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Bungee Jump

Activity Information

Learning Goals

  • Students will use their understanding of energy and free fall to manipulate difference scenarios related to bungee jumping

Prior Knowledge Required

  • Conservation of Energy
  • Hooke's Law
    • $F=-kx$
  • Kinematics

Code Manipulation

  • Interpret minimally working code
  • Add to preexisting code
  • Create new code to model scenario

—-

Activity

Handout

Bungee Jumping Mr. Spencer's physics class wants to go bungee jumping. The closet spot that Western will pay for them to go is the Parma Adventure Park. Below is some information from their website:

Looking for the best bungee jumping in Spring Arbor? The Parma Adventure Park has an exciting option for your favorite adrenaline junkee. Get your maximum rush at our relatively reliable Freefall Bungee Jump Tower. Prepare yourself for that impending, gut-wrenching feeling as you climb to the top, and then fall through our trap door for an exhilarating free fall.
Our tower, harnesses, and gear are specially engineered with a safety record of 98%! Our staff will assist you in making his the experience of a lifetime, whether you need some calming reassurance or the big “1-2-3-Go!” Feel the thrill as you hurtle towards the ground below, only to stop right before you reach the ground*
*Parma Adventure Park is not responsible for accidents resulting from patrons giving incorrect information

The tower is 25 meters high. Before you climb the steps to the top, everyone needs the right bungee cord for them. The bungee cords are all the same length, but some stretch more easily than others. Develop a method for determining which cord to assign to each member of your group using the following minimally working program.

Challenge activity: The highest numbered bungee cord is not enough for your chaperone. The staff wants to attach two different bungee cords to his harness, one on each side. Modify your computer model to include a second bungee cord and use it to develop a method for determine which two bungee cords the staff needs to use.

Code

Link

  1. GlowScript 2.7 VPython
  2. # Set up display window
  3. scene.width = 500
  4. scene.height = 400
  5. scene.background=color.white
  6. scene.center = vec(0, 20, 0)
  7.  
  8. # Intial information: Enter your assigned height
  9. #h=int(prompt("What is your assinged height?"))
  10. #height = vec(0, h ,0)
  11. height = vec(0, 25, 0)
  12. pivot = height + vec(0,10,0)
  13.  
  14.  
  15. # Create a ceiling, a person, a floor, the rocks and a spring.
  16. ceiling=box(size=vec(10,2,10), color=color.magenta)
  17. ceiling.pos = pivot + vec(0, ceiling.size.y/2,0)
  18.  
  19. person=sphere(radius=2, velocity = vec(0,0,0), color=color.yellow)
  20. person.pos = height + vec(0,person.radius,0)
  21.  
  22. floor=box(size=vec(10,1,10), color=color.magenta)
  23. floor.pos=vec(0,person.pos.y-person.radius-(floor.size.y/2),0)
  24.  
  25. rocks=box(pos=vec(0,-1,0), size=vec(10,2,10), color=color.gray(.5))
  26.  
  27. Spring=helix(pos=pivot, axis=person.pos-pivot, coils=10, radius=2)
  28. lengthSpring = Spring.axis #initial length of the spring (fixed)
  29.  
  30.  
  31. # Define parameters
  32. mPerson = 70
  33. g = vec(0,-9.81,0)
  34. t=0
  35. tf = 20
  36. dt = 0.01
  37.  
  38. #ENERGY
  39. #How do energy concepts help us know which bungee cord to use?
  40.  
  41. #Define the spring constant
  42.  
  43.  
  44. ####################EXTRA: Create a force vector########################
  45. # FnetArrow = arrow(pos=person.pos, axis=vec(0, 0, 0), color=color.red)#
  46. ########################################################################
  47.  
  48. ############EXTRA: Create an energy graph#####################
  49. # energyGraph = graph(xtitle='time (s)', ytitle='energy (J)')#
  50. # TotalGraph= gcurve(color=color.black, label='Total Energy')#
  51. ##############################################################
  52.  
  53. # Set up a disappearing floor for the trapdoor
  54. scene.pause('Click to remove floor')
  55. floor.visible = False
  56.  
  57.  
  58. # Dropping the person once the floor is gone
  59. while True:
  60. rate(100)
  61.  
  62. #FORCES
  63. #Define the forces acting on the person (Remember Hooke's Law)
  64. #Define the net force
  65.  
  66. # MOVEMENT
  67. # Update the person's velocity
  68. # Update the person's position
  69. Spring.axis = person.pos-pivot # Update the length of the spring
  70.  
  71. # Change the person's color to red if they hit the rocks
  72. if person.pos.y< (rocks.pos.y+.99+person.radius):
  73. person.color=vec(1,0,0)
  74.  
  75. # Update the clock
  76. t = t + dt
  77.  
  78. #####EXTRA: FORCE VECTORS######
  79. # FnetArrow.pos = vec(0,0,0) #
  80. # FnetArrow.axis = vec(0,0,0) #
  81. ###############################
  82.  
  83. ##EXTRA: ENERGY GRAPHS###
  84. # TotalGraph.plot(t,TE) #
  85. #########################
  86.  
  87. #Have the computer print the height of the person at the end of the program (won't happen until the while loop ends)
  88. #print("h =", (person.pos.y-person.radius))
  89. #Compared to the floor's surface
  90. #print("floor = ", floor.pos+1)

