Respuesta :
Explanation:
Given that,
Distance = 0.6 m
Force = 40 N
(a). We need to calculate the spring constant
Using Hooke's law
[tex]F=kx[/tex]
Put the value into the formula
[tex]40=k\times0.1[/tex]
[tex]k=\dfrac{40}{0.1}[/tex]
[tex]k=400 [/tex]
We need to calculate the work done
[tex]W=\int_{0}^{0.6}{kx}dx[/tex]
[tex]W=\int_{0}^{0.6}{400x}dx[/tex]
On integrating
[tex]W=400\times{\dfrac{x^2}{2}}_{0}^{0.6}[/tex]
[tex]W=400{\dfrac{0.6^2}{2}-0}[/tex]
[tex]W=72\ J[/tex]
(b). We need to calculate the spring constant
Using formula of work done
[tex]W=\int_{0}^{0.1}{kx}dx[/tex]
[tex]40=\int_{0}^{0.1}{kx}dx[/tex]
[tex]40=k(\dfrac{x^2}{2})_{0}^{0.1}[/tex]
[tex]40=k\times{\dfrac{0.1^2}{2}-0}[/tex]
[tex]40=k\times0.005[/tex]
[tex]k =\dfrac{40}{0.005}[/tex]
[tex]k=8000[/tex]
We need to calculate the work done
[tex]W=\int_{0}^{0.6}{k x}dx[/tex]
[tex]W=8000\times(\dfrac{x^2}{2})_{0}^{0.6}[/tex]
[tex]W=8000\times\dfrac{0.6^2}{2}-0}[/tex]
[tex]W=1440\ J[/tex]
Hence, This is the required solution.
