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Consider a system of two toy rail cars (i.e., frictionless masses).
Suppose that car 1 has mass and is traveling
at toward the other car. Suppose car 2
has mass and is moving toward the other car
at .
There is a bumper on the second rail car that
engages at the moment the cars hit and does not let go (it connects
the two cars). The bumper acts as a spring with spring constant
. The second car is
from a wall.
Let be the time that the cars link up. Let be
the displacement of the first car from its position at ,
and let be the displacement of the second car from its original
position.
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