Question

A vertical solid steel post of diameter d = 26cmand length L = 2.40m is required to support a load of mass m = 7800kg . You can ignore the weight of the post. Take free fall acceleration to be g=9.8m/s2.Part AWhat is the stress in the post?Express your answer using two significant figures.Part BWhat is the strain in the post?Express your answer using two significant figures.Part CWhat is the change in the post's length when the load is applied?Express your answer using two significant figures.

Answer 1

Answer

given,

diameter of steel = d = 26 c m

         radius = 13 cm = 0.13 m

length = L = 2.4 m

mass = 7800 Kg

g = 9.8 m/s²

a) stress = F/A

stress = $\dfrac{mg}{\pi\ r^2}$

stress = $\dfrac{7800 \times 9.8}{\pi\ 0.13^2}$

stress = 1.44 x 10⁶ N/m²

b) Young's modulus x  strain = stress

 Young's modulus for steel = 200 x 10⁹ N/m²

    200 x 10⁹ x strain = 1.44 x 10⁶

     strain = 7.2 x 10⁻⁶ m

c) change in length

  $Strain= \dfrac{\Delta L}{L}$

  $7.2 \times 10^{-6} = \dfrac{\Delta L}{2.4}$

  $\Delta L= 17.28\times 10^{-6}\ m$