Chris jumps off a bridge with a bungee cord (a heavy stretchable cord) tied arou

Question

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: chris (2) Initial SE terata 15 m Final State: (3) Choose zero point for potential energy(s): Ay ? y- 0 (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

The system consists of a bungee cord and a person falling off

The initial point is at the start where the person is at rest

The final point is the point at which the person starts to come up due to elasticity

Here, Work done = change in energy

The potential energy at the top will convert into elastic potential energy as he falls down

mgh = 1/2*k*x2 ...............where x = h -15

75*9.8*h = 0.5*55*(h-15)2

735h = 27.5 (h2 + 225 - 30h)

735h = 27.5h2 + 6187.5 - 825h

27.5h2 + 6187.5 - 825h - 735h = 0

27.5h2 + 6187.5 - 1560h = 0

h2 - 56.73h + 225 = 0

solve for h using quadratic equation formula given below

x = - b +/- sqrt(b2 - 4ac) / 2a

here x = h (unknown)

h = 56.73 +/- sqrt ( 3218.3 - 900) / 2

h = 56.73 +/- 64.17 / 2

h = 60.45 m , -3.72 m ( reject the negative value of h)

so, h = 60.45 m

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