Finding the Displacement of a piston in circular motion

Fennec

1. The problem statement, all variables and given/known data
A 1.86 g piston is attached to a rotating disc. The radius is 25.5 cm when the disc is stationary. A spring attached to the piston has a spring constant of 31.3 N/m. The piston is rotating at a frequency of 10 Hz. How har will the piston move outward
k = 31.3
r = 25.5 cm = 0.255 m
Frequency = 10 Hz
m = 1.86 g



2. Relevant equations
1/2kx^2 = Es
ac = v^2/r
W = change in Energy


3. The attempt at a solution

I really don't even know where to start. Please help. How am I supposed to relate frequency to speed?

Delphi51

Does that mean the piston's centrifugal force stretches the spring?
If so, begin with centrifugal force = spring force
Fill in the detailed formulas and see if you can find the stretch.

Fennec

Okay so

Fc = -kx
m*ac = -31.3* x
0.00186*v^2/0.255 = -31.3* x

How do I find both v and x?

Delphi51

You can write another equation using the 10 turns per second.
That is v = 2πr*10.
The question is not very clear, but looks like r = 0.255 + x.
You have a system of two equations to solve.

Fennec

I found the strech of the spring to be 1.525 cm. Is that all I have to do for this problem?

Delphi51

The stretch is the answer but that 1.5 cm seems low.
It would be interesting to see how you worked it out.