Collision of Frictional Elastic Spheres

For each ball, the angular momentum about the center of contact O is conserved provided that the contact area is small and no external torque exists. Hence, we have 

substituting the preceding equation into Eq. (2.140) yields m dVi m2 dV2 

For the case in Fig. 2.17, the tangential velocities of the colliding spheres are not equal to each other before the impact, which would most likely lead to a sliding on the contact interface. Consider the simple case of two colliding spheres without relative rotation. To 

It is clear that the collision between two elastic but frictional spheres is inelastic due to the inevitable sliding at contact which yields the kinetic energy loss by frictional work. Furthermore, the preceding analyses of both Hertzian collision and frictional collision can also be applied to the particle-wall collision, where the radius of the wall is simply set to be infinitely large. 

Example 2.2 Consider an impact between a polyethylene particle (dp = 1 cm) and a copper wall. The incident velocity is 2 m/s, and the incident angle is 30°. The friction coefficient of the interface is 0.2. The densities of polyethylene and copper are 950 and 8,900 kg/m3, respectively. What is the contact time duration for the collision Estimate the rebound velocity of the particle. Repeat the problem for a copper particle colliding with a polyethylene wall. 

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