Module 3 2 Modeling Bungee Jumping Angela B

Hooke's Law Within elastic limit of spring, F = -ks F - applied force k - spring constant s - displacement (distance) from spring's equilibrium position

Model of undamped vertical spring • Initial length • unweighted_length + weight_displacement + init_displacement • weight_displacement using Hooke’s Law • -weight / spring_constant • With down being positive, acceleration_due_to_gravity = +9. 81 m/sec 2 • restoring_spring_force = -spring_constant * (length - unweighted_length)

Model of undamped vertical spring

Model of undamped vertical spring Let x = distance from the equilibrium position, then

Model of diagram of undamped vertical spring

Simple harmonic motion

Length of damped spring

Damped spring

Modeling a bungee jump if (length > unweighted_length) then restoring_spring_force -spring_constant * (length - unweighted_length) else restoring_spring_force 0 The model is similar to that of the weighted spring under the influence of air friction except for the restoring spring force is conditional. Total force = weight – air friction – restoring spring force

Diagram for motion of bungee jumper

Length (m) and velocity (m/sec) for bungee jump