Engineering Mechanics
The loss of kinetic energy during inelastic impact, is given by (where m1 = Mass of the first body,m2 = Mass of the second body, and u1 and u2 = Velocities of the first and second bodies respectively.)

[2(m₁ + m₂)/m₁ m₂] (u₁ - u₂)²
[m₁ m₂/2(m₁ + m₂)] (u₁ - u₂)²
[2(m₁ + m₂)/m₁ m₂] (u₁² - u₂²)
[m₁ m₂/2(m₁ + m₂)] (u₁² - u₂²)

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Engineering Mechanics
One joule means that

Work is done by a force of 1 dyne when it displaces a body through 1 cm
Work is done by a force of 1 N when it displaces a body through 1 m
Work is done by a force of 1 kg when it displaces a body through 1 m
Work is done by a force of 1 g when it displaces a body through 1 cm

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