Determining the oscilation of a ruler resting on two spinning cylinders

• daffy
In summary, the problem involves a 75 gram ruler placed between two spinning cylinders with a coefficient of friction of 0.2. The ruler is pushed to the right by 0.12 meters and then returns to its starting point, going a total of 0.11 meters to the left. The equation for simple harmonic motion is given and the attempt at a solution involves drawing a force diagram and considering the reaction forces of the cylinders and the force of the hand pushing the ruler.
daffy

Homework Statement

A 75 gram ruler is evenly placed between two cylinders spinning clockwise on the left and counter clockwise on the right. The coefficient of friction between the ruler and the spinning cylinders is 0.2. You push the ruler to the right by 0.12 meters. It returns to you by moving left and continues past it's starting point, going a total of 0.11 meters to the left.

What is the frequency of oscillation of the ruler?

Homework Equations

We are given the equation for simple harmonic motion. We are not expected to use any differential equations in this physics course.

The equation of the location of the ruler is x(t) = A*cos(ωt+$\phi$)

The Attempt at a Solution

I drew a force body diagram by of the ruler resting on each spinning cylinder, but I found that the force of both of the cylinders cancels out. In addition, I don't know how to find the acceleration of the hand pushing the ruler, so I don't know how to find the force of the hand.

I'm mainly looking for some help getting this problem started. I'm having trouble conceptualizing this in a way that I can use it to get an answer.

Last edited:
hi daffy!
daffy said:
… I found that the force of both of the cylinders cancels out. In addition, I don't know how to find the acceleration of the hand pushing the ruler, so I don't know how to find the force of the hand.

the reaction forces will be different (and therefore so will the friction forces)

and you can assume that the hand pushes gently, and releases the ruler when its speed is zero

What is the purpose of determining the oscillation of a ruler resting on two spinning cylinders?

The purpose of determining the oscillation of a ruler resting on two spinning cylinders is to measure the rotational motion and stability of the cylinders. This can provide insight into the structural integrity of the cylinders and their ability to maintain a consistent rotation.

What equipment is needed to determine the oscillation of a ruler resting on two spinning cylinders?

To determine the oscillation of a ruler resting on two spinning cylinders, you will need a ruler, two spinning cylinders, a stopwatch, and a measuring tool (such as a protractor or ruler with markings).

What is the process for determining the oscillation of a ruler resting on two spinning cylinders?

The process for determining the oscillation of a ruler resting on two spinning cylinders involves placing the ruler on top of the spinning cylinders and measuring the angle of oscillation using the measuring tool. The stopwatch is used to time the oscillations and calculate the frequency and period of the oscillations.

How does the speed of the spinning cylinders affect the oscillation of the ruler?

The speed of the spinning cylinders will directly affect the oscillation of the ruler. As the speed increases, the ruler will experience greater forces and will oscillate at a higher frequency and with a larger amplitude. This can also impact the stability of the ruler on the cylinders, as higher speeds may cause the ruler to slip or fall off.

What factors can influence the accuracy of determining the oscillation of a ruler resting on two spinