There are 5 interactive lessons: Impulse, Free Fall with Air Resistance, Simple Harmonic Motion, Mechanical Waves and Lunar Motion. All of these are designed for the student to gain a deeper understanding of force and motion.
The unit was designed by Stephen Dickman, Jacob Kelter and Kelvin Lao for classes at Evanston Township High School.
In these lessons, students explore the relationships between the graphs of acceleration, velocity and displacement as a function of time. The students will calculate slope and areas to express the relationships between these quantities of motion. The overall goal is for student to increase their understanding of the all important quantity of acceleration.
In this lesson, you will explore the relationships between the graphs of acceleration, velocity and displacement as a function of time. In addition, you will learn some syntax of NetLogo coding by reading the code responsible for this simulation.
Just interact with the simulation. Note especially what happens when you change Ax(the acceleration). Do some of the motion graphs remind you of earlier activities in class? Which ones?
Do the dot spacings make sense in each case? What does a dot represent? What does the interval between dots represent? Write down the set of initial conditions that would match the graphs of the "Dot Lab" you ran a few days ago. What was your acceleration in the "Dot Lab"?
Set Vxi to 0 and Ax to a positive value on their respective sliders. Now, use your mouse on the velocity graph to find two (x, y) pairs and calculate the slope of the velocity graph. Does this value match the acceleration? Remember the "Dot Lab"! Next, calculate the area under the velocity-time graph. Does this area match the displacement for your interval? Check your calculations with the data table values to the right.
Now set both Vxi and Ax to a positive value and repeat the steps above. Remember, check your results with the data table!
Now set Vxi to a positive value and Ax to a negative one. What happens initially? (Look at the dots) Repeat the steps in #2.
Note: Can you have a "negative area" in this case? What do you think a negative area means? Remember, check your results with the data table!
Now set Vxi to a negative value and Ax to a positive one. What is the difference between these graphs and the ones in #3? What is the sign of the net area under the velocity graph? Does this make sense?
Please look at the code. On what lines are the actual Kinematics Equations? What do you think "set" means at the beginning of these lines of code? How does one multiply variables in this code?
Students will take data from a model of a ball falling on Earth undergoing air resistance. The student will be able to control the mass of one ball and compare it to the fall rate of another ball of greater or less mass. The balls have the same surface area. The students will observe motion graphs and make predictions based on Newton's 2nd Law.
In addition, students will see how code is used to model Newton's Laws.
This model was created by Stephen Dickman, Jacob Kelter and Kelvin Lao.
Directions:
Press "Setup" and then "Go" buttons to run the simulation.
Learning Objectives:
Press "Set up" and "Go" to run the simulation. Make sure the balls have different masses. What do you see happening? Does this make sense- why? Think about the upward and downward driving forces.
After you have run the program, which two graphs are similar? Why must this be so?
Record the terminal velocity of 2 balls of different mass. Which one reaches terminal velocity in a shorter amount of time? Why? Think about question 1.1.
Write down Newton's 2nd law for the turtle when it has achieved terminal velocity. Fnet = ma!
Sketch both forces on a ball as it is moving down before terminal velocity and after it reaches terminal velocity. Draw the vectors to scale as best as you can. Draw the net force vector in each case.
Consider a ball initially thrown up with air resistance. Sketch the force of gravity, air resistance, and velocity vectors on the ball as it is ascending. What is different in this case?
This shows the same model as on the previous page but with force vectors for gravity and air resistance showing.
Run the model with zero initial velocity. Do the vectors shown match what you drew on the previous page? If not, what makes your diagram different?
Set mass 1 to 8kg. As it falls from rest, what is the average acceleration from the start until it reaches terminal velocity? Do this using the velocity-time graph and compare your value to the acceleration-time graph.
Set the initial velocity to be positive. Does the mass travel very far upwards? Why? Answer in terms of F=ma!
As the mass is traveling upwards, what is the sign of the slope of the velocity-time graph? What is the value of the velocity?
