Problem

Rubber bumpers are commonly used in marine applications to keep boats and ships from getti...

Rubber bumpers are commonly used in marine applications to keep boats and ships from getting damaged by docks. Consider a boat with a mass of 35,000 kg and a bumper with a force compression profile given by FB = βx3, where β is a constant and x is the compression of the bumper. Treating the boat C as a particle, neglecting its vertical motion, and neglecting the drag force between the water and the boat C, determine β so that if the boat were to impact the bumper with a speed of 4 m/s, the maximum compression of the bumper would be 18 cm.