Lesson 2. Free Fall with Air Resistance

Stephen Dickman, Jacob Kelter
Physics
Estimated time for students: two 45 minute periods.
AP Physics 1
v3

Overview

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.

Standards

Computational Thinking in STEM 2.0
  • Computational Modeling and Simulation Practices
    • [CT-MODEL-1] Using computational models to understand a complex phenomenon
    • [CT-MODEL-2] Using computational models to hypothesize and test predictions
    • [CT-MODEL-3] Using a computational tool to understand a system's compenents and dynamics
Next Generation Science Standards
  • Physical Science
    • [HS-PS2-1] Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.
    • [MS-PS4-2] Develop and use a model to describe that waves are reflected, absorbed, or transmitted through various materials.

Credits

This model was created by Stephen Dickman, Jacob Kelter and Kelvin Lao.

Activities

  • 1. Free Fall Model with Air Resistance
  • 2. Free Fall with Force Vectors Displayed
  • 3. Coding Questions

Student Directions and Resources


Directions:

Press "Setup" and then "Go" buttons to run the simulation.

Learning Objectives:

  • The student will better learn the application of Newton's 2nd Law
  • The student will review graphs of motion vs. time
  • Students will learn to manipulate computational codes and make predictions due to these changes

1. Free Fall Model with Air Resistance


 


Question 1.1

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.



Question 1.2

After you have run the program, which two graphs are similar? Why must this be so?



Question 1.3

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.



Question 1.4

Write down Newton's 2nd law for the turtle when it has achieved terminal velocity. Fnet = ma!



Question 1.5

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.

Note: Draw your sketch in the sketchpad below


Question 1.6

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?

Note: Draw your sketch in the sketchpad below


2. Free Fall with Force Vectors Displayed


This shows the same model as on the previous page but with force vectors for gravity and air resistance showing. 


Question 2.1

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?



Question 2.2

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.



Question 2.3

Set the initial velocity to be positive. Does the mass travel very far upwards? Why? Answer in terms of F=ma!



Question 2.4

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?



Question 2.5

As the mass is traveling upwards, what is the sign of the net force on the mass?



Question 2.6

Why does the larger mass have a greater force of gravity acting on it? You must use an equation in your answer.



Question 2.7

Hard: But think about it!!!!! Why does the smaller mass have a lower terminal velocity? Think about F=ma!



Question 2.8

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?



Question 2.9

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. 

Note: Draw your sketch in the sketchpad below


3. Coding Questions


On this page you will slightly alter the NetLogo code that produces the model and see what happens. 

 


Question 3.1

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. 



Question 3.2

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?



Question 3.3

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?