Block attached to spring is kicked,what distance will the spring stretch?

[kabailey]

A block, no friction, of 1 kg is attached to a spring rests on a horizontal surface with a length L. The spring is connected to a fixed point. The 1kg block is kicked and has a velocity of 1 m/s. As the block swings around the fixed point, the spring stretches to a total distance of L + x, at position 90 degrees counter-clockwise from rest.. What is the distance in meters the spring stretches?

L=1m
m=1kg
k=1 N/m
Vi=1 m/s
x=?
F=-kxI am having a difficult time getting this problem started. Thanks!

 

[jbsteele]

We can use the Conservation of Mechanical Energy equation to solve for x. Mechanical energy = Kinetic energy + Potential energyKE = 1/2mv^2PE = 1/2kx^21/2mv^2 + 1/2kx^2 = 0 Rearranging, we have:x^2 = -(2mv^2)/kSubstituting the values given in the problem, we get:x^2 = -(2*1*1^2)/1 = -2Therefore, the distance the spring stretches is x = √2 m ≈ 1.41 m