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.)

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

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Engineering Mechanics
The principle of transmissibility of forces states that, when a force acts upon a body, its effect is

Minimum, if it acts at the center of gravity of the body
Same at every point on its line of action
Maximum, if it acts at the center of gravity of the body
Different at different points on its line of action

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Engineering Mechanics
Varingon's theorem of moments states that if a number of coplanar forces acting on a particle are in equilibrium, then

Their algebraic sum is zero
Their lines of action are at equal distances
The algebraic sum of their moments about any point is equal to the moment of their resultant force about the same point
The algebraic sum of their moments about any point in their plane is zero

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