to the 1st rule of energy: "All energy is stored. It must be stored someplace (a real place) and we can "see" something about it." Energy was discussed as a transfer of information and energy as currency. Currency or information can change form but it is still currency or information.
A few other questions had to be established, such as "Where is energy stored?", "Where does it come from?", "Where does it go?", and "What does energy do?" This was the lens we had to look through to see if what we thought was energy really was energy.
We looked at a battery operated dune buggy and established the system as the dune buggy, the battery and the surroundings. We drew pie charts to represent the energy Before it starts moving, another to represent After it starts moving and another to represent After it moves for two minutes. Then we did the same thing with other systems on a worksheet.
We noticed that energy is really just a book keeping term to keep track of and make sense of the world.
Next we did a lab looking at the relationship between the distance a spring is stretched and the force applied. We noticed a direct linear relationship and different groups had different types of springs. After we were looking at the graphs, we were asked "Where is the energy?" We noticed it was not in the slope - that represented the tightness of the spring, and the energy is not in the values - that represented the stretch distance and the force. We were led to look at the area under the curve and that was determined as the elastic energy. We established Hooke's Law and the formula for Elastic Energy in this experiment.
We then looked at L O L energy flow diagrams where we would see the initial energy condition , the energy flow diagram (the system) and the after condition. Energy was shown as blocks and if you start with four blocks, you would have to account for all four blocks somewhere.
We then looked at the following relationships and did experiments and whiteboards and discussed them. "What is the relationship between energy stored in rubber band and velocity?" , "What is the relationship between energy stored in rubber band and vertical height?" , and "What is the relationship between energy stored in rubber band and slide distance of friction block?" The setup of these experiments had a rubber band stretched between two C-clamps with a track between the C-clamps so that the cart would bounce back off the rubber band. We first had to find the spring constant of the rubber band and then looked at the following relationships. These experiments helped us to establish the formula for Elastic energy and kinetic energy and gravitational field energy.
A few other questions had to be established, such as "Where is energy stored?", "Where does it come from?", "Where does it go?", and "What does energy do?" This was the lens we had to look through to see if what we thought was energy really was energy.
We looked at a battery operated dune buggy and established the system as the dune buggy, the battery and the surroundings. We drew pie charts to represent the energy Before it starts moving, another to represent After it starts moving and another to represent After it moves for two minutes. Then we did the same thing with other systems on a worksheet.
We noticed that energy is really just a book keeping term to keep track of and make sense of the world.
Next we did a lab looking at the relationship between the distance a spring is stretched and the force applied. We noticed a direct linear relationship and different groups had different types of springs. After we were looking at the graphs, we were asked "Where is the energy?" We noticed it was not in the slope - that represented the tightness of the spring, and the energy is not in the values - that represented the stretch distance and the force. We were led to look at the area under the curve and that was determined as the elastic energy. We established Hooke's Law and the formula for Elastic Energy in this experiment.
We then looked at L O L energy flow diagrams where we would see the initial energy condition , the energy flow diagram (the system) and the after condition. Energy was shown as blocks and if you start with four blocks, you would have to account for all four blocks somewhere.
We then looked at the following relationships and did experiments and whiteboards and discussed them. "What is the relationship between energy stored in rubber band and velocity?" , "What is the relationship between energy stored in rubber band and vertical height?" , and "What is the relationship between energy stored in rubber band and slide distance of friction block?" The setup of these experiments had a rubber band stretched between two C-clamps with a track between the C-clamps so that the cart would bounce back off the rubber band. We first had to find the spring constant of the rubber band and then looked at the following relationships. These experiments helped us to establish the formula for Elastic energy and kinetic energy and gravitational field energy.
Unit 6 -- 2 dimensional Particel Models
We started this unit with a thought experiment. If something falls at the same time something is propelled horizontally from the same height, which will hit the ground first? Then we were shown video of a projectile (steel sphere) being shot across the screen and it was slowed down with a screen shot every two seconds, then someone put sticky notes at the location of the sphere and there was a nice parabolic path shown by the sticky notes. The horizontal distance between each sticky note was the same distance apart. When there is a projectile, only Earth pulls it down. In the horizontal direction, there is constant speed, and in the vertical direction, there is constant acceleration. These were concepts that we were familiar about because we had developed a model for them earlier. We have a conceptual framework now because we talked about forces before talking about projectile motion, which is opposite of most textbooks.
