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19. Two objects of equal masses collide head-on while moving in the opposite directions and join together. Show that the fractional loss of original KE of the objects is given by the 1 expression.
E=(1/2)+(V1V2/V1²+V2²)
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Respuesta :

Answer:

Explanation:

mass of each object = m

momentum conservation: mv₁ + mv₂ = 2mv, so v = (v₁ + v₂)/2

Initial KE = mv₁²/2 + mv₂²/2 = m(v₁² + v₂²)/2

final KE = (2m)v²/2 = m(v₁ + v₂)²/4

Change in KE = m(v₁² + v₂²)/2 - m(v₁ + v₂)²/4 = m(v₁ + v₂)²/4

= m(v₁² + v₂² + 2v₁v₂)/4 = (1/2) m(v₁² + v₂²)/2 + mv₁v₂/2

Fraction loss = change in KE / initial KE = 1/2 + v₁v₂/(v₁² + v₂²)

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