Question

A support cable on a bridge has a cross-sectional area of 0.0067m2 and a length of 24 m. It ia made of a high stress material of young’s modulus 2.8x1011 Pa. The tension in the cable is 720 Kn. Calculate the extension of the cable and the strain energy stored in the cable.

Answer 1

Given that,

Area = 0.0067 m  

Length = 24 m

Young modulus $Y=2.8\times10^{11}\ Pa$

Tension = 720 kN

We need to calculate the extension of the cable

Using formula of young modulus

$Y=\dfrac{\dfrac{F}{A}}{\dfrac{\Delta L}{L}}$

$Y=\dfrac{FL}{A\Delta L}$

$\Delta L=\dfrac{FL}{A\times Y}$

Where, F = force = tension

L = length

$\Delta L$ = extension

Y = young modulus

A = area

Put the value into the formula

$\Delta L=\dfrac{720\times10^{3}\times24}{0.0067\times2.8\times10^{11}}$

$\Delta L=0.0092\ m$

$\Delta L=9.2\times10^{-3}\ m$

$\Delta L=9.2\ mm$

We need to calculate the strain energy stored in the cable

Using formula of energy

$E=\dfrac{1}{2}F\times\Delta L$

Where, F = force

$\Delta L$ = extension

Put the value into the formula

$E=\dfrac{1}{2}\times720\times10^{3}\times9.2\times10^{-3}$

$E=3312\ J$

Hence, (I). The extension of the cable is 9.2 mm.

(II). The strain energy stored in the cable is 3312 J.