As the mass is traveling upwards, what is the sign of the net force on the mass?
Why does the larger mass have a greater force of gravity acting on it? You must use an equation in your answer.
Hard: But think about it!!!!! Why does the smaller mass have a lower terminal velocity? Think about F=ma!
Does the sign of the acceleration and the net force acting on the ball change when the ball starts with an upward velocity and then switches directions?
The net force vs time graph below was produced with the NetLogo model with mass 1 starting with an initial positive (upwards) velocity. There are four regions labeled on the graph: two with positive slope each of which is followed by a region of zero slope. Draw a force vector diagram corresponding to each of these regions. The 2 forces must have appropriate magnitude and direction! For each diagram, also draw an arrow (or a dot if it is equal to zero) for (1) the direction of the velocity and (2) the direction of acceleration. Label all arrows.
On this page you will slightly alter the NetLogo code that produces the model and see what happens.
Click on the bar titled "NetLogo code" to open the code tab. Look for the Newton's 2nd Law lines (they are after line 105) and the lines for air resistance in the code. Set the air resistance coefficient to 0. What should happen? Would the mass matter when the coefficient is 0? Write your best guess and then use the model to check. If you weren't right, then describe what actually happened.
Set the masses to two different values. Change the coefficient of air resistance back to the value -1 and record the terminal velocity for each mass. Then increase and decrease the coefficient of air resistance. What happens to the terminal velocity of the masses when the coefficient of air resistance goes up and down?
Assuming the air resistance coefficient on earth is -1, what would you expect the coefficient of air resistance to be on (1) the moon, (2) Mars and (3) Venus? Why?
Simple Harmonic Motion(SHM) is represented here using a mass that is attached to a spring. The other end of the spring is fixed to the middle of a horizontal surface. In this model there is no friction. This SHM simulation was designed to help students better conceive the relationship between position, velocity and acceleration.
The simulation allows the student to vary the mass of the oscillating mass and the strength constant of the spring. Thus, the student will be able to make conjectures on subsequent motion as the inertia and net force have changed. These variances will help the student gain a deeper understanding of Newton's Laws.
Finally, the SHM simulation can be done in 2 dimensions creating elliptical motion. Newton wrote this is the Principia and the motion is similar to planetary orbits.
The coding was done by Jacob Kelter. Help uploading and editing the lesson was given by Kelvin Lao.
Learning Objectives:
Directions:
This is a simulation of a mass and a spring oscillating on a frictionless table in 1 dimension. Observe the code and observe the motion of the turtle. (You will probably need to increase the speed slider for it to move quickly enough)
Observe the motion of the turtle. What do you notice?
Motion Graphs:
Point out the slope of the x-coordinate vs time graphs and see if it matches the velocity graph below.
Point out the slope of the x-velocity vs time graphs and see if it matches the acceleration graph below.
Calculate the period for one full cycle.
Calculate the frequency for one full cycle.
When velocity is zero what is the position? When the position graph has a negative slope, what is the sign of the velocity? The acceleration?
Increase the mass of the turtle and make a prediction. What should happen? What did happen? Why is this so?
Increase the spring constant and make a prediction. What should happen? What did happen? Why is this so?
Draw the force and velocity vectors on the turtle when it is:
Play with the code as much as you like. Please observe the motion change of the turtle as you change the spring constant and mass of the turtle.
For the following questions, you can look into the NetLogo code tab under the simulation. What does the “SETUP” button initiate?
What does the “GO” button initiate?
Identify which part of the code represents the spring force and paste it below.
Why is the force of gravity, mg, not in play here?
Now the turtle can move in 2 dimensions. If Vy=0, will it move in 2D motion? Explore the model and answer the questions below. (Again you will need to increase the slider speed)
Now, set the turtle in 2 dimensional motion. Play with the model as much as you like. Please observe the motion change of the turtle as you change the spring constant and mass of the turtle. Describe what you see.
Draw the 2D trajectory and include the velocity and force vectors on the turtle at the far end of ellipse and two other points of your choosing.