We did Unit 6: Worksheet #1 problems and then took turns facilitating whiteboard sessions about some of these problems. This was time well spent because we needed to learn how to facilitate these for when we return to our classrooms to lead them in modeling. In this worksheet, we utilized the algebraic formulas and/or graphs of the situation to look at the area under the curve when applicable.
We then were given a situation for everyone to whiteboard. An object was projected off a cliff at a height of 45 meters at an initial horizontal velocity of 40 m/s. We were to accurately draw a motion map to scale where each dot has a change in time of 1 second. It took three seconds for the object to reach the ground. We made a data table to determine the horizontal and vertical position of each point, and drew the velocity vectors in both the horizontal and vertical directions. The question was then asked "At what velocity (angle and magnitude) does the object hit the ground?" We came up with 50 m/s at 37 degrees below the horizontal. This was cool because I had never seen this done before.
We then had a challenge to perform as a lab group. We had to setup a ramp onto the track (the track was a straightaway) so that we could determine how far a steel sphere would hit the top of an upside down cup. We determined what the constant velocity of the steel sphere would be and used that along with the height to determine where to place the cup. When we did the challenge, it landed right on top of the cup. Even when repeated, it landed on the cup again and again. Really cool.
Another challenge was to launch a projectile at a certain angle to hit a cup on the floor.
We then looked at a reading out of the 5 practices book and discussed them. There were some really good insights there.
We did Unit 6: Worksheet #1 problems and then took turns facilitating whiteboard sessions about some of these problems. This was time well spent because we needed to learn how to facilitate these for when we return to our classrooms to lead them in modeling. In this worksheet, we utilized the algebraic formulas and/or graphs of the situation to look at the area under the curve when applicable.
We then were given a situation for everyone to whiteboard. An object was projected off a cliff at a height of 45 meters at an initial horizontal velocity of 40 m/s. We were to accurately draw a motion map to scale where each dot has a change in time of 1 second. It took three seconds for the object to reach the ground. We made a data table to determine the horizontal and vertical position of each point, and drew the velocity vectors in both the horizontal and vertical directions. The question was then asked "At what velocity (angle and magnitude) does the object hit the ground?" We came up with 50 m/s at 37 degrees below the horizontal. This was cool because I had never seen this done before.
We then had a challenge to perform as a lab group. We had to setup a ramp onto the track (the track was a straightaway) so that we could determine how far a steel sphere would hit the top of an upside down cup. We determined what the constant velocity of the steel sphere would be and used that along with the height to determine where to place the cup. When we did the challenge, it landed right on top of the cup. Even when repeated, it landed on the cup again and again. Really cool.
Another challenge was to launch a projectile at a certain angle to hit a cup on the floor.
We then looked at a reading out of the 5 practices book and discussed them. There were some really good insights there.
Friday, July 10, 2015
Unit 5 - Constant Force Particle Model
We began this unit by looking at the relationship between mass and weight. We knew it was a direct relationship and when mass increases, weight increases. We used different objects and spring scales to determine their weight in Newtons and triple beam balances to determine the mass of each object and then determined the relationship which was linear with a slope of 10 N/kg. This led to a For every 1 kg, the force exerted by the Earth changes by 10 Newtons.
At this point, we were asked for an operational definition for mass. What is mass? and we could not use the traditional answers for it. We did not have a good definition; however, we did know that something that is more massive resists change in motion more than something with less mass. Again, we reiterated the fact that An object in motion will stay in motion in a straight line at a constant speed as long as the forces are balanced.
The model so far:
Next, we pushed an air puck across two tables and we had to keep constant contact with it. We ended up running at the end of the two tables (We had someone there at the end of the table to catch the air puck :) ) This was a good introduction to Newton's Second Law. Now we had to determine this again with a lab. Again we used the cart and the tracks. We had to find the relationship between Force, acceleration and mass. For one experiment, we kept mass constant. We used a spring scale (push type) to apply a constant force of 0.5 N, then 1 N, up to 2.5 N and measured the acceleration by using the digital sonic ranger at the end of the track. This was a tricky lab for two reasons. One was trying to keep the force constant at the 5 different forces and the other reason was we had to stop the cart before it crashed into the digital sonic ranger. We found a linear relationship, as force increased, acceleration also increased in a linear fashion. Next experiment, we kept force constant while we increased the mass. We noticed a linear relationship but as mass increased, the acceleration decreased. In both of these labs, acceleration was the dependent variable. This led us to the right causal effect where acceleration is caused by the force. Newtons 2nd Law was established as acceleration = Force (unbalanced) / mass
Mass (in kg) is a quantitative measurement of resistance to change in velocity. 1 N applied to 1 kg will accelerate 1 m/s/s, and 2 N applied to 1 kg will accelerate 2 m/s/s.
