Chapter 14, Problem 92A

To determine

The spring constant of bungee cord.

Answer to Problem 92A

The spring constant of bungee cord is $\text{0}\text{.57}\text{N/m}$

Explanation of Solution

Given:

Mass of bungee cord: $\text{68}\text{kg}$

Old Length of bungee cord: $\text{540}\text{m}$

New Length of bungee cord: $\text{1710}\text{m}$

Formula used:

The formula to calculate the spring constant,$k=\frac{\text{F}}{\text{x}}\text{=}\frac{\text{mg}}{\text{x}}$

Where,

  $k$ $=$ Spring constant

  $\text{F}$ $=$ Force

  $\text{x}$ $=$ Length of String$\text{g}$ $=$ Gravitational Force

Calculation:

Here, the old length and new length of the bungee cord is given.

Hence,formula can be written as,

  $k$ $=$ $\frac{\left(\text{mg}\right)}{\left(\text{new}\text{length-old}\text{length}\right)}$

  $k=\frac{\left(\text{68}\text{kg}\right)\text{×}\left(\text{9}\text{.8}\text{N/kg}\right)}{\text{1710-540}}$

  $k=\frac{\left(666.4\right)}{\left(1170\right)}$

  $k$ $=$

  $\text{0}\text{.57}\text{N/m}$

Conclusion:

Hence, the spring constant is $0.57\text{N/m}$ .