Question

A long elastic bungie cord with a Young's modulus of 30MPa has initial length of 20m and cross-section of 55mm2 Taking care to convert the units correctly, determine the length of the cord when a person weighing 55 Kg is hanging in static equilibrium. Take g as 9.81N/Kg

Answer 1

Cross section area = 55 mm² = 5.5 x 10^-5 m²

Y = 30 MPa

Force on the cord = mg = 55 x 9.81 = 539.55 N

Young's modulus is: Y = stress/strain = FL/al

$30 \times 10^6 = \frac{539.55(20)}{5.5\times 10^{-5}l}$

=> $l = 6.54 m$

so, the length of the cord when the person hangs on it is:

L' = 20 + 6.54 = 26.54 m.