Respuesta :
Explanation:
Formula for work using change in volume and Young's modulus is as follows.
W = [tex]E \Delta V[/tex]
= [tex]E \frac{D^{2}}{4} \pi \Delta L[/tex]
= [tex]\frac{21}{10^{-4}} \times \frac{(0.005)^{2} \pi}{4} \times 0.03 kJ[/tex]
= 0.124 kJ
Therefore, we can conclude that 0.124 kJ work is required to stretch this rod.
Answer:
The work done is [tex]1.85\times10^{-4}\ kJ[/tex]
Explanation:
Given that,
Length = 10 m
Diameter = 0.5 cm
Young modulus = 21 kN/cm²
Stretched length = 3 cm
We need to calculate the wok done
Using formula of work done
[tex]W=\dfrac{1}{2}P(\delta l)[/tex]...(I)
We know the deformation is,
[tex]\delta l=\dfrac{PL}{AE}[/tex]
Where, [tex]P=\dfrac{AE(\delta l)}{L}[/tex]
Put the value in the equation (I)
[tex]W=\dfrac{1}{2}\times\dfrac{AE(\delta l)^2}{L}[/tex]
[tex]W=\dfrac{\dfrac{\pi\times d^2}{4}\times E\times(\delta l)^2}{2L}[/tex]
Where,
E = Young modulus
d = diameter
l = length
Put the value into the formula
[tex]W=\dfrac{\dfrac{\pi}{4}\times(0.5)^2\times21\times(3)^2}{2\times1000}[/tex]
[tex]W=0.01855\ N-cm[/tex]
[tex]W=1.85\times10^{-4}\ kJ[/tex]
Hence, The work done is [tex]1.85\times10^{-4}\ kJ[/tex]