What other bodies in nature has a trajectory of this shape?
If you increase the mass, is the trajectory larger or smaller? Why is this so?
If you vary the spring constant while keeping the mass fixed, is the trajectory larger or smaller? Why is this so?
This simulation involves the modeling of a basketball hitting the ground and bouncing back up: it is a force, plus, impulse effect. All the physical quantities involved are graphically displayed in this model. Thus, the model reinforces the understanding of Newton's Laws.
This simulation and lesson would created by Stephen Dickman, Kelvin Lao and Jacob Kelter.
7/27/2020
Learning Objectives
On this page you will explore the simulation below which contains a single ball falling and bouncing off the ground.
Note: You will have to increase the speed slider to get it run at a good speed, but, if you want to explore the behavior at a certain moment, you can slow it back down.
Where is the acceleration not -9.8 m/s^2? Why? What is the name of the non-gravitational force acting during contact with the floor? What is the nature of this force, i.e., gravitational or electrical?
Manipulate the value of the mass. During the initial fall, what is the different factor between the acceleration and the force graph? (Hint: there's just one quantity difference)
How many different slopes are there on the velocity graph? Which one is the greatest slope? Why do you think this is so?
How does each slope on the velocity graph relate to the acceleration graph?
From which two graphs can you calculate the impulse?
During which two parts of the trip (in the air or contact with the ground) is the greatest change in momentum?
What quantities will change as you vary the mass? What quantities don't?
During what part of the trip is the gravitational potential + kinetic energy constant? Where is it not constant? What do we call this part of the trip?
You'll notice a downward spike in the (kinetic + gravitational) energy when the ball is stopped on the floor. Where do you think the energy is?
Draw the shape that a real ball would have (1) when it is falling and (2) when its gravitational + kinetic energy is zero.
Why is the Kinetic Energy vs. time graph quadratic?
List which physical quantities change when you change the mass of the ball.
Sketch the force vs. time graph during the whole trip. What does the area under/over force value represent?
Sketch the forces on the ball during free fall, neglect air resistance. Sketch the forces on the ball during the contact with the floor. Draw according to appropriate magnitude.
Sketch a graph of the ball's momentum vs. time. Which displayed graph is this very nearly like?
General Review: Describe each of Newton's Laws in play as the ball falls. As the ball strikes the floor.
The students must press set up and go to run the simulation.
Note: You can make the model run faster by sliding the model speed icon to the right.
In this simulation, we are modeling a basketball with 7 "atoms" connected by springs. So each turtle (circle) in the simulation feels the force of gravity, the force of the springs it is connected to, and the force of hitting the ground.
What is the state of motion of the upper two middle turtles when the lowest one first makes contact with the floor? Why is this so? Which law(s) of Newton is in play here?
What exactly does the area under the force vs time graph equal?
Why does the ball not achieve it original height after one bounce? How does the simulation demonstrate this?
Is the ball always undergoing a change in momentum during this simulation? Why do you know this?
What is the value of the ball's momentum at some point during the initial fall? If the mass were doubled, what would it be?
Draw the force vectors on the ball as it is falling and during contact with the ground.
What, exactly, represents heat in this model. Do you think that heat could lift up the ball to its original height again?
Force Considerations
Change the strength of the impact force(How do you do this?) and see what happens?
Change the strength of the spring force holding these turtles together, what happens? How do you do this?
What do you think elasticity represents in this model or in the whole physical world?
What line would you have to edit to make this model appropriate for a falling ball on the Moon? If the acceleration due to gravity on the Moon is 1/6 the value on Earth, what value would you change in this code line?
This page asks you to answer some reflection questions related to all the CT-STEM lessons you have done so far.
Write at least one big idea that you learned about physics in this lesson or in earlier CT-STEM lessons.
Pick any computational tool/activity that you have used in this lesson or in earlier CT-STEM lessons. Briefly describe the tool and explain how you used it to learn.
