Potential energy of a spring and transverse motion

[jskro]

Homework Statement

L = Stretched distance
L₀ = Unstretched distance

Homework Equations

W = 1/2kL²

The Attempt at a Solution

In attempting to help a friend with this problem, having taken this same physics class under a different professor, i was completely stumped by this problem. I know that Fx = kL, but i can't make any headway on figuring out the part of the problem that involves the transverse of the spring that leads to a distance pulled of x_m with the same applied force that stretches the spring the same distance. Is there something easy that I'm missing?

 

[gash789]

For a) you need to parameterise the amount it has stretched in fig b as a function of x. Geometrically think of take the stretched spring in b, and rotating it back to vertical. Then consider the relation between the extrat height L(x) and the distance it was moved x. After this I presume you are okay?

 

[jskro]

For a) you need to parameterise the amount it has stretched in fig b as a function of x. Geometrically think of take the stretched spring in b, and rotating it back to vertical. Then consider the relation between the extrat height L(x) and the distance it was moved x. After this I presume you are okay?

So basically, because the work done in each of the two scenarios is the same?

Fx*xm = 1/2kL^2
xm = (kL^2)/(2Fx)

 

[gash789]

You do not know that the work done is the same, you just follow the prescribed method to determine it. I'm getting a bit confused by what you mean by

Fx*xm = 1/2kL^2
xm = (kL^2)/(2Fx)

What do you think is the answer to question a), Ie L(x)=? once you know this, then you can consider the force needed to extend the spring by L(x), and that is the answer to question b).

 

[jskro]

By rotating b back vertically, the distance it was pulled is x_m

L(x) = x_m

 

[gash789]

Exactly, so now you can find the magnitude of the force easily enough, the rest follows from this.