Physics Formula Collision

Physics Formula for Collision

In physics, a collision is an event where two or more bodies exert forces on each other for a relatively short period of time. Collisions are classified into two main types: elastic and inelastic. Understanding the formulas related to collisions helps in predicting the outcomes of these interactions, such as changes in velocity and energy.

1. Elastic Collision

An elastic collision is one in which both momentum and kinetic energy are conserved. The general formula for conservation of momentum in a two-body collision is:

m₁v₁ + m₂v₂ = m₁v'₁ + m₂v'₂

Where:

m₁ and m₂ are the masses of the two objects.
v₁ and v₂ are the initial velocities of the objects.
v'₁ and v'₂ are the final velocities after the collision.

For elastic collisions, the following equation also holds for kinetic energy:

(1/2)m₁v₁² + (1/2)m₂v₂² = (1/2)m₁v'₁² + (1/2)m₂v'₂²

Example: Elastic Collision of Two Balls

Consider two balls, one with mass 2 kg moving at 3 m/s and another with mass 3 kg moving at 1 m/s. After an elastic collision, their velocities change. Using the conservation of momentum and kinetic energy formulas, we can calculate the final velocities.

2. Inelastic Collision

An inelastic collision is one where momentum is conserved, but kinetic energy is not. In a perfectly inelastic collision, the two objects stick together after the collision. The formula for momentum conservation is the same as in elastic collisions:

m₁v₁ + m₂v₂ = (m₁ + m₂)v'

Where:

v' is the final velocity of the combined mass after the collision.

Example: Inelastic Collision of Two Cars

Suppose two cars collide head-on. One car (1000 kg) is traveling at 20 m/s, and the other car (1500 kg) is traveling at -10 m/s. After the collision, they stick together. Using the momentum conservation formula, the final velocity of the combined cars can be calculated.

Conclusion

Collisions are fundamental events in physics, and understanding the difference between elastic and inelastic collisions is essential for analyzing real-world scenarios. The formulas for momentum and energy conservation help in predicting the outcomes of these interactions.