Horizontal Spring, Find Unstretched length

[ZxcvbnM2000]

Homework Statement

A spring of stiffness 1500 N m-1 is stretched between two points 2 m apart. If the tension in the spring is 200 N, what was the unstretched length of the spring? And what is the energy stored in the spring when it is stretched between the two points?

Homework Equations

F=-K*x

U = 0.5 K*(x²)

The Attempt at a Solution

I don't even know where to begin from !

X₀ is the position of equilibrium of the spring , so this is our reference point , meaning that if X₀ is our first point and X₁ is our second point , then A= 2 m , right ? So F=-kA but this isn't true ?! what can i do ? I thought we always measured everything relevant to X₀ , so how can we find the unstretched part ?!

 

[Doc Al]

In Hooke's law (your first equation), x stands for the amount of stretch (beyond the unstretched length). You're given the tension, so you can figure out x.

 

[ZxcvbnM2000]

But we know x , it is 2m ( A=2m ) But 200 = 1500*2 isn't true .

 

[Doc Al]

But we know x , it is 2m ( A=2m ) But 200 = 1500*2 isn't true .

Nope. 2m is the total length of the stretched spring, not the amount of stretch. Use Hooke's law to find the amount of stretch.

 

[ZxcvbnM2000]

So it should be F= k ( streched length - natural length ) = k( X1 - X0 )

Xo = X1 - 2/15 = 1.866666 m Therefore A=0.13333333333333 m .

so U=13.3 J . Thank you :)