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

Answer:

$Y = 2.27 \times 10^{10} N/m^2$

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

$strain = \frac{\Delta L}{L}$

$strain = \frac{{10 cm}{43 cm}$

$strain = 0.23$

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

$A = 40 \times 10^{-6} m^2$

now the stress in the string is given as

$Stress = \frac{T}{A}$

$Stress = \frac{mg}{A}$

$Stress = \frac{3.7 \times 9.81}{40 \times 10^{-6}}$

$stress = 9.07 \times 10^5 N/m^2$

Now Young's Modulus is given as

$Y = \frac{stress}{strain}$

$Y = \frac{9.07 \times 10^5}{40\times 10^{-6}}$

$Y = 2.27 \times 10^{10} N/m^2$