## Finding the Displacement of a piston in circular motion

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?
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 Recognitions: Homework Help 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?

Recognitions:
Homework Help

## Finding the Displacement of a piston in circular motion

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