In the bungee jumping scenario where a jumper leaps from a bridge and the total energy at the top of the jump is 60,000 J (ignore air resistance), what is the total energy when the jumper first jumps and when the cord is fully stretched?

What this question is really testing

You are being asked whether the total energy of the bungee-jumper system changes as the jumper falls and the cord stretches. The key phrase is “air resistance is ignored”, which means no energy is lost to the surroundings.

Conservation of mechanical energy

With no non-conservative forces doing work (no air resistance), the total mechanical energy stays constant:

$$E_{\text{total}} = E_g + E_k + E_{\text{elastic}} = \text{constant}$$

You are told that at the top of the jump,

$$E_{\text{total}} = 60{,}000\ \text{J}$$

So at any other point in the motion, the total is still $60{,}000\ \text{J}$.

Filling in the blanks

• When the bungee jumper first jumps: $60{,}000\ \text{J}$
• When the cord is fully stretched: $60{,}000\ \text{J}$

Quick check (why it makes sense)

As the jumper falls, gravitational potential energy $E_g$ decreases while kinetic energy $E_k$ increases. When the cord stretches, kinetic energy is converted into elastic potential energy $E_{\text{elastic}}$. These forms trade off, but their sum stays $60{,}000\ \text{J}$.