Question

home / study / science / physics / physics questions and answers / tom d. spends his spare time running a bungee jumping service off the henley street bridge. ... Question: Tom D. spends his spare time running a bungee jumping service off the Henley Street bridge. He ha... Tom D. spends his spare time running a bungee jumping service off the Henley Street bridge. He has a 120 ft long bungee cord (un-stretched) that has a spring stiffness of 24 lb/ft. To test his bungee, he ties the bungee cord to the bridge railing, ties the other end to an unnamed person weighing 123 pounds, and then gently nudges the person off of the bridge.

The person's speed when the bungee cord starts to stretch= 87.91 ft/sec

B) Assuming they haven't hit the water, how much has the bungee chord stretched when the person is at the bottom of the jump? (include units with answer)

- And the answer is not 199.01 ft

Answer 1

As the cord length 120 ft, the man will free-fall 120 ft and after that the cord will stretch to a certain distance of x ft. The stiffness or the spring constant (k) of the cord is 24 lb/ft. The elastic energy stored due to a stretch of x ft will be

Where, acceleration due to gravity is g = 32 ft/s² in FPS unit, Hence, stiffness, k = 24 lb/ft. = 24g lb.ft/s².

The man´s mass (m) is 123 lb and let us consider the velocity of the person after free-fall of 120 ft is v ft/s. According to the laws of motion for free falling body (, where u, v, h and g are initial velocity, final velocity, height travelled and the acceleration due to gravity), the velocity v will be

Hence, the kinetic energy of the person will be

Now, the total mechanical energy of the man will be stored in the cord in the form of elastic potential energy. The man will come to rest at the lowest point after falling downward a distance of x ft. Hence the change in potential energy due to the falling distance of is

According to conservation of energy,

Solving this quadratic equation in the form of , we can obtain the solution for x as

Here, in the above equation a = 384, b = -3936 and c = -475282.34, Hence,

The value of x should not be the negative value. Hence the value of the x is 40.68 ft. Assuming they haven't hit the water, the bungee cord will stretch of a distance of 40.68 ft when the person is at the bottom of the jump.