Perfectly inelastic collision

Definition

A perfectly inelastic collision is a type of collision where two objects collide and stick together after impact, moving as a single entity. In this type of collision, the maximum amount of kinetic energy is lost, while momentum is conserved, leading to a combined mass that moves at a common velocity after the collision. This scenario is crucial for understanding how energy and momentum interact during collisions.

5 Must Know Facts For Your Next Test

1. In a perfectly inelastic collision, the two colliding objects have the same final velocity after the impact.
2. The formula for conserving momentum during this type of collision can be expressed as $$m_1 v_1 + m_2 v_2 = (m_1 + m_2)v_f$$, where \(v_f\) is the final velocity.
3. Since kinetic energy is not conserved in perfectly inelastic collisions, some of it is transformed into other forms of energy, such as heat or sound.
4. Perfectly inelastic collisions are often represented in real-world scenarios like car crashes, where vehicles crumple and move together post-collision.
5. This type of collision represents the extreme case of inelastic collisions, where the objects stick together and move as one mass after impact.

Review Questions

• Explain how momentum conservation applies to perfectly inelastic collisions and provide an example.
  • In perfectly inelastic collisions, momentum is conserved despite the loss of kinetic energy. This means that the total momentum before the collision equals the total momentum after the collision. For example, if a 2 kg object moving at 3 m/s collides with a stationary 1 kg object and they stick together, their combined momentum after the collision can be calculated. The initial momentum is \( (2 kg)(3 m/s) + (1 kg)(0 m/s) = 6 kg m/s \), and after sticking together, their total mass becomes 3 kg moving at 2 m/s to satisfy momentum conservation.
• Discuss the significance of kinetic energy transformation during perfectly inelastic collisions.
  • In perfectly inelastic collisions, while momentum is conserved, kinetic energy is not; it transforms into other forms of energy like heat or sound. This transformation reflects the reality that some energy is lost to deformation or internal friction when two objects stick together. Understanding this concept helps explain why vehicles involved in such collisions are often damaged and why they don't simply bounce apart with unchanged velocities.
• Evaluate how perfectly inelastic collisions differ from elastic and other types of collisions regarding energy conservation and real-world applications.
  • Perfectly inelastic collisions differ significantly from elastic and other types of inelastic collisions because they do not conserve kinetic energy. In elastic collisions, both momentum and kinetic energy are conserved, meaning objects bounce off each other without any deformation. In contrast, in perfectly inelastic collisions, maximum kinetic energy loss occurs as objects stick together. Real-world applications like vehicle accidents illustrate this principle well; vehicles crumple and combine post-collision rather than rebounding as they would in an elastic scenario. Analyzing these differences helps inform safety designs in engineering.

Related terms

momentum:

A measure of the motion of an object, calculated as the product of its mass and velocity. Momentum is conserved in all types of collisions.

kinetic energy: The energy an object possesses due to its motion, which can be transformed into other forms of energy during a collision.

inelastic collision:

A collision in which kinetic energy is not conserved, but momentum is. Perfectly inelastic collisions are a specific case of inelastic collisions.