PHYS171
Principles of Physics I
Numerical Solution of the
Equations of Motion
Task:
Calculate a 2D trajectory.
Calculate projectile motion, including drag force.
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Trajectories including drag
0
5
10
15
12
10
8
6
4
2
0
acceleration (m/s
2
)
time (s)
a
x
a
y
a
x
including drag
a
y
including drag
0
5
10
15
0
200
400
600
800
1000
1200
position (m)
time (s)
x
y
x including drag
y including drag
Trajectories including drag
0
5000
10000
15000
0
1000
2000
3000
4000
v
0
= 100 m/s
v
0
= 200 m/s
v
0
= 400 m/s
v
0
= 100 m/s with drag
v
0
= 200 m/s with drag
v
0
= 400 m/s with drag
y (m)
x (m)
Trajectories including drag
0
1000 2000 3000 4000 5000 6000 7000
0
500
1000
1500
2000
2500
3000
3500
v
0
= 1000 m/s with drag
y (m)
x (m)
Chapter 6
Kepler’s Laws
•
All planets move in elliptical orbits with the sun at
one focus
•
The radius vector drawn from the sun to a planet
sweeps out equal area in equal time
•
The square of the orbital period of any planet is
proportional to the cube of the semimajor axis of
the elliptical orbit
Components of scientific method here, a compact set of rules defined which
describe complicated phenomena.
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 Fall '11
 LA PORTA
 mechanics, Force, Projectile Motion, Sir Isaac Newton, Kepler's laws of planetary motion

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