determine what fraction of the kinetic energy of the ball before collision is lost during teh collsion. what happens to it?

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08-11-2022
Physics

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determine what fraction of the kinetic energy of the ball before collision is lost during teh collsion. what happens to it?

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contexto115 contexto115 · Answer 1 · 2022-11-14T14:23:59-05:00

1/2 m₁v₁²(m₁ / m₁+ m₂ ) is the fraction of Kinetic energy lost during an inelastic collision.

From the concept of law of conservation of energy, In an elastic collision when two objects collide with a particular velocity then the kinetic energy before the collision will be the same after the collision as well but that's not the case in an Inelastic collision where there's always loss of kinetic energy.

In case of inelastic collision,

pi = pf

here p = momentum

m₁v₁ = (m₁ + m₂)v₂

v₂= m₁v₁ / (m₁ + m₂) ------- equation 1

Ki = Kf

1/2m₁v₁² = 1/2 (m₁+m₂) v₂²

Put the value of v₂ from equation 1

1/2mv² = 1/2 (m₁ + m₂) [m₁v₁ / m₁+m₂]²

=> 1/2 (m₁v₁)² / ( m₁+m₂ )

∴ Fraction of Kinetic energy lost

= 1/2 m₁v₁² - 1/2 (m₁v₁)² / (m₁+m₂)

=> 1/2 m₁v₁²( m₁ / m₁ + m₂ )

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