How to Calculate the Mass of a Bungee Jumper

What is the formula to calculate the mass of a bungee jumper?

How does the motion of a bungee jumper resemble a mass on a spring?

Calculating the Mass of a Bungee Jumper

The motion of a bungee jumper can be modeled as simple harmonic motion (SHM), similar to a mass on a spring. The formula for the period (T) of SHM is T = 2π * √(m/k), where m is the mass of the jumper and k is the spring constant. Given that the jumper oscillates 5 times over 30 seconds, we can find the period and use it to calculate the mass.

After taking the leap, the bungee jumper oscillates with SHM over 30 seconds, oscillating 5 times. The spring constant of the cord is 53.2 N/m. To calculate the mass of the jumper, we can use the formula T = 2π * √(m/k) where T is the period, m is the mass, and k is the spring constant.

The period (T) of 5 oscillations over 30 seconds is calculated as T = 30 s / 5 = 6 s. Using this period, we can find the mass of the jumper using the formula m = (6 / (2π))^2 * 53.2 ≈ 7.93 kg. Therefore, the mass of the bungee jumper is approximately 7.93 kg.

This calculation helps us understand the behavior of the mass-spring system and how it relates to the motion of a bungee jumper during oscillation. The similarity between the two proves that the motion of a bungee jumper can be effectively modeled as simple harmonic motion.