In an inelastic collision, the objects involved stick together and move as one after the collision. Energy is lost in the form of heat and deformation. In an elastic collision, the objects bounce off each other and move separately after the collision. Energy is conserved in an elastic collision.
The final velocities in an inelastic collision can be calculated using the principle of conservation of momentum, which states that the total momentum before and after the collision remains constant. The equation for final velocity is: vf = (m1v1i + m2v2i) / (m1 + m2), where m1 and m2 are the masses of the objects and v1i and v2i are the initial velocities of the objects.
The coefficient of restitution is a measure of how much kinetic energy is conserved in an elastic collision. It is the ratio of the relative velocities of the objects before and after the collision. A higher coefficient of restitution means that more kinetic energy is conserved, resulting in a more "bouncy" collision.
Inelastic collisions can be seen in everyday life, such as a car crashing into a wall, a baseball hitting a catcher's mitt, or a person jumping onto a trampoline. In all of these examples, the objects involved stick together and move as one after the collision.
The easiest way to determine if a collision is inelastic or elastic is to observe the objects after the collision. If they stick together and move as one, it is an inelastic collision. If they bounce off each other and move separately, it is an elastic collision. Additionally, you can calculate the coefficient of restitution to determine the type of collision. If the coefficient is close to 1, it is an elastic collision, and if it is less than 1, it is an inelastic collision.