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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