You can use these two equations in order to solve for differences in velocity in two objects undergoing a collision because there are two equations for mass and velocity that can be used to solve for two variables. Simply isolate the two equations and solve for the different velocities v1’ and v2’ if you know the initial velocities and masses of the two objects. Because solving for velocity squared involves a quadratic equation, you will need to use this equation to solve for the v1’ and v2’.
INELASTIC COLLISIONS IN ONE DIMENSION In inelastic conditions in one dimension, the internal kinetic energy is not conserved. It means that forces between two objects that are colliding may remove or add some internal kinetic energy and that internal forces may change forms of energy in the system. It can involve colliding objects sticking together and can involve heat transfer of energy. It may also convert stored energy into internal kinetic energy (as when something explodes and separate from the central mass). An example of an inelastic collision is when two equal objects of equal speed stick together. The total kinetic energy is ½ mass times velocity squared plus ½ mass times velocity squared equals mass times velocity squared. The momentum is conserved but the internal kinetic energy is equal to zero after the collision. This is a perfect inelastic collision because it reduces the internal kinetic energy to the minimum it can have while still conserving momentum. Figure 41 shows this situation. After the collision, the kinetic energy equals zero, while before, it is mass times velocity squared.
Figure 41.
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