We then looked at an elevator example. We feel heavy when I am accelerating upward (This happens when the elevator starts going up and when it stops going down.) The force of the floor on me is greater then the force of the entire Earth on me, then I feel heavy. We feel light when we are accelerating downward (This happens when you stop going up or start going down.) If the force of the floor on me is less than the force of the entire Earth on me, then I feel lighter. We named 10 N/kg as the gravitational field strength on Earth. On the moon, it is 1.6 N/kg.
After we did some more worksheet problems dealing with force diagrams, and really getting a good grasp of Newton's 3rd Law, we did some more whiteboarding along with a debate as to whether a pair of forces was actually a Newton's 3rd Law Force Pair. (Even though forces are equal and opposite, does not mean they are necessarily a force pair.)
Then we did some lab experiments to determine the difference between static friction and kinetic friction and developed the coefficient of friction by using the force sensors and different surfaces dragged across a wood surface. We determined that static friction was always greater then kinetic friction for the same situation and developed a mathematical model for force of friction.
Something else we discovered is that Earth pulls more on more massive objects. It is due to Newton's 2nd law that everything falls at an acceleration of 10 m/s/s.
We then did some work with Modified Atwood machines and discussed two - body systems (two carts attached by a string and being pulled by a string, or a cart being pulled by a mass on a pulley). We did some practice problems dealing with these type of problems and then had some practice facilitating whiteboard sessions. This was an awesome experience and difficult as well. It made me realize how difficult this can be and yet mentally stimulating at the same time. According to research, students learn better this way.
At this point, we were asked for an operational definition for mass. What is mass? and we could not use the traditional answers for it. We did not have a good definition; however, we did know that something that is more massive resists change in motion more than something with less mass. Again, we reiterated the fact that An object in motion will stay in motion in a straight line at a constant speed as long as the forces are balanced.
The model so far:
- Weight is a measure of gravitational field strength
- Schema tool leads to a Force diagram
- Forces at angles have components
- If the change in velocity is 0, then forces are balanced (in vertical and horizontal directions)
- Acceleration is in direction of unbalanced force
- 10 N/kg is the gravitational field strength on Earth
- Schema
- Force Diagram
- Shadow parts (components)
- Change in velocity = 0 then there are balanced forces
Next, we pushed an air puck across two tables and we had to keep constant contact with it. We ended up running at the end of the two tables (We had someone there at the end of the table to catch the air puck :) ) This was a good introduction to Newton's Second Law. Now we had to determine this again with a lab. Again we used the cart and the tracks. We had to find the relationship between Force, acceleration and mass. For one experiment, we kept mass constant. We used a spring scale (push type) to apply a constant force of 0.5 N, then 1 N, up to 2.5 N and measured the acceleration by using the digital sonic ranger at the end of the track. This was a tricky lab for two reasons. One was trying to keep the force constant at the 5 different forces and the other reason was we had to stop the cart before it crashed into the digital sonic ranger. We found a linear relationship, as force increased, acceleration also increased in a linear fashion. Next experiment, we kept force constant while we increased the mass. We noticed a linear relationship but as mass increased, the acceleration decreased. In both of these labs, acceleration was the dependent variable. This led us to the right causal effect where acceleration is caused by the force. Newtons 2nd Law was established as acceleration = Force (unbalanced) / mass
Mass (in kg) is a quantitative measurement of resistance to change in velocity. 1 N applied to 1 kg will accelerate 1 m/s/s, and 2 N applied to 1 kg will accelerate 2 m/s/s.
