# Finding the Displacement of a piston in circular motion

• Fennec
In summary, the problem involves a 1.86 g piston attached to a rotating disc with a radius of 25.5 cm and a spring with a spring constant of 31.3 N/m. The piston is rotating at a frequency of 10 Hz. By using the equations for centrifugal force, spring force, and energy, we can find the stretch of the spring. Using two equations, we can solve for this stretch, which is the answer to the problem. The calculated stretch for the spring is 1.525 cm, which may seem low and could be further investigated.
Fennec

## 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?

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.

## 1. What is the formula for finding the displacement of a piston in circular motion?

The formula for finding the displacement of a piston in circular motion is given by Δx = rθ, where Δx is the displacement, r is the radius of the circular path, and θ is the angle of rotation in radians.

## 2. What is circular motion and how does it relate to displacement of a piston?

Circular motion is a type of motion where an object moves along a circular path at a constant speed. In the case of a piston, it rotates around a fixed axis, causing the piston to move in a circular motion. The displacement of the piston is the distance between its starting and ending positions along this circular path.

## 3. How does the radius of the circular path affect the displacement of a piston?

The radius of the circular path directly affects the displacement of a piston. As the radius increases, the distance traveled by the piston also increases. This means that a larger radius will result in a larger displacement for the piston.

## 4. Can the displacement of a piston in circular motion be negative?

Yes, the displacement of a piston in circular motion can be negative. This happens when the piston moves in a clockwise direction, resulting in a negative angle of rotation. In this case, the displacement is calculated as a negative value.

## 5. How is the angle of rotation measured in circular motion?

The angle of rotation in circular motion is measured in radians. One full rotation of a circle is equal to 2π radians. This means that the angle of rotation can range from 0 to 2π, depending on the number of rotations made by the piston.

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