The force-compression profile of a rubber bumper B is given by FB = βx3, where β = 3.5 × 1...

The force-compression profile of a rubber bumper B is given by FB = βx3, where β = 3.5 × 106 lb/ft3 and x is the bumper’s compression measured in the horizontal direction. Determine the expression for the potential energy of the bumper B. In addition, if the cruiser C weighs 70,000 lb and impacts B with a speed of 5 ft/s, determine the compression required to bring C to a stop. Model C as a particle and neglect C’s vertical motion as well as the drag force between the water and the cruiser C.

Figure P4.36