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physicsfun

**Impulse and momentum... really stuck... please help!**

Consider a collision between two spheres where we have both elastic force and dissipative force.

Let x is a variable where it is let to be the sum of their radii when they are just touching, and that distance decreasing during the collision. After the collision, x is irrelevant.

Given, u*(dv/dt)= F_elastic+F_dissipative = -h*x - k*v*x^(1/2) ---------(1)

where v= dx/dt, and u=m1*m2/(m1+m2)

QUESTION: Corresponding to the two forces are impulses, both during compression and during restitution. Impulses corresponding to the dissipative force F_dis are: P_dis-c and P_dis-r.

PROVE that ---------> P_dis-c= - P_dis-r ----------------(2)

Note: I was also told that the above results hold for a more general solution, and that the x does not matter, all that is necessary is remembering that the F_dissipative is proportional to velocity, i.e. can treat the two forces as a function in that:

u*(dv/dt) = -f(x) - g(x)*v ---------(3)

Please please... ANY suggestion will help... Thank YOU!

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