Consider a collision between two spheres where there was an elastic force acting between the two bodies.(adsbygoogle = window.adsbygoogle || []).push({});

F=u*dv/dt=-h*x^3/2

where velocity v=dx/dt, h is a constant, u is the reduced mass (m1*m2/m1+m2), and x is the "change in distance" between the centers of the two bodies. Maximum compression distance is X_m, and initial velocity is v_i.

Show that the collision time, t, is given by

t=2(X_m)/(v_i)* [Integral from 0 to 1 of (1-k^5/2)^(-1/2) dk],

where k is a dimensionless variable replaced in the integral for x.

Just some idea to start this off would be much appreciated. Thanks!

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# Homework Help: Collision Time

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