Okay, I’m struggling. I understand how to define the system, but everything else

Question

Okay, I’m struggling. I understand how to define the system, but everything else is pretty confusing so send help!

Okay, I’m struggling. I understand how to define the system, but everything else is pretty confusing so send help! Chris jumps off a bridge with a bungee cord (a heavy stretchable cord) tied around his neek ankle, as shown in the figure below. He falls for 15 m before the bungee cord begins to stretch. Chris's mass is m - 75 kg and we assume the cord obeys Hooke's law just like a spring), with stiffness constant k 55 N/m. If we neglect air resistance, estimate what distance d below the bridge Chris's foot will be before coming to a stop. Ignore the mass of the cord and treat Chris as a particle (1) Define the system: (2) Initial State: (b (e) 15 m Final State: (3) Choose zero point for potential energy (s): Ay-? (4) Work done by none conservative forces: (5) Apply conservation of energy equation and solve the problem: (If you get a quadratic formula and don't know how to solve it, check appendix A-4)

Explanation / Answer

Let us consider that the zero potential energy point is the one where Chris comes to a stop. Let that be at a height d from the initial state

loss in potential energy of Chirs = 75*9.8*d=735*d

length by which the chord stretches = d-15

energy stored in chord = 0.5*55*(d-15)2

From conservation of energy, 735*d = 0.5*55*(d-15)2

735*d = 27.5*(d2-30d+225)

735d=27.5d2-825d+6187.5

Or, 27.5d2-1560d+6187.5=0

d=52.4 m

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