Elastic Collision Formula Derivation
Momentum formula for Elastic Collision is:
m1u1 + m2u2 = m1v1 + m2v2
∴ m(u1-v1) = m(v2-u2) ⇢ (Equation A)
Kinetic energy formula for elastic collisions is:
1/2(m1u12) + 1/2(m2u22) = 1/2(m1v12) + 1/2(m2v22)
∴ m1(u12-v12) = m2(v22-u22)
∴ m1(u1+v1)(u1-v1) = m2(v2+u2)(v2-u2) ⇢ (Equation B)
Divide Equation B to Equation A,
u1 + v1 = v2 + u2
∴ u1 – u2 = -(v1 – v2)
Relative velocity of Approach = Relative Velocity of Receding
Momentum formula for Elastic Collision is:
m1u1 + m2u2 = m1v1 + m2v2
We have,
u1 + v1 = v2 + u2
∴ v2 = u1 + v1 – u2
Put v2 in the momentum formula for Elastic Collision,
∴ m1u1 + m2u2 = m1v1 + m2(u1 + v1 – u2)
∴ m1u1 + m2u2 = m1v1 + m2u1 + m2v1 – m2u2
∴ m1u1 – m2u1 +2m2u2 = v1(m1 + m2)
v1 = ((m1 – m2)u1 + 2m2u2) / (m1 + m2)
v2 = ((m2 – m1)u2 + 2m1u1) / (m1 + m2)
Elastic Collision Formula
Elastic Collision is the collision in which the kinetic energy of the system is conserved. A collision occurs when two or more object comes in direct contact with each other. the collision can be of two types that includes, Elastic Collision and Inelastic Collision.
In this article, we will learn about, Elastic Collision, Examples of Elastic Collision, Difference between Elastic Collision and Inelastic Collision, and others in detail.
Table of Content
- What is Elastic Collision?
- Examples of Elastic Collision
- Elastic Collision Formula
- Elastic Collision Formula Derivation
- Elastic Vs Inelastic Collision
- Applications of Elastic Collision