Assignment -
A. Investigate the effect of backspin and dimples on the motion of a golf ball. In this case, assume that the initial velocity is 70 m/s. The effect of dimples on a golf ball can have a significant effect on the range of the ball.
For this case assume that Cd = 0.5 for speeds up to 14 m/s and Cd =7.0/v for higher speeds.
For the Magnus force, use Sω0/m ≈ 0.25 s-1.
The mass of a golf ball is 0.04593 kg and its radius is 3 cm.
Plot a few sample trajectories for different launch angles.
What is the optimal angle for achieving maximum range?
Compare that to the results for a smooth ball where Cd is constant Cd =0.5.
[Computer. Turn in the program, results and 2 plots for the smooth versus non-smooth ball. Be sure to label your plots.]
- In question (A), modify your range program to compute the range for a golf ball.
- To find the correct optimal angle, make sure you sample a large range of angles.
Pendulums -
1. In the small angle approximation, the total energy of a simple pendulum is
E = ½mL2ω2 + ½mgLθ2 - mgL
Show analytically that E monotonically increases with time when the Euler method is used to compute the motion. [Pencil]
2. Write a version of the pendul program that uses:
(a) the Euler-Cromer method
(b) the Leap-Frog method
(c) the mid-point method
Run your program for the cases in figures 2.7 - 2.8 of the text. Compare your results with the Euler and Verlet methods. A table of input parameters is shown below.
|
Figure number
|
Initial angle θ0 (degrees)
|
Timestep τ (sec.)
|
Number of steps
|
|
2.7
|
10
|
0.1
|
300
|
|
2.8
|
170
|
0.1
|
300
|
Attachment:- Assignment Files.rar