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What is the type of force that acts on a spring? Explain work energy theorem with respect to a spring. |
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Answer» Solution :The type of force that acts on a spring is a CONSERVATIVE force and as well as a variable force. The force law also called as Hooke's law with respect to the force on the spring `f_(s)=-KX` where k - is known as the spring constant in `Nm^(-1)` and x - is elongation. For a compression the displacement will be '-x' so that `F_(s)=+kx`. For extension `W_(s)=underset(0)overset(x_(m))intF_(s)dx=-underset(0)overset(x_(m))intkxdx=-(kx_(m)^(2))/(2)` The work done by the spring force for displacement `x_(i)` to `x_(F)` is given by `W_(s)=-underset(x_(i))overset(x_(f))intkxdx=-(k)/(2)(x_(i)-x_(f))` It is clear that if the spring returns to initial state W = 0. Since there is no loss in the ENERGY, and the force is retrieved, the force is conservative. Using `(1)/(2)mv_(m)^(2)=(1)/(2)kx_(m)^(2)` We get `v_(m)=sqrt((k)/(m)).x_(m)` |
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