The way I read it, vA, vB are given, so it's 3 equations and 2 unknowns. Still not good. Could choose to ignore the elasticity condition.Dr. Courtney said:
To solve for three ball collisions with elastic collisions and masses M and m, you can use the equations of conservation of momentum and conservation of kinetic energy. These equations allow you to calculate the final velocities of the balls after the collision.
In an elastic collision, both momentum and kinetic energy are conserved, meaning that the total momentum and total kinetic energy of the system before and after the collision remain constant. In an inelastic collision, only momentum is conserved, but kinetic energy is not. Some energy is lost to heat or sound.
The coefficient of restitution is a measure of the elasticity of a collision. It is defined as the ratio of the relative velocity of separation to the relative velocity of approach. In three ball collisions, the coefficient of restitution can help determine the final velocities of the balls after the collision.
Yes, there are a few assumptions that are made when solving for three ball collisions. These include assuming that the balls are perfectly spherical, that there is no external force acting on the system, and that the collision is happening in a vacuum.
One real-life application of solving for three ball collisions is in the game of billiards. When the cue ball hits two other balls, the collision between the three balls can be modeled and predicted using the equations of conservation of momentum and kinetic energy. This can help players strategize and make accurate shots.
