Answer:
W = -1.152 mJ
Explanation:
given,
F = −α x + β x³
α = 5.2 N/m and β = 700 N/m³
Work done = ?
length of stretch = ?
we know,
W = F . ds
[tex]W = \intF . dx[/tex]
[tex]W = \int_0^{0.12} (-\alpha x + \beta x^3).dx[/tex]
[tex]W = \int_0^{0.12}(-5.2 x +700 x^3).dx[/tex]
[tex]W = [\dfrac{-5.2x^2}{2} +700\dfrac{x^4}{4}]_0^{0.12}[/tex]
now,
[tex]W = [\dfrac{-5.2(0.12)^2}{2} +700\dfrac{(0.12)^4}{4}][/tex]
W = -0.001152 J
W = -1.152 mJ
work done by the spring is equal to W = -1.152 mJ
