1.

Object #1 moves toward object #2, whose mass is twice that of object #1 and which is initially at rest. After their impact, the object lock together and move with what fraction of object #1's initial kinetic energy?

Answer»

`(1)/(18)`
`1/9`
`1/6`
`1/3`

Solution :FIRST, apply conservation of linear momentum to calculate the speed of the COMBINED object after the (perfectly inelastic) collision.
`m_(1)v_(1)+m_(2)v_(2)=(m_(1)+m_(2))v'`
`v'=(m_(1)v_(1)+m_(2)v_(2))/(m_(1)+m_(2))` LTBRGT `=(m_(1)v_(1)+(2m_(1))(0))/(m_(1)+2m_(1))`
Therefore, the ratio of the kinetic energy after the collision to the kinetic energy before the collision is
`(K')/(K')=((1)/(2)m'v^('2))/((1)/(2)m_(1)v_(1)^(2))=((1)/(2)(m_(1)+2m_(1))((1)/(3)v_(1))^(2))/((1)/(2)m_(1)v_(1)^(2))=(1)/(3)`.


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