When a bungee jumper jumps, ignoring the mass of the bungee cord, the jumper initially falls in freefall before an inelastic collision occurs between the jumper and cord, and the cord extends as the jumper continues to accelerate downwards.

The only force acting downwards on the jumper is their weight. The extension of the cord when the jumper and cord are in their equilibrium position is given by e = F/k (Hooke's law). Given that the force acting downwards is constant (the jumper's weight), why does the cord continue to extend beyond this equilibrium extension as the jumper moves downwards? What force is further extending it? Why doesn't the jumper come to an instantaneous rest (implausible as this clearly is)?


Let's look at what happens right when the falling jumper passes that equilibrium point (EP). At that point, as you correctly pointed out, the force on them (up, from the bungee) is equal to the force down (gravity). So, there is a total net force of zero.

However, they already have momentum from falling. Newton's first law tells us that if there's no net force on an object, it will continue on its trajectory. So the jumper continues on their downward trajectory, past the EP. As they go farther down, the bungee force starts getting bigger than the gravitational force, which causes them to slow down.

But at the EP, the force on them equals zero. That causes them not to move when they're at equilibrium (if they were carefully placed there, for example), but it also means it won't stop them from moving if they're moving at that point.


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