Difference between hooke's law and the work done in a spring?

[dnt]

hooke's law says the spring force = -kx

but the work done in stretching a spring = 1/2 kx^2

isnt work = Fd?

so using W=Fd and F=-kx (hooke's law) shouldn't the work come out to:

W = -kx^2? (arent d and x the same? both are distance stretched)

where does the 1/2 come from in the equation 1/2kx^2?

can someone help clarify the difference and when to use each equation. thanks.

 

[OlderDan]

hooke's law says the spring force = -kx

but the work done in stretching a spring = 1/2 kx^2

isnt work = Fd?

so using W=Fd and F=-kx (hooke's law) shouldn't the work come out to:

W = -kx^2? (arent d and x the same? both are distance stretched)

where does the 1/2 come from in the equation 1/2kx^2?

can someone help clarify the difference and when to use each equation. thanks.

W = Fd is only correct when the force is constant and in the direction of a displacement of distance d. The force is not constant for a spring. Have you taken calculus?

 

[Hootenanny]

isnt work = Fd?

That is correct, provided the force is constant. However, generally work can be expressed thus;

$$W=\int^{x_{1}}_{x_{0}}\; F \cdot dx$$

Edit: Too slow again

 

[radou]

That is correct, provided the force is constant. However, generally work can be expressed thus;

$$W=\int^{x_{1}}_{x_{0}}\; F \cdot dx$$

Edit: Too slow again

...which, after plugging in F = - k x, answers your question.