Indicate how much you agree or disagree with the following statements:
I enjoyed learning with computational tools/activities so far in this unit.
Indicate how much you agree or disagree with the following statement:
I feel that I successfully learned the content of this lesson.
Compared to lessons without computational tools/activities, I found this lesson more engaging.
Indicate how much you agree or disagree with the following statement:
Compared to lessons without computational tools/activities, I found this lesson more challenging.
Indicate how much you agree or disagree with the following statement:
I felt stressed by the computational tools/activities we have done in this lesson.
Is anything that you learned in this unit relevant to your personal aspirations? If yes, please explain.
The simulation consists of a string of masses linked together by springs to simulate a medium through which energy can travel. The medium allows for transverse and longitudinal waves.
Learning Objectives
Play around with the simulation for a while. Create both kind of waves.
Describe how you make a transverse wave.
Describe how you make a longitudinal wave.
What actually do you do to the medium to create a wave? Must use proper terms!
Explain exactly how you performed "work" on the medium.
Sketch both a longitudinal and transverse wave.
Coding Questions:
Increase the exponent of the spring displacement term. What happens? Why?
Decrease the exponent of the spring displacement term. What happens? Why?
If you increased the mass of each turtle, what would happen to the speed of the wave?
This imperfect model attempts to show the Moon's orbit as it is being perturbed by the Sun. The student will have to state why the model does not accurately simulate the Lunar orbit as the Moon will leave its orbit about the Earth.
This model was created by Jacob Kelter and Stephen Dickman
Learning Objectives
Run the simulation and see what happens. You will have to increase the speed of the model. Change the intial(vx) velocity of the Moon and repeat.
What do you notice the or of the Moon doing? What is this effect called?
State why you believe the orbit of the Moon is doing this?
Sketch all the force and velocity vectors on the Moon at 12, 3, 6 and 9 o'clock. Point out where a new, full and half-moon would be.
Eventually, the Moon will fly away from the Earth, what did it gain in order for this to happen? Thus, why is the model imperfect?
Why do the graphs show negative energy? Why do these graphs oscillate? Do they make sense?
Coding Question:
Try to make a plot of the angular momentum of the Moon about the Earth. What should this plot exhibit? You need to look into the code for this.
In these lessons, students explore the relationships between the graphs of acceleration, velocity and displacement as a function of time. The students will calculate slope and areas to express the relationships between these quantities of motion. The overall goal is for student to increase their understanding of the all important quantity of acceleration.
In this lesson, you will explore the relationships between the graphs of acceleration, velocity and displacement as a function of time. In addition, you will learn some syntax of NetLogo coding by reading the code responsible for this simulation.
Just interact with the simulation. Note especially what happens when you change Ax(the acceleration). Do some of the motion graphs remind you of earlier activities in class? Which ones?
Do the dot spacings make sense in each case? What does a dot represent? What does the interval between dots represent? Write down the set of initial conditions that would match the graphs of the "Dot Lab" you ran a few days ago. What was your acceleration in the "Dot Lab"?
Set Vxi to 0 and Ax to a positive value on their respective sliders. Now, use your mouse on the velocity graph to find two (x, y) pairs and calculate the slope of the velocity graph. Does this value match the acceleration? Remember the "Dot Lab"! Next, calculate the area under the velocity-time graph. Does this area match the displacement for your interval? Check your calculations with the data table values to the right.
Now set both Vxi and Ax to a positive value and repeat the steps above. Remember, check your results with the data table!
Now set Vxi to a positive value and Ax to a negative one. What happens initially? (Look at the dots) Repeat the steps in #2.
Note: Can you have a "negative area" in this case? What do you think a negative area means? Remember, check your results with the data table!
Now set Vxi to a negative value and Ax to a positive one. What is the difference between these graphs and the ones in #3? What is the sign of the net area under the velocity graph? Does this make sense?
Please look at the code. On what lines are the actual Kinematics Equations? What do you think "set" means at the beginning of these lines of code? How does one multiply variables in this code?
