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@rhettallain /oned_collisions.py
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This calculation uses vpython to model one dimensional collisions between two carts.
from visual import *
from visual.graph import *
#import pylab as pb
# the pylab module is used for making prettier graphs
### These are the three curves for plotting
fun1=gcurve(color=color.cyan)
fun2=gcurve(color=color.red)
fun3=gcurve(color=color.yellow)
## the following two can be turned on if you want to use the pylab plot
#dis=display()
#dis.visible=false
## these are lists used to plot in pylab
#rx=[]
#bx=[]
#tp=[]
L=.16 # the length of a cart
#this draws a track. You don't really need it
track=box(pos=vector(0,-.015,0), length=1.2, width=.1, height=.03,
color=(.5,.5,.5), material=materials.chrome)
#This is the red cart
red=box(pos=vector(.5, 0.025, 0), length=L, width=.08, height=0.05,
color=color.red, material=materials.plastic)
#the blue cart. Isn't this obvious?
blue=box(pos=vector(0, 0.025, 0), length=L, width=.08, height=0.05,
color=color.blue, material=materials.plastic)
t=0
dt=0.0001 #this is something you might want to play with changing.
red.m=.2535
blue.m=.2545
v0=.9738 #initial speed of launched cart
red.p=red.m*vector(-v0,0,0) #starting momentum of red
blue.p=vector(0,0,0) #starting momentum of blue
#This is the spring constant for the collision model
k=9000 #k needs to be set high, but you should try changing this
## A note about k. In order to make non-elastic collisions, I have a
## differential spring constant. I make the spring stiffer (higher k)
## while the two carts are moving towards each other and softwer (lower k)
## while moving away. k0 is the starting spring constant
k0=k
## s is the length of the spring. When the two carts are closer
## than this distance, the spring exerts a force. You should try chaning
## this value
s=0.003
F=vector(0,0,0) #the starting force
#e = 1 means completely elastic collision
#e = 0 means completely inelasitic
#for e not equal to 1, I will change k for when the carts are moving away from
# each other. for inelastic, if vb-vr = 0, then k=0
e=1.
## old_r is just used to tell if the two carts are moving towards or
## away from each other
old_r = red.pos.x-blue.pos.x-L
while blue.pos.x>-.6:
rate(10000)
# calc the distance between the carts
r=red.pos.x-blue.pos.x-L
# if they are close enough, turn on the force
if red.pos.x-blue.pos.x<s+L:
# if they are moving away, turn on the lower spring constant
if abs(r)>abs(old_r):
k=e*k
else: k=k0
#this calculates the actual spring force
F=k*(r-s)*vector(1,0,0)
# dt=0.001
else:
#if they aren't close enough, put the force back to zero
F=vector(0,0,0)
# dt=0.01
## Update momentum
blue.p=blue.p+F*dt
red.p=red.p-F*dt #notice this has a negative force. Newton's 3rd law
## Update position
blue.pos=blue.pos+blue.p*dt/blue.m
red.pos=red.pos+red.p*dt/red.m
old_r=r
## Update time
t=t+dt
## these are used for plotting in pylab
## rx=rx+[red.pos.x]
## bx=bx+[blue.pos.x]
## tp=tp+[t]
## calculate the kinetic energy
KEr=.5*mag(red.p)**2/red.m
KEb=.5*mag(blue.p)**2/blue.m
KET=KEr+KEb
## plotting. You can plot position, momeutm or KE. Whatever makes you
## happy.
fun1.plot(pos=(t,red.p.x))
fun2.plot(pos=(t,blue.p.x))
fun3.plot(pos=(t,red.p.x+blue.p.x))
## this is stuff for printing in pylab
##print(123)
##pb.figure()
##pb.plot(tp,rx, linewidth=3, c='r')
##pb.plot(tp, bx, linewidth=3, c='b')
##pb.xlabel('Time [s]')
##pb.ylabel('Horizontal Position [m]')
##pb.grid(True)
###pb.show()
##pb.savefig('collision1.png')
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