A man attached to a rope jumps from a bridge The bridge is 2

A man attached to a rope jumps from a bridge. The bridge is 200 ft above the water level. The natural length of the rope is 100 ft, the man weighs 190 lb, the spring constant of the rope is 2 Ibf/in, and the maximum elongation of the rope is 48.49 ft. What is the maximum energy stored in the rope?

Solution

Energy stored in rope = Change in PE

0.5*kx^2 = mg*(100 + x)

0.5*(2*12)*32.2*x^2 = 190*32.2*(100 + x)

Solving, x = 48.49 ft

Max. energy stored is thus = 190*(100 + 48.49) = 28213.1 ft-lb