Question

Max (mass = 15 kg) is hanging from one end of a 13-m long bungee cord that has its other end fixed to a bridge above. The bungee cord has a circular cross section with a diameter of 2. 5 cm, and a young’s modulus of 17 mpa. What is the stress in the bungee cord due to max’s weight?

Answer 1

The stress experimented by the bungee cord due to Max's weight is approximately 299.680 kilopascals.

How to find the stress experimented by the bungee cord

Let suppose that the stress ($\sigma$), in pascals, experimented by the bungee cord is entirely elastic and uniform. By Newton's Laws we know that the tension ($T$), in newtons, experimented by the cord equals Max's weight. The stress on the bungee cord is axial and is described by following formula:

$\sigma = \frac{m\cdot g}{\frac{\pi\cdot D^{2}}{4} }$   (1)

Where:

• $m$ - Max's mass, in kilograms
• $g$ - Gravitational acceleration, in meters per square second
• $D$ - Diameter of the circular cross section, in meters

If we know that $m = 15\,kg$, $g = 9.807\,\frac{m}{s^{2}}$ and $D = 0.025\,m$, then the stress experimented by the bungee cord is:

$\sigma = \frac{(15\,kg)\cdot \left(9.807\,\frac{m}{s^{2}} \right)}{\frac{\pi}{4}\cdot (0.025\,m)^{2} }$

$\sigma \approx 299679.845\,Pa\, (299.680\,kPa)$

The stress experimented by the bungee cord due to Max's weight is approximately 299.680 kilopascals. $\blacksquare$

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