Finding the Displacement of a piston in circular motion

AI Thread Summary
The discussion revolves around calculating the displacement of a piston attached to a rotating disc, given its mass, radius, spring constant, and frequency. The user seeks to relate frequency to speed and determine how the centrifugal force affects the spring's stretch. By equating the centrifugal force to the spring force, they derive a system of equations involving the variables of speed and displacement. The calculated stretch of the spring is found to be 1.525 cm, which the user questions as potentially low. The conversation highlights the need for clarity in the problem statement and encourages sharing of methodologies for better understanding.
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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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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:
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?
 
The stretch is the answer but that 1.5 cm seems low.
It would be interesting to see how you worked it out.
 
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