Respuesta :
Answer:
The work done will be 0.115 J.
Explanation:
Given that,
[tex]k=100\ N/m[/tex]
[tex]b=700\ N/m^2[/tex]
[tex]c=12000\ N/m^3[/tex]
A force along the x-axis with x-component,
[tex]F(x)=kx-bx^2+cx^3[/tex]
Suppose, How much work must be done to stretch this spring by 0.050 m from its unstretched length?
We need to calculate the work done
Using formula of work done
[tex]W(x)=\int{F(x)dx}[/tex]
Put the value into the formula
[tex]W(x)=\int{(kx-bx^2+cx^3)dx}[/tex]
[tex]W(x)=\dfrac{kx^2}{2}-\dfrac{bx^3}{3}+\dfrac{cx^4}{4}[/tex]
Put the value of k,b,c and x
[tex]W(0.050)=\dfrac{100\times(0.050)^2}{2}-\dfrac{700\times(0.050)^3}{3}+\dfrac{12000\times(0.050)^4}{4}[/tex]
[tex]W(0.050)=0.115\ J[/tex]
Hence, The work done will be 0.115 J.
The value of spring displacement is greater than zero. Therefore, spring is stretched.
Force in spring :
It is given as, [tex]F=kx[/tex]
Where k is constant and x is amount of displacement.
The force function is given that,
[tex]F(x)=kx-bx^{2}+cx^{3}[/tex]
Here given that, [tex]k=100N/m, b=700N/m^{2} , c=12000N/m^{3} .[/tex]
Substitute all values in above equation,
[tex]F(x)=100x-700x^{2} +12000x^{3}[/tex]
To check, the spring is stretched or it is compressed.
Substitute f(x) = 0
We get x is greater than zero.
Thus, The value of spring displacement is greater than zero. Therefore, spring is stretched.
Learn more about the spring force here:
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