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Perfectly Inelastic Collision

In such types of collisions the bodies move independently before collision but after collision as a single body.
 
When the colliding bodies are moving in the same direction (Fig. 8) By the law of conservation of momentum
 
40540.png
Fig. 8
 
m1u1 + m2u2 = (m1 + m2)vcomb
⇒ 40534.png
 
Loss in kinetic energy
40527.png
40521.png
[By substituting the value of vcomb]
 
When the colliding bodies are moving in the opposite direction (Fig. 9) By the law of conservation of momentum
 
40514.png
Fig. 9
 
m1u1 + m2(–u2) = (m1 + m2)vcomb
(Taking left to right as positive)
 
∴ 40508.png
 
When m1u1 > m2u2, then vcomb > 0 (positive), i.e., the combined body will move along the direction of motion of mass m1.
 
When m1u1 < m2u2 then vcomb < 0 (negative), i.e., the combined body will move in a direction opposite to the motion of mass m1.
 
Loss in kinetic energy
 
ΔK = Initial kinetic energy – Final kinetic energy
40502.png
40496.png




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