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 ankle. (Figure 1). He falls for 15 in before the bungee cord begins to stretch. Chris's mass is 79 kg and we assume the cord obeys Hooke's law. F = - kx, with 60 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 (not realistic, however) and treat Chris as a particle. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

m= mass = 79 kg

k= force constant = 60 N/m

let maximum elonagation of cord ( as shown in fig)= x

at point A , from fig:

Total energy = potential energy

EA = mgd ( d= 15 + x)

EA = 79*9.8*( 15 +x)

at point C, Total energy = elastic energy stored in cord

Ec= ( 1/2)*k*x2

Ec= (1/2)*60*x2

from conservation of energy , EA= Ec

   79*9.8*( 15 +x) = (1/2)*60*x2

1548.4 (15 +x) = 60 x2

23226 + 1548.4 x = 60x2

  60x2 - 1548.4 x- 23226 = 0

after solving this quadratic equation: x= 36.43m

d= 15 + 36.43 = 51.43 m

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