Question

A 56 kg bungee jumper jumps from a bridge. She is tied to a bungee cord whose unstretched length is 11 m, and falls a total of 38 m. Calculate the spring stiffness constant k of the bungee cord, assuming Hooke's law applies. Calculate the maximum acceleration she experiences.

Answer 1

This is an example of how to do this problem in MasteringPhysics


A)
GPE lost is mgh = 55 x 9.8 x 31 = 16709 J
this turns into strain energy in the bungee cord (assuming no friction, sound, etc)
strain energy = 1/2 k x^2
x = 31 - 13 = 18 m

so 16709 = 1/2 * k * (18)^2 = 162 k
so k = 16709 = 103 N m^-1 = 100 to 2 sf (well, 103 is 3 sf so what can I do?)

B)
acceleration = F / m
F = k x = 103 * 18 = 1854 N
so acceleration = 1854 / 55 = 33.7 m s^-2 = 33 m s^-2 to 2 sf

Answer 2

final acceleration minus 9.8m/s^2 is the maximum acceleration because gravity is always there to pull you down