We then looked at an elevator example. We feel heavy when I am accelerating upward (This happens when the elevator starts going up and when it stops going down.) The force of the floor on me is greater then the force of the entire Earth on me, then I feel heavy. We feel light when we are accelerating downward (This happens when you stop going up or start going down.) If the force of the floor on me is less than the force of the entire Earth on me, then I feel lighter. We named 10 N/kg as the gravitational field strength on Earth. On the moon, it is 1.6 N/kg.
After we did some more worksheet problems dealing with force diagrams, and really getting a good grasp of Newton's 3rd Law, we did some more whiteboarding along with a debate as to whether a pair of forces was actually a Newton's 3rd Law Force Pair. (Even though forces are equal and opposite, does not mean they are necessarily a force pair.)
Then we did some lab experiments to determine the difference between static friction and kinetic friction and developed the coefficient of friction by using the force sensors and different surfaces dragged across a wood surface. We determined that static friction was always greater then kinetic friction for the same situation and developed a mathematical model for force of friction.
Something else we discovered is that Earth pulls more on more massive objects. It is due to Newton's 2nd law that everything falls at an acceleration of 10 m/s/s.
We then did some work with Modified Atwood machines and discussed two - body systems (two carts attached by a string and being pulled by a string, or a cart being pulled by a mass on a pulley). We did some practice problems dealing with these type of problems and then had some practice facilitating whiteboard sessions. This was an awesome experience and difficult as well. It made me realize how difficult this can be and yet mentally stimulating at the same time. According to research, students learn better this way.
Unit 4 - Free Particle Model - Inertia and Interactions
First of all, we brainstormed about what a force actually is. What comes to mind when you state the word "force?" We were led to understand the 1st rule of forces which is that "All forces must be caused by a physical object made of matter" and then to realize that a force is a push or pull caused by a physical object made of matter. We looked at something simple as a hand holding a book and developed a schema which is a tool to help draw a force diagram. All objects involved with the object are included in the schema and then ultimately we only look at the interactions between objects (We decided to ignore air for now because it has little effect on the book right now, we may include it later.) Here is an example of a schema and its corresponding force diagram.
At this point, we also looked at force diagrams and talked about "shadow vectors" based upon shining light onto the vector from on top or from the side and we would get different sized vectors.
We looked at how the table could be exerting a force onto the bowling ball. We looked at a spring and a person holding a book and how they always sprung back after the weight of the book was added. We also looked at magnets with holes on a rod and how they repelled each other. We related that to the electrons in atoms on the table how they repel. Another way to convince students that there is a force exerted from the table is to reflect a laser beam from a pointer onto a mirror onto the ceiling and the press on the table and it adjusts a little.
We also established that if there is no change in velocity, then the forces are balanced. We also looked at the non-contact forces and established that contact forces would be everything else. We then did some worksheet problems and whiteboarded them. We also had a good discussion about what constitutes a Newton's 3rd Law force pair. We setup a lab where we connected force sensors onto two different carts and did a number of tests on them. Here is a picture of one possible setup:
Other setups included where one car was moving and other over took the first one; connected springs between them; among other scenarios. All showed equal and opposite forces.
Basically, the force units melded into each other, so I am not really sure where one ended and the other one began :)
I will continue on with the next unit as a continuation of forces by discussing Newtons Second Law
We looked at how the table could be exerting a force onto the bowling ball. We looked at a spring and a person holding a book and how they always sprung back after the weight of the book was added. We also looked at magnets with holes on a rod and how they repelled each other. We related that to the electrons in atoms on the table how they repel. Another way to convince students that there is a force exerted from the table is to reflect a laser beam from a pointer onto a mirror onto the ceiling and the press on the table and it adjusts a little.
We also established that if there is no change in velocity, then the forces are balanced. We also looked at the non-contact forces and established that contact forces would be everything else. We then did some worksheet problems and whiteboarded them. We also had a good discussion about what constitutes a Newton's 3rd Law force pair. We setup a lab where we connected force sensors onto two different carts and did a number of tests on them. Here is a picture of one possible setup:
Other setups included where one car was moving and other over took the first one; connected springs between them; among other scenarios. All showed equal and opposite forces.
