PHYS-1500 PHYSICAL MODELING
Class 8: Drag Forces
FALL 2006
NAME __________KEY_______________________
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. Use the model to do the
following for a 16 lb shot, a baseball, and a ping-pong ball:
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 = ___4.50 s__________
t = 0.05 s
units
v = _____- 42.8 m/s______
units
Baseball: t = ____4.90 s________
t = 0.05 s
units
v = _____- 34.3 m/s______
units
Ping-pong: t = ____11.6 s__________
t = 0.12 s
units
v = _____- 9.0 m/s_______
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:
ym = ______30.7 m_____
t = 0.055 s
units
ttotal = _____5.005 s______
units
tup = ______2.475 s__________
units
vf = ______- 24.1 m/s_____
units
There is more on the back of the sheet.
Baseball: ym = _____26.5 m______
t = 0.05 s
units
tup = ____2.25 s__________
units
ttotal = ___4.65 s________
units
vf = ____- 21.1 m/s_______
units
Ping-pong: ym = ____8.15 m________
t = 0.03 s
units
tup = ____1.08 s__________
units
ttotal = ___2.55 s________
units
vf = _____- 8.32 m/s_______
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.
Shot:
Displacement with Drag
Velocity with Drag
35
30
30
20
25
20
10
10
y (m)
y (free)
5
v (m/s)
y (m)
15
0
0
1
2
3
0
-5 0
1
2
3
4
5
-20
6
-10
-30
-15
-40
-20
t (s)
t (s)
Acceleration with Drag
-9.3
-9.4
0
1
2
3
4
5
6
-9.5
a (m/s²)
-9.6
-9.7
a (m/s²)
-9.8
a (free)
-9.9
-10
-10.1
-10.2
t (s)
4
5
6
v (m/s)
v (free)
-10
Baseball:
Velocity with Drag
Displacement with Drag
30
35
30
20
25
10
15
y (m)
10
y (free)
v (m/s)
y (m)
20
v (m/s)
0
0
1
2
3
4
5
6
v (free)
-10
5
0
0
1
2
3
4
5
-20
6
-5
-30
-10
t (s)
t (s)
Acceleration with Drag
0
0
1
2
3
4
5
6
-2
a (m/s²)
-4
-6
a (m/s²)
a (free)
-8
-10
-12
-14
t (s)
Ping pong:
Velocity with Drag
Displacement with Drag
35
30
30
25
25
20
15
15
y (m)
10
y (free)
10
v (m/s)
5
v (free)
5
0
0
-5
0
0.5
1
1.5
2
2.5
3
3.5
0.5
1
1.5
2
-15
t (s)
t (s)
Acceleration with Drag
0
-10
0
-10
-5
-10
0
0.5
1
1.5
2
2.5
3
3.5
-20
-30
a (m/s²)
v (m/s)
y (m)
20
-40
a (m/s²)
-50
a (free)
-60
-70
-80
-90
t (s)
2.5
3
3.5