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A 4.45 g object moving to the right at 18.6 cm/s makes an elastic head-on collision with an 8.9 g object that is initially at rest.
18.6 cm/s
4.45 g
8.9 g
Find the velocity of the first object immediately after the collision. The acceleration of gravity is 9.8 m/s 2 . Answer in units of cm/s.

Respuesta :

cjrodriguez89

Answer:

v₁f = -6.2 cm/s

Explanation:

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

        [tex]m_{1} *v_{1o} = m_{1}* v_{1f} + m_{2}* v_{2f}[/tex]

  • As the collision is elastic, total kinetic energy must be conserved also:

       [tex]\frac{1}{2}*m_{1}*v_{1o}^{2} = \frac{1}{2}*m_{1}*v_{1f} ^{2} + \frac{1}2}*m_{2}*v_{2f}^{2}[/tex]

  • From the givens, we know that m₂ = 2* m₁
  • Replacing in the above equations, rearranging both sides and simplifying, we can find the following expression for v₁f:

       [tex]v_{1f} = \frac{-m_{1} }{3*m_{1}} *v_{1o} =\frac{-v_{1o}}{3} = -\frac{18.6 cm/s}{3} = -6.2 cm/s[/tex]

  • v₁f = -6.2 cm/s (which means that it bounces back after the collision).

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