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A 5.92 g object moving to the right at 17.1 cm/s makes an elastic head-on collision with an 11.84 g object that is initially at rest Find the velocity of the first object immediately after the collision. The acceleration of gravity is 9.8 m/s 2 .

User Ielyamani
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Answer:

v₁f = -5.7 cm/s

Step-by-step explanation:

  • Assuming no external forces acting during the collision, total momentum must be conserved, as follows:


m_(1) * v_(10) = m_(1) *v_(1f) + m_(2) * v_(2f) (1)

  • Rearranging terms, we have:


m_(1) * (v_(10) - *v_(1f) ) = m_(2) * v_(2f) (2)

  • We also know that the collision is elastic, so total kinetic energy must be conserved , as follows:


\Delta K = 0 \\ \\ (1)/(2) * m_(1) *v_(10) ^(2) = (1)/(2)* m_(1) *v_(1f) ^(2) + (1)/(2)* m_(2) *v_(2f) ^(2) (3)

  • Rearranging , and simplifying common terms, we have:


m_(1)* (v_(10) ^(2) -v_(1f) ^(2) ) = m_(2) *v_(2f) ^(2) (4)

  • Replacing by the givens, doing some algebra and dividing (4) by (2), we find the following relationship:


v_(10) + v_(1f) = v_(2f)

  • Replacing the expression above in (1), as m₂ = 2*m₁, we can find the value of v₁f, as follows:


m_(1) * v_(10) = m_(1) * v_(1f) +2*m_(1) * (v_(10) + v_(1f))\\ \\ -(m_(1) * v_(10)) = 3* m_(1) *v_(1f) \\ \\ v_(1f) = - (v_(10) )/(3) = (-17.1cm/s)/(3) = -5.7 cm/s

User JayC
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