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Terminal Velocity

Activity Information

Learning Goals

  • $\Sigma F = 0$ does not mean no motion
  • Relationship between terminal velocity and net force
  • Use a computer simulation to model the impact of proposed solutions to a complex real-world problem with numerous criteria and constraints on interactions within and between systems relevant to the problem HS-ETS1-4
  • 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 accelerations HS-PS2-1
    • Assessment Boundary: limited to one-dimensional motion and to macroscopic objects moving at non-relativistic speeds

Prior Knowledge Required

  • Newton's second law of motion
  • Drag equation
    • $D=\dfrac{1}{2}C\rho v^2A$
  • Terminal velocity
    • $V=\sqrt{\dfrac{2W}{C\rho A}}$
  • Gravitational force

Code Manipulation

  • Copying/pasting code
  • Creating code from scratch
    • Translating equations into code
  • While loops and if statements

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Activity

Handout

Terminal Velocity A coin is being dropped from the top of a building. When will it reach terminal velocity? How does the force of gravity compare to the force of air resistance? Take a look at the unfinished code and answer the following questions:

Pre-coding Questions
  1. Create a graph showing how you think the velocity of the coin will change over time
  2. Create a graph showing how you think the forces of gravity, air resistance, and net force change as the coin approaches the ground.

Code

Link

  1. GlowScript 2.8 VPython
  2. #Window Setup
  3. scene.width = 500
  4. scene.height = 400
  5.  
  6. #Objects
  7. ground = box(pos=vec(0,-250,0), size=vec(700,100,2), texture="https://images.pexels.com/photos/207204/pexels-photo-207204.jpeg?auto=compress&cs=tinysrgb&h=750&w=1260" )
  8. coin = cylinder(pos=vector(0,0,0), axis=vector(0.5,0,0), radius=15.305, textures=textures.metal)
  9. coin.rotate(angle=90, axis=vector(1,1,1))
  10.  
  11. #Initial Object Properties and Constants (time and time step)
  12. g = vec(0,-9.81,0) #Acceleration due to Gravity
  13. coin_m = 0.01134 #mass of the object
  14. drag_co = 1.15 #Drag Coefficient of
  15. t = 0 #Initial Time
  16. dt = 0.01 #Time Step
  17. tf = 0 #Final Time
  18. air_density = 1.2754 #Density of the air
  19. coin_r = .015305
  20. Fgrav = vec(0,0,0)
  21. Fdrag = vec(0,0,0)
  22.  
  23. #Initial Velocity (coin_v) and Momentum Vectors (coin_p)
  24. #coin_v =
  25. #coin_p =
  26.  
  27. #Create an arrow to visualize the particle's forces
  28.  
  29.  
  30. #Set up the graphs
  31. force_comparison_graph = graph(title='Comparison of Forces on a Coin Reaching Terminal Velocity',xtitle='time (s)',ytitle='Force (N)',fast=False,width=1000)
  32. velocity_graph = graph(title='Velocity of a Coin in Freefall Over Time',xtitle='time (s)', ytitle='Velocity (m/s)',fast=False,width=1000)
  33. #Drag and Fgrav and Fnet on the same plot
  34. Fdrag_f = gcurve(graph=force_comparison_graph,color=color.red,width=4,markers=False,label='Drag Force')
  35. Fgrav_f = gcurve(graph=force_comparison_graph,color=color.blue,width=4,markers=False,label='Fgrav')
  36. Fnet_f = gcurve(graph=force_comparison_graph,color=color.purple,width=4,markers=False,label='Fnet')
  37. #Velocity on its own plot
  38. velocity_f = gcurve(graph=velocity_graph,color=color.green,width=4,markers=False,label='Coin Velocity')
  39.  
  40. #Calculation Loop
  41. while True: #Change this so the coin stops when it hits the ground
  42. rate(100)
  43. #Make the coin move
  44.  
  45.  
  46. #Keep the arrows representing the particle's velocity and acceleration
  47.  
  48.  
  49. #Plot on the graphs
  50. velocity_f.plot(t,coin_v.y)
  51. Fdrag_f.plot(t,Fdrag.y)
  52. Fgrav_f.plot(t,Fgrav.y)
  53. Fnet_f.plot(t,Fnet.y)
  54.  
  55. t += dt #Advance the time by 1 time step

Answer Key

Handout

Code

  1.  

See Also

  • repository/terminal_velocity.1598976986.txt.gz
  • Last modified: 2020/09/01 16:16
  • by porcaro1