Heavy vs. Light Bungee Jumpers: Stored Energy Explained

[Sam1234]

Homework Statement

Bungee jumpers use an elastic rope to halt their fall when they are just a short distance from the ground. Using the idea of stored energy, explain whether heavy jumpers should use a shorter or longer length of rope than lighter jumpers.

Homework Equations

W=mg
strain energy = 1/2*k*x

The Attempt at a Solution

The work here is done my the weight of the jumper. We have W=mg. Assume that k is constant for a rope, we have that F=mg=k*Delta x ==> Delta x is larger when m is larger, so the jumper might hight the ground. He should use a shorter rope.

This is how i would answer the question, but it doesn't use the concept of stored energy and I was hoping someone could help me with that.

 

[Fightfish]

I don't think the assumption that k remains the same for the longer and shorter ropes is valid. If the ropes are identical in every respect except their length, then their effective k should differ, similar to the case of springs being attached in series.

 

[kerimek]

I would approach this question by first defining what we mean by stored energy. Stored energy, also known as potential energy, is the energy that an object possesses due to its position or configuration. In the case of bungee jumping, the potential energy is stored in the elastic rope when it is stretched.

Now, let's consider the two different scenarios of heavy and light jumpers using the same length of rope. In both cases, the potential energy stored in the rope is the same, as the rope is stretched by the same amount for both jumpers. However, the difference lies in the amount of kinetic energy that the jumpers possess before they reach the end of the rope.

A heavier jumper will have a greater mass and therefore a greater gravitational potential energy (W=mg). This means that they will have a higher velocity and more kinetic energy before reaching the end of the rope. As a result, a longer rope is needed to absorb this higher amount of kinetic energy and bring the jumper to a safe stop.

On the other hand, a lighter jumper will have a lower mass and therefore a lower gravitational potential energy. This results in a lower velocity and less kinetic energy before reaching the end of the rope. In this case, a shorter rope can be used as it does not need to absorb as much kinetic energy.

In summary, heavy jumpers should use a longer length of rope than lighter jumpers as they possess more kinetic energy before reaching the end of the rope. This ensures that the rope can safely absorb and dissipate the energy, bringing the jumper to a gentle stop.