Conservation of Momentum
The momentum of a body is defined as the product of its mass and velocity
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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
MT = m1 v1 + m2 v2 + .. + mn vn
= m1 u1 + m2 u2 + .. + mn un (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:
MT = (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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Related Topics
- Mechanics - Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects
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