Collisions in Two Dimensions | Definition, Formulas – Work, Energy and Power

Two Dimensional Collision Physics or Oblique Collision Definition:
If the initial and final velocities of colliding bodies do not lie along the same line, then the collision is called two dimensional or oblique collision.

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Collisions in Two Dimensions | Definition, Formulas – Work, Energy and Power

In horizontal direction,
m₁u₁ cos α₁ + m₂u₂ cos α₂ = m₁v₁ cos β₁ + m₂v₂ cos β₂

In vertical direction,
m₁u₁ sin α₁ – m₂u₂ sin α₂ = m₁v₁ sin β₁ – m₂v₂ sin β₂
If m₁ = m₂ and
α₁ + α₂ = 90°
then
β₁ + β₂ = 90°

If a particle A of mass m₁ is moving along X-axis with a speed u and makes an elastic collision with another stationary body B of mass m₂, then

From conservation law of momentum,
m₁u = m₁v₁ cos α + m₂v₂ cos β
0 = m₁v₁ sin α – m₂v₂ sin β

Work, Energy and Power:
Work, energy and power are the three quantities which are inter-related to each other. The rate of doing work is called power. An equal amount of energy is consumed to do a work. So, basically the power is the rate at which energy is consumed to complete a work.