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--- repository:terminal_velocity [2020/09/01 16:48]
porcaro1 [Answer Key]
+++ repository:terminal_velocity [2021/02/18 19:17] (current)
porcaro1 [Answer Key]
@@ Line 22: / Line 22: @@
 ====Activity====
 ===Handout===
+{{ :repository:terminal_velocity.png?nolink&600|}}
 ** 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 [[https://www.glowscript.org/#/user/david.pastula/folder/MyPrograms/program/TerminalVelocity-MinimalProgram/edit | unfinished code]] and answer the following questions:
 ==Pre-coding Questions==
@@ Line 29: / Line 31: @@
   - Using information provided by the code, calculate the terminal velocity of the falling coin. Label each part of the terminal equation, including units.
-==Post-coding Questions==
+Now with your group, complete the provided code. Be sure to include arrows showing the magnitude of forces acting on the coin. As well, create a velocity vs. time graph and a forces vs. time graph (Pre-coding Questions 1 and 2). When your code is complete, answer the following questions:
+==Post-coding Questions/Reflection==
   - Describe your contributions to the coding process within your group.
   - What did you find the terminal velocity to be based on the graph produced by the code? Does this agree with your calculations?
   - Reflect on your predicted graphs. Explain how they were similar/different than your coding graphs. Revise your graphs as needed.
 ===Code===
-[[https://www.glowscript.org/#/user/david.pastula/folder/MyPrograms/program/TerminalVelocity-MinimalProgram/edit | Link]]
+[[hthttps://www.glowscript.org/#/user/porcaro1/folder/RepositoryPrograms/program/TerminalVelocity-Incomplete | Link]]
 <code Python [enable_line_numbers="true"]>
 GlowScript 2.8 VPython
@@ Line 96: / Line 99: @@
 ===Handout===
 ==Pre-coding Answers==
-  - INSERT PICTURE
+  - {{:repository:terminal_velocity_velocity.png?nolink&600|}}
-  - INSERT PICTURE
+  - {{:repository:terminal_velocity_forces.png?nolink&600|}}
-  - The equation for terminal velocity is $V=\sqrt{\dfrac{2W}{C\rho A}}$, where
+  - The equation for terminal velocity is $v=\sqrt{\dfrac{2W}{C\rho A}}$, where
-    - $W$ is the weight of the coin (N)
+    * $W$ is the weight of the coin (N)
-      - this is calculated by multiplying the mass of the coin by the acceleration of gravity: $W= 0.01135 \text{kg} * 9.81 \text{m/s/s} = 0.111 \text{N}$
+      * this is calculated by multiplying the mass of the coin by the acceleration of gravity: $W= 0.01135 \text{kg} * 9.81 \text{m/s/s} = 0.111 \text{N}$
-    - $C$ is the drag coefficient (1.15, no units)
+    *  $C$ is the drag coefficient (1.15, no units)
-    - $\rho$ is the density of air (1.2754 kg/m³)
+    *  $\rho$ is the density of air (1.2754 kg/m³)
-    - $A$ is the area of the coin
+    *  $A$ is the area of the coin
-      - this is calculated by squaring the radius of the coin and multiplying it by pi: $A= (0.015305 \text{m})^2 * \pi = 0.000736 \text{m²}$
+      *  this is calculated by squaring the radius of the coin and multiplying it by pi: $A= (0.015305 \text{m})^2 * \pi = 0.000736 \text{m²}$
-    - $v=\sqrt{\dfrac{2*0.111}{1.15*1.275*0.000736}}=14.3 \text{m/s}$
+    *  $v=\sqrt{\dfrac{2*0.111}{1.15*1.275*0.000736}}=14.3 \text{m/s}$
+==Post-coding Answers==
+Use the previous answers and the completed code below to guide your reflection.
 ===Code===
-<code Python [enable_line_numbers="true", highlight_lines_extra=""]>
+[[https://www.glowscript.org/#/user/porcaro1/folder/RepositoryPrograms/program/TerminalVelocity-Solution | Link]]
+<code Python [enable_line_numbers="true", highlight_lines_extra="24,25,28,29,44,46,47,48,49,50,51,54,55,56,57"]>
+GlowScript 2.8 VPython
+#Window Setup
+scene.width = 500
+scene.height = 400
+#Objects
+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" )
+coin = cylinder(pos=vector(0,0,0), axis=vector(0.5,0,0), radius=15.305, textures=textures.metal)
+coin.rotate(angle=90, axis=vector(1,1,1))
+#Initial Object Properties and Constants (time and time step)
+g = vec(0,-9.81,0) #Acceleration due to Gravity
+coin_m = 0.01135 #mass of the object
+drag_co = 1.15 #Drag Coefficient of
+t = 0 #Initial Time
+dt = 0.05 #Time Step
+tf = 0 #Final Time
+air_density = 1.2754 #Density of the air
+coin_r = .015305
+Fgrav = vector(0,coin_m*g.y,0)
+Fdrag = vec(0,0,0)
+#Velocity and Momentum Vectors
+coin_v = vec(0,0,0) #Initial Velocity
+coin_p = coin_m*coin_v #Initial Momentum
+#Create an arrow to visualize the particle's forces
+FdragArrow = arrow(pos=coin.pos, axis = Fdrag*1000, color = color.green)
+FgravArrow = arrow(pos=coin.pos, axis = Fgrav*1000, color = color.red)
+#Set up the graphs
+force_comparison_graph = graph(title='Comparison of Forces on a Coin Reaching Terminal Velocity',xtitle='time (s)',ytitle='Force (N)',fast=False,width=1000)
+velocity_graph = graph(title='Velocity of a Coin in Freefall Over Time',xtitle='time (s)', ytitle='Velocity (m/s)',fast=False,width=1000)
+#Drag and Fgrav and Fnet on the same plot
+Fdrag_f = gcurve(graph=force_comparison_graph,color=color.red,width=4,markers=False,label='Drag Force')
+Fgrav_f = gcurve(graph=force_comparison_graph,color=color.blue,width=4,markers=False,label='Fgrav')
+Fnet_f = gcurve(graph=force_comparison_graph,color=color.purple,width=4,markers=False,label='Fnet')
+#Velocity on its own plot
+velocity_f = gcurve(graph=velocity_graph,color=color.green,width=4,markers=False,label='Coin Velocity')
+#Calculation Loop
+while coin.pos.y > -200: #Makes the coin stop when it hits the ground
+    rate(100)
+    Fgrav = vector(0,coin_m*g.y,0)
+    Fdrag = vec(0,air_density*drag_co*pi*coin_r**2*coin_v.y**2/2,0)
+    Fnet = Fgrav+Fdrag
+    coin_p += Fnet*dt
+    coin.pos += (coin_p/coin_m)*dt
+    coin_v = coin_p/coin_m
+    #Keep the arrow representing the particle's velocity and acceleration
+    FdragArrow.pos = coin.pos
+    FdragArrow.axis = Fdrag*1000
+    FgravArrow.pos = coin.pos
+    FgravArrow.axis = Fgrav*1000
+    #Plot on the graphs
+    velocity_f.plot(t,coin_v.y)
+    Fdrag_f.plot(t,Fdrag.y)
+    Fgrav_f.plot(t,Fgrav.y)
+    Fnet_f.plot(t,Fnet.y)
+    t += dt #Advance the time by 1 time step
 </code>
 ----
 ====See Also====
-  *
+  *[[beating_the_train | Beating the Train]]