Finding the Displacement of a piston in circular motion

Homework Statement

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

Homework Equations

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

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?

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Delphi51
Homework Helper
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.

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?

Last edited:
Delphi51
Homework Helper
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.

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

Delphi51
Homework Helper
The stretch is the answer but that 1.5 cm seems low.
It would be interesting to see how you worked it out.