PHYS-1500 PHYSICAL MODELING
9/22/2006, Class 8: Drag Forces
FALL 2006
NAME _________________________________
Use the modified Euler method to construct a spreadsheet model of one dimensional motion in a
constant gravitational field with an atmospheric drag force present.
Below is a picture of the program for one dimensional motion with air drag present.
To set up the program, enter the following:
B4: = 0.1; B5 and B6: 0; E4: 9.8; E5: =E4/E6^2; E6: 1E10
A9: 0; A10: =A9+$B$4;
B9: =B5; B10: =B9+C10*$B$4
C9: =B6; C10: =C9+D9*$B$4
D9: =-$E$4-$E$5*C9*ABS(C9)
E9: =$B$5+$B$6*A9-0.5*$E$4*A9^2
F9: =$B$6-$E$4*A9
G9: =-$E$4
The labels and titles can be copied from the picture.
Then, copy the formulas in cells A10, B10, C10, D9, E9, F9, and G9 to all the cells below them
through row 109.
Then have the spreadsheet make a graph of y as a function of t, with both the model version of y
and the “free” version on the same set of axes. Make a similar graph of both velocities as
functions of time, and do the same for acceleration.
1
Use the model that you just constructed to do the following for a 16 lb shot, a baseball, and a
ping-pong ball. In each case adjust the time interval in cell B4 so that the most of the time
available for calculation is used for the motion of interest. In other words, set the time interval so
that y is positive for most of the motion.
1. If dropped from rest from a height of 100 m, how long will each take to reach the ground, and
what will be its speed when it gets there?
Shot:
t = __________________
units
v = ___________________
units
Baseball:
t = __________________
units
v = ___________________
units
Ping-pong: t = __________________
units
v = ___________________
units
The following information should be useful:
Some Terminal Velocities
16 lb Shot
Baseball
Tennis Ball
Basketball
Ping-Pong Ball
Raindrop(r = 1.5 mm)
145 m/s
42 m/s
31 m/s
20 m/s
9 m/s
5 m/s
2. If thrown upward from y = 0, with a speed of 25 m/s, what maximum height will each reach?
How long will each take to reach that maximum height, and how long will each be in flight?
Finally, what will be the speed of each when it returns to y = 0?
Shot:
Baseball:
ym = __________________
units
tup = ___________________
units
ttotal = __________________
units
vf = ___________________
units
ym = __________________
units
tup = ___________________
units
ttotal = __________________
units
vf = ___________________
units
2
Ping-pong: ym = __________________
units
tup = ___________________
units
ttotal = __________________
units
vf = ___________________
units
3. Sketch graphs of y, v, and a as functions of time for all three in question 2, from the time they
are thrown until they hit the ground.
3