Linear Momentum

The momentum of a body is defined as the product of its mass and velocity

The momentum of a body is defined as the product of its mass and velocity. Since velocity is a vector quantity, momentum is a vector quantity.

The momentum can be expressed as

M = m v         (1)

where

M = momentum (kg m/s, lb ft/s)

m = mass (kg, lb)

v = velocity (m/s, ft/s)

The momentum of a body remains the same as long as there is no external forces acting on it. The principle of conservation of momentum can be sated as

the total linear momentum of a system is a constant

The total moment of two or more bodies before collision in a given direction is equal to the total momentum of the bodies after collision in the same direction and can be expressed as

M_T = m₁ v₁ + m₂ v₂ + ..  + m_n v_n

        =  m₁ u₁ + m₂ u₂ + ..  + m_n u_n         (2)

where

v = velocity before collision (m/s, ft/s)

u = velocity after collision (m/s, ft/s)

Example - Linear Momentum

A body with mass 30 kg and 30 m/s collides with a body with mass 20 kg with velocity 20 m/s in the same direction. Assuming both bodies have the same velocity after the impact, the resulting velocity can be calculated as:

   M_T = (30 kg) (30 m/s)  + (20 kg) (20 m/s) 

        =  u ((30 kg) + (20 kg))

        = constant

        >

    u = (30 kg) (30 m/s)  + (20 kg) (20 m/s)  /  ((30 kg) + (20 kg))

        = 26 m/s

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