Computational Dynamics Lab¶
name: __
Answer the questions below by performing the necessary computation. Much of the code can be copied from the Intro to Computational Dynamics notebook.
After completion, turn in this ipynb
file on Blackboard and the paper lab
report in class.
from numpy import *
import matplotlib.pyplot as plt
A. Projectile Motion¶
Use the code from the Intro to Computational Dynamics notebook to perform the following trials and answer the corresponding questions in the lab report.
- Test the flight with a different mass $m$. Does this affect the trajectory?
- The example code uses $\Delta t=0.01$ s. Smaller values of $\Delta t$ will also give accurate results. Try to run the projectile motion with $\Delta t=0.4$ s. Is the range and maximum height correct with $\Delta t = 0.4$ s? Find the $\Delta t$ value at which the range is inaccurate by about 10%.
- Find the projectile range for several initial angles. Print the range at the end of each loop. Record the angle that provides the maximum range. (Optional bonus step: make a plot of range versus launch angle.)
Hint: Copy the whole code block from the section called "A Loop in a Loop" into this notebook. Then edit it to answer the questions above.
# your code here
B. Projectile with Air Drag¶
Write a new force function for a spherical projectile that experiences air drag throughout its flight. Refer to the text section 6.4 if necessary. Use the density of air, $\rho = 1.2 \; \rm{kg}/\rm{m}^3$, drag coefficient $C = 0.5$, and initial velocity 10 m/s at $60^\circ$.
Hint: Your function should get the input parameters that it needs for the calculation. Something like
def drag_force(C,A,v):
...
- Projectile motion in a vacuum is independent of mass, as you found above. What about projectiles with air drag? Consider an iron cannonball and a styrofoam ball of the same size (radius 3.8 cm). Find the range of the iron cannonball (mass 1.8 kg) and the range of a styrofoam ball (mass 12 g).
- Suppose you go skydiving.
What is your terminal velocity if you're tucked into a spherical shape
($C \approx 0.5$)?
What is your terminal velocity if you're spread-eagle ($C \approx 1.3$)?
(Make reasonable estimates of your own body's mass and size.)
You must show how to use the same code to find the terminal velocity
-- your answer should agree with (but not use)
the equation in section 6.4.
Hint: start with an initial position of
(10e3,0)
and a very small initial velocity. Then check the final $y$-velocity valuevv[-1,1]
.
# your code here