# Computer Simulations in Physics by murplelake73

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```									Computer Simulations
in Physics

W.P. Dykshoorn
wp.dykshoorn@utoronto.ca
* Newton’s
Equation:

F = ma

* equation predicts
future particle
motion if F is
specified
a simple example: air resistance

Fdown = Fgravitation -
Fair resistance
= mg - v

Therefore,

mv/t = mg - v
Since v = vfuture - vpresent

We can now rewrite our equation:

vfuture = gt + (1 - t/m)vpresent

Let gt = 1/2m/s2 and t/m = 1/2

Iteration Equation: vfuture = (1 + vpresent)/2
Time(s)   Velocity (m/s)

0.0       0.00
1.0       0.50
2.0       0.75
3.0       0.88
4.0       0.94
5.0       0.97
6.0       0.98
7.0       0.99
8.0       1.00
9.0       1.00
Exact Solution:
1.25

1.00
v(t) = [1 -
velocity (m/s)

0.75
(1/2)t/t]m/s
0.50

0.25

0.00
0.0   2.5     5.0      7.5   10.0
time (s)
Improvements:

* choose smaller t
* Feynman method:
v  vav = (v1+v2)/2
Rewards:
* dynamic nature of Newton’s equation
revealed
* computer programming experience
Challenges:
* students with no programming
experience?
Resources:
M.L. de Jong, Introduction to Computational Physics (Addison Wesley, 1991).
R.P. Feynman, Feynman Lectures of Physics, Vol.1 (Addison Wesley, 1963).
D. Greenspan, Computer-Oriented Mathematical Physics (Pergamon, 1980).

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