Overview of inelastic collisions

Inelastic collisions are a type of collision between two objects where the kinetic energy is not conserved. In an inelastic collision, the objects involved stick together after the collision, or some of the kinetic energy is converted into other forms of energy such as sound or heat. Inelastic collisions are common in real-life scenarios, like car accidents or the collision of two billiard balls.

Solving inelastic collision problems

To solve problems involving inelastic collisions, we use the laws of conservation of momentum and energy. The conservation of momentum states that the total momentum of the system before the collision is equal to the total momentum of the system after the collision. The conservation of energy states that the total energy of the system before the collision is equal to the total energy of the system after the collision. By applying these laws, we can solve for the final velocities of the objects involved.

Example of an inelastic collision problem

Suppose two balls of mass 1 kg and 2 kg are moving towards each other with velocities of 3 m/s and -2 m/s, respectively. After they collide, they stick together and move with a common velocity. What is their final velocity?

Using the conservation of momentum, we have:

m1v1 + m2v2 = (m1 + m2)vf

(1 kg)(3 m/s) + (2 kg)(-2 m/s) = (1 kg + 2 kg)vf

vf = 1/3 m/s

Therefore, the final velocity of the two balls after the collision is 1/3 m/s.

Real-world applications of inelastic collisions

Inelastic collisions have many real-world applications. In car accidents, the collision between two cars is often inelastic, and the kinetic energy is converted into deformation of the car and heat. This is why airbags are designed to deploy during a collision to reduce the impact on the passengers. In sports, like billiards or pool, inelastic collisions are used to control the direction and speed of the balls. The collision between a golf club and a golf ball is also an inelastic collision, where the kinetic energy of the club is transferred to the ball, causing it to move.