One-dimensional elastic collisions.

Version 0.1 [11-16-06]
To do:
(i) Generalize to completely inelastic collisions.
(ii) Generalize to partially inelastic collisions. (f? Q?)
(iii) Add collision special effect.
(iv) Two dimensions.


m1, m2 = object masses; M – total mass; V1,V2 – object initial velocities;

Mass and velocity of second mass are defined as multiples of those of first mass.

V_1=slider([0,20])

p=slider([-4,1,40])

V_2=p*V_1

m_1=slider([0,5,40])

q=slider([0,10,40])

m_2=q*m_1

M=m_1+m_2,D=m_1-m_2

W1, W2 – final object velocities.

W_1=D/M*V_1+2*m_2/M*V_2,W_2=2*m_1/M*V_1-(D/M*V_2)

Positions of mass centers. Constructed to collide at the origin at t=0 given initial time n_initial=-2 (so x1_init = V1*n_initial and same for mass 2.) Shifts account for finite size of masses.

function(X_1,s)=branch(if(V_1*s-a_1,s<0),if(W_1*s-a_1,s>0))

function(X_2,s)=branch(if(V_2*s+a_2,s<0),if(W_2*s+a_2,s>0))

a, b – size of masses.

a_1=1,b_1=1,a_2=1,b_2=1

Masses:

[(x-function(X_1,n))/a_1]^10+[(y-b_1)/b_1]^10<1

[(x-function(X_2,n))/a_2]^10+[(y-b_2)/b_2]^10<1




Author: David A. Craig <http://web.lemoyne.edu/~craigda/>

Graph of the formula

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