Spring Force as Centripetal Force?

[lavenderbaby]

Homework Statement

A 2.1 kg mass is connected to a spring with spring constant k=150 N/m and unstretched length 0.18 m. The pair are mounted on a frictionless air table, with the free end of the spring attached to a frictionless pivot. The mass is set into circular motion at 1.4 m/s. Find the radius of its path.

Homework Equations

Fs= -kx
Fc= mv^2/r

The Attempt at a Solution

Since the centripetal force that keeps the mass moving in a circle is provided by the spring, I set Fs = Fc. However, I only equated their magnitudes. Thus, I have this equation:

mv^2/r = kx
r = mv^2 / kx
r = (2.1kg)(1.4m/s)^2 / (150N/m)(0.18m) = 0.15 m

What I am not sure about is the value for x in the equation Fs = -kx. Since the x in the equation is the change in spring length after the spring has been compressed/stretched, the x here should be zero for an unstretched spring. But then, what is the significance of the 0.18 m?

Please let me know if my solution is correct or if I need to change the x.
Thanks in advance!

 

[PhanthomJay]

The force in the spring is kx, where x is the stretched distance beyond the initial 0.18 m unstretched length. So what would be the radius of the path?

 

[lavenderbaby]

The force in the spring is kx, where x is the stretched distance beyond the initial 0.18 m unstretched length. So what would be the radius of the path?

Since the question states that the spring is unstretched, wouldn't the radius of the path be the unstretched length of the spring, which is 0.18 m?

 

[PhanthomJay]

The question states that the spring is unstretched before it is set into motion. That 0.18 m is just the length of the spring you bought off the shelf, with no loading on it. Once you set it into motion with the mass on it, it will stretch due to the centripetal force acting on it as caused by the centripetal acceleration. Draw a quick sketch to find the equation of the radius of the circle in terms of the unstretched length and x.

 

[lavenderbaby]

The question states that the spring is unstretched before it is set into motion. That 0.18 m is just the length of the spring you bought off the shelf, with no loading on it. Once you set it into motion with the mass on it, it will stretch due to the centripetal force acting on it as caused by the centripetal acceleration. Draw a quick sketch to find the equation of the radius of the circle in terms of the unstretched length and x.

Ohhhhh, I get it now! the stretched length must be (radius of path - unstretched length) then! Thanks a lot!