Answer Key

Handout

Code

Link

  1. GlowScript 2.7 VPython
  2. # Set up display window
  3. scene.width = 500
  4. scene.height = 400
  5. scene.background=color.white
  6. scene.center = vec(0, 20, 0)
  7.  
  8.  
  9. # Intial information: Enter your assigned height
  10. #h=int(prompt("What is your assinged height?"))
  11. #height = vec(0, h ,0)
  12. height = vec(0, 25, 0)
  13. pivot = height + vec(0,10,0)
  14.  
  15.  
  16. # Create a ceiling, a person, a floor, the rocks and a spring.
  17. ceiling=box(size=vec(10,2,10), color=color.magenta)
  18. ceiling.pos = pivot + vec(0, ceiling.size.y/2,0)
  19.  
  20. person=sphere(radius=2, velocity = vec(0,0,0), color=color.yellow)
  21. person.pos = height + vec(0,person.radius,0)
  22.  
  23. floor=box(size=vec(10,1,10), color=color.magenta)
  24. floor.pos=vec(0,person.pos.y-person.radius-(floor.size.y/2),0)
  25.  
  26. rocks=box(pos=vec(0,-1,0), size=vec(10,2,10), color=color.gray(.5))
  27.  
  28. Spring=helix(pos=pivot, axis=person.pos-pivot, coils=10, radius=person.radius)
  29. lengthSpring = Spring.axis #initial length of the spring (fixed)
  30.  
  31.  
  32. # Define parameters
  33. mPerson = 70
  34. g = vec(0,-9.81,0)
  35. t=0
  36. tf = 20
  37. dt = 0.01
  38.  
  39. #Use energy to determine the spring constant
  40. Egrav = abs(mPerson*g.y*height.y)
  41. kSpring = abs(2*Egrav/(height.y**2))
  42. #kSpring = 47
  43.  
  44.  
  45.  
  46. #Create the force vectors
  47. FgravArrow = arrow(pos=person.pos, axis=vec(-2,0,0), color=color.red)
  48. FspringArrow = arrow(pos=person.pos+vec(2, 0, 0), color=color.blue)
  49. FnetArrow = arrow(pos=person.pos, axis=vec(0, 0, 0), color=color.black)
  50.  
  51. #Energy graph showing kinetic energy (max at eq) and spring potential (0 at eq)
  52. energyGraph = graph(xtitle='time (s)', ytitle='energy (J)')
  53. KineticGraph = gcurve(color=color.green, label='Kinetic')
  54. SpringGraph = gcurve(color=color.blue, label='Spring Potential')
  55. GravGraph = gcurve(color=color.red, label='Grav. Potential')
  56. TotalGraph= gcurve(color=color.black, label='Total Energy')
  57.  
  58.  
  59.  
  60. # Set up a disappearing floor for the trapdoor
  61. scene.pause('Click to remove floor')
  62. floor.visible = False
  63.  
  64.  
  65. # Dropping the person once the floor is gone
  66. while t<tf:
  67. #while person.velocity.y <=0:
  68. rate(200)
  69.  
  70. #Define the forces so they update as time goes on
  71. Fgrav = mPerson * g
  72. Fspring = -kSpring * (Spring.axis-lengthSpring) #Fspring = -k * delta x
  73. Fnet = Fspring + Fgrav
  74.  
  75. # Movement - update the velocity of the person, the position of the person and the length of the spring
  76. person.velocity = person.velocity + (Fnet/mPerson)*dt
  77. person.pos = person.pos + person.velocity*dt
  78. Spring.axis = person.pos-pivot
  79.  
  80. # Change the person's color to red if they hit the rocks
  81. if person.pos.y< (rocks.pos.y+.99+person.radius):
  82. person.color=vec(1,0,0)
  83.  
  84. # Update the clock
  85. t = t + dt
  86.  
  87. #Show the force vectors
  88. FgravArrow.pos = person.pos+vec(-2,0,0)
  89. FgravArrow.axis = Fgrav/(1e2)
  90. FspringArrow.pos = person.pos+vec(2, 0, 0)
  91. FspringArrow.axis = Fspring/(1e2)
  92. FnetArrow.pos = person.pos
  93. FnetArrow.axis = Fnet/(1e2)
  94.  
  95. #Calculate the energies in each moment
  96. KE=0.5*mPerson*mag(person.velocity)**2
  97. SPE=0.5*kSpring*mag(Spring.axis-lengthSpring)**2
  98. GPE=abs(mPerson*g.y*(person.pos.y-person.radius))
  99. TE=KE+SPE+GPE
  100.  
  101. #Graph the energies
  102. KineticGraph.plot(t, KE)
  103. SpringGraph.plot(t,SPE)
  104. GravGraph.plot(t,GPE)
  105. TotalGraph.plot(t,TE)
  106.  
  107.  
  108.  
  109. #Have the computer print the height of the person at the end of the program (won't happen until the while loop ends)
  110. #print("h =", (person.pos.y-person.radius))
  111. #Compared to the rocks's surface
  112. #print("rocks = ", rocks.pos.y+1)

See Also

  • repository/bungee_jump.1605476799.txt.gz
  • Last modified: 2020/11/15 21:46
  • by porcaro1