This model illustrates the physical quantities that dominate the merger of a binary star system.
I am greatly indebted to Jacob Kelter for helping with the coding of this simulation!
TBD
This model illustrates the physical quantities that dominate the merger of a binary star system.
I am greatly indebted to Jacob Kelter for helping with the coding of this simulation!
TBD
Simulation
During this lesson, you will driving a spaceship, through space, and attempting to dock it safely. The rocket engines fire an impulse in order to accelerate. How do spaceships navigate?
CT-STEM, Northwestern University.
This lesson was coded by Jacob Kelter.
In this lesson you will program a spaceship to reach its destination by scheduling when the engines produce an impulse. Remember, Impulse = F*t!
Attempt to dock the rocket to the green patch(Space Station). To do it safely, the spaceship must be stopped at the station. Once you have figured out a code, take a screenshot and upload it below.
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Explain the process you went through to find your solution to question 1. What did you do try first? What did you notice? What did you then have to change? etc. Try to explain all the steps you took and how you figured out what to do next.
When the left engine is turned on, which direction is the rocket accelerated in? Why is this?
After an engine has been fired and no engines are on anymore, what does the rocket do motion-wise? Why is this? In your response make sure to note which of Newton's laws explains the motion.
Sketch the graph of the force of the left engine vs. time from your solution to question 1.
Sketch the graph of the force in the x direction (regardless of which engine caused it) vs. time from your solution to question 1.
What is the sum of the area under the curve for your sketch in the previous section? Is the spaceship displaced as a result of these impulses?
What is the sum of the impulses from your solution to question 1? Will this be true for any solution? Explain.
Considering a real rocket: why does burning fuel and allowing the resulting hot gas to only shoot out in one direction propel the rocket?
In our model, the mass of the rocket is constant, but a real rocket loses mass due to burning fuel and ejecting the resulting hot gas. How would this affect the motion and how could we make our model more realistic to take this into account?
Your job now is to negotiate Maze 1 and 2. Remember, you must dock the spaceship safely.
Upload a screenshot of your successful blocks for Maze 1.
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Explain the process you went through to find your solution to the previous question. What did you try first? What did you notice? What did you then have to change? etc. Try to explain your thinking.
How would you get the ship to accelerate up and to the right? Draw the 2 force vectors on the ship. Also, draw the resultant force on the ship.
Upload a screenshot of your successful code of Maze 2.
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Again, explain the process you went through to find your solution to the previous question. Explain your thinking.
Now switch the maze to "none horizontal." Play around and try to get to the station as fast as possible (in terms of ticks). How did you do this? How many ticks did it take?
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Keep the maze on "none horizontal." Now try to get to the station as slowly as possible (in terms of ticks). How did you do this? How many ticks did it take?
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Sketch two force vs time graphs. One for the minimum time travel and one for the maximum time travel from the last two questions. Label the ticks on the x-axis for the middle and end of each graph.
Write out the impulse equation for the left engine firing for a time, t. Write out the impulse equation for the right engine firing for a time, t. Remember the direction matters in the equation!
Assume the rocket is 5kg and is moving at 4m/s to the right. The left engine is now fired which applies a 1N force and is kept on for 15 seconds. What will the final velocity be?
Assume the rocket is 5kg and is moving at 4m/s to the right. This time, the right engine is fired which applies a 1N force and is kept on for 15 seconds. What will the final velocity be?
Now things get trickier. Each time you click "setup target," the green target will be in a new place. That means you can't use trial and error to figure out the engine schedule that will get you there. Instead you need to figure out a way to calculate it. You can use the "ruler" button to measure how far the ship is from the target. In this version, you can also adjust how strongly the engines fire, not just how long they fire for.
Start with the "target-mode" option set to "random target 1D." In this mode, the target will always be at the same y-coordinate as the space ship, but will be a random distance away in the x-direction each time you click "setup target". Your job is to figure out a way to calculate what the engine schedule should be to reach the target. There are multiple ways to do this.
