Momentum Conservation in Bungee Jumps
Conservation of momentum - Bungee jumps
How is momentum conserved when a Bungee jumper's velocity drops to
zero at the end of a stretched Bungee rope?
Whenever some object's momentum changes, the momentum goes to whatever
was supplying the force
that caused the momentum change. In bungee jumping, that object is
usually the Earth. Nobody ever
notices the difference because the Earth is so massive.
Kinetic energy (K.E.=1/2*M*V^2)and potential energy (U = -K*X, assuming
Hooke's law) are exchanged between the jumper and the elastic cord after
the "free-fall" part of the jump when the chord begins to stretch. Assume
for the sake of simplicity that there is no "free-fall" and the elastic
chord begins to stretch the instant the jumper jumps. In that case the
initial momentum of the jumper is also zero since the jumper is not moving
TOTAL momentum is conserved, not the momentum of one object. The jumper and
Bungee cable exert force on each other. The Bungee cable and support exert
force on each other. The support and Earth exert force on each other.
Also, gravity allows the jumper and Earth to exert force each other
directly. Most of the momentum is temporarily passed to the Earth, the
entire planet. When the cable pulls the jumper back up, the momentum passes
back into his body.
Dr. Ken Mellendorf
Illinois Central College
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Update: June 2012