Basically, the force units melded into each other, so I am not really sure where one ended and the other one began :)
I will continue on with the next unit as a continuation of forces by discussing Newtons Second Law
Unit 3 Constant Acceleration
In Unit 3, we placed a cart on a ramp that was set at an angle and measured its position on the track after we released it from the top of the ramp. We also had the option of using a 1 in steel sphere instead of the cart. We had to mark its position at a set time interval using a dry erase marker and then measure its position away from the beginning. When we graphed the data, we noticed that we got a parabolic curve. We used a graphing utility such as LoggerPro or Plotly or Excel to come up with an equation for the graph. We noticed that when we used a steeper ramp that there was a larger coefficient to the equation. We were asked why the graph was parabolic and we noticed that when we doubled the time, we quadrupled the position.
Then we looked at the relationship between velocity and time and we noticed that we had a linear relationship here. When we compared the coefficients of the position vs time graph with the velocity vs time graph, the coefficients appeared to double.
So we looked at the model so far, by looking at the motion map for carts on a ramp with velocity and acceleration arrows and we had noticed that the velocity increased while the acceleration remained constant. We noticed that with constant acceleration, the position - time graph was a parabolic shape and the velocity - time graph was linear and the acceleration - time graph was constant.
We did another lab where we collected data where different groups had their carts go up or down the ramp with either positive or negative velocities and let the cart come back down. We noticed a relationship between acceleration and velocity. See following picture.
Then we looked at a scenario where the steel sphere went down a ramp onto a flat surface and noticed that it accelerated down the ramp and when with a constant velocity along the flat surface. We looked at the corresponding graphs. We looked at how the area under a velocity - time graph was the displacement of the object and used the graph to develop a math model for displacement. We collected data using different scenarios with the carts down a ramp and found that the values of the acceleration, initial velocity and displacement matched up nicely to the equations.
We then dropped a bean bag onto the motion detector to determine what the free-fall acceleration actually meant. We came up with a value that was pretty close to 9.8 m/s/s and we were comfortable with using 10 m/s/s as the value for future use.
Then we looked at the relationship between velocity and time and we noticed that we had a linear relationship here. When we compared the coefficients of the position vs time graph with the velocity vs time graph, the coefficients appeared to double.
So we looked at the model so far, by looking at the motion map for carts on a ramp with velocity and acceleration arrows and we had noticed that the velocity increased while the acceleration remained constant. We noticed that with constant acceleration, the position - time graph was a parabolic shape and the velocity - time graph was linear and the acceleration - time graph was constant.
We did another lab where we collected data where different groups had their carts go up or down the ramp with either positive or negative velocities and let the cart come back down. We noticed a relationship between acceleration and velocity. See following picture.
We then dropped a bean bag onto the motion detector to determine what the free-fall acceleration actually meant. We came up with a value that was pretty close to 9.8 m/s/s and we were comfortable with using 10 m/s/s as the value for future use.
Thursday, July 9, 2015
Unit 2 Constant Velocity..cont.
The next part of the modeling process is to apply your model by working out problems. We did this with doing problems on a worksheet and then we whiteboarded some of the problems.
We also introduced the idea that displacement is the area under the curve of the velocity - time. And then that led us to our model thus far. We started to attribute algebraic models to our model as well.
I was introduced to motion maps as well. I had never seen these before; however, I like these even though it was hard to do at first. Every dot shows the objects position in a given unit of time, usually one second and there are velocity and acceleration arrows showing the direction and magnitude of each. (We have not introduced acceleration yet, but that is the next unit.)
It was helpful to draw the motion map on the same whiteboard as the graph and connect position - time graph with the velocity - time graph. The great thing about a graphical model is its predictive power. As in a position - time graph, you can predict the position of the object at a given time. The graphical model can give rise to a math model and we can also use a pictoral model such as vectors which we saw on the motion maps.
At this point, we did some whiteboard training and discussed which problems were decided to be whiteboarded and in what order. We went from least complex problem to more complex to lead students to see key ideas for themselves. This is the process of selecting (choosing which problems to whiteboard - due to time constraints we won't always whiteboard every problem) and sequencing (timing of problems - which to do first and so on.) You want to determine the level of group because you want them to struggle but still be successful. Start slow, point out key ideas and realize that nobody cares about the answer, it is about the process. Let students have the "ah-ha" moment. As a teacher, if I tell them what they should have noticed, I rob them of the full learning experience and I just serve to reiterate the notion that I am the source of all answers (which I am not.) In this training, I experienced some of those "ah-ha" moments myself and it was really cool. I want my students to have that same experience.
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