In the box below, describe your method each time you try, even if it doesn't work yet. It will probably take you at least a few tries to perfect your method so that you can consistently land on the target. So, each time you try, describe your method and what happened. Then describe how you are changing your method. Repeat this until you have a method that consistently works.
After the engine stops firing, what happens to the velocity? To the momentum?
Take the initial velocity as zero and the mass as 8 kg. If the left rocket applied 10N of force for 8 seconds, what would the final velocity be? What would the momentum be? How far would it travel in those 8 seconds?
Sketch an exact graph of the velocity vs. time for the scenario in question 3.
What does the area under the graph equal?
If the mass in question 3, was 4 kg, what would the final velocity be after the 8 seconds? What is the momentum after the 8 seconds?
Sketch an exact graph of the force vs. time for the scenario in question 3.
What does the area under the graph equal?
Now set the "target-mode" to "random target 2D." In this mode, the target will be at a random distance from the rocket in both directions each time you click "setup target". Once again, your job is to figure out a way to calculate what the engine schedule should be to reach the target.
Again, in the box below, describe your method each time you try, even if it doesn't work yet. It will probably take you at least a few tries to perfect your method so that you can consistently land on the target. So, each time you try, describe your method and what happened. Then describe how you are changing your method. Repeat this until you have a method that consistently works.
If you've gotten to this point, it's time to celebrate by drawing something cool with the rocket! Play around with setting the engine schedule to get the rocket to draw a shape or a design. When you have something you like, take a screen shot of your blocks and upload them here.
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During this lesson, you will driving a spaceship, in space, and attempting to dock it safely. The rocket engines fire an impulse in order to accelerate. How do they achieve this acceleration?
CT-STEM, Northwestern University.
This lesson was coded by Jacob Kelter.
In this lesson you will program a spaceship to reach its destination by scheduling when to turn its four engines on and off.
Attempt to dock the rocket to the green patch(Space Station). To do it safely, the spaceship must be stopped at the station. Once you have figured out a code, take a screenshot and upload it below.
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After the rocket engine has been fired, what does the rocket do motion-wise? What law governs this motion?
Considering a real rocket: what laws govern its motion as it forces hot gas in one direction?
Note: the rocket loses gas/mass as it does this. Would this affect the motion? How?
Sketch the graph of the force of the left engine vs. time. Assume the force is constant throughout the firing. Take the firing time to be 5 seconds.
Write out the impulse equation for the left engine firing for a time, t. Write out the impulse equation for the right engine firing for a time, t. Remember the direction matters in the equation!
Now, assume the rocket is moving at 4m/s to the right. The left engine is now fired, what is the resulting motion? If the mass is 5kg and the left engine applies a 1N force for 15 seconds, what will the final velocity be?
Now, assume the rocket is moving at 4m/s to the right. The right engine is now fired, what is the resulting motion? If the mass is 5kg and the left engine applies a 1N force for 15 seconds, what will the final velocity be?
Say you got the rocket to move and then come to a complete stop. What would be the sum of the impulses?
How would you get the rocket to accelerate up and to the right? Draw the force vectors on the rocket, include the resultant force and velocity vectors.
Your job now is to negotiate Maze 1 and 2. Remember, you must dock the spaceship safely.
Upload your successful code for Maze 1.
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Upload a screenshot of your successful code of Maze 2.
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How would you get to the station in the least amount of time? How would you get there in the most amount of time?
Sketch the force vs time graphs for the maximum and minimum time travel.
Here, you will explore the difference between displacement, velocity, acceleration, time, force and mass!
Take the initial velocity as zero and the mass as 8 kg. If the left rocket applied 10N of force for 8 seconds, how long would it take to travel 1000m? What would the final velocity be at 1000m? What would the momentum be at 1000m?
Sketch a graph of the velocity vs. time.
If the mass in #1, was 4 kg, what would the final velocity be after 1000m? What is the momentum at 1000m?
