Question

A block weighing 3.7 kg is suspended from the ceiling of a truck trailer by a hanging bungee cord. The cord has a cross-sectional area 40 mm2 and an unstretched length of 43 cm.

The truck begins stopped at a red light on a state highway. While stopped, the block hangs straight down to a distance 53 cm below the hook that attaches the bungee cord to the ceiling of the truck.

(a) What is the Young's modulus of the cord?

Answer 1

`Y = 2.27 * 10^(10) N/m^2`

Step-by-step explanation:

Natural length of the string is given as

`L_o = 43 cm`

length of the string while block is hanging on it

`L = 53 cm`

extension in length is given as

`\Delta L = 10 cm`

now we have strain in the string is given as

`strain = (\Delta L)/(L)`

`strain = 0.23`

similarly we will have cross-sectional area of the string is given as

`A = 40 * 10^(-6) m^2`

now the stress in the string is given as

`Stress = (T)/(A)`

`Stress = (mg)/(A)`

`Stress = (3.7 * 9.81)/(40 * 10^(-6))`

`stress = 9.07 * 10^5 N/m^2`

Now Young's Modulus is given as

`Y = (stress)/(strain)`

`Y = (9.07 * 10^5)/(40* 10^(-6))`

`Y = 2.27 * 10^(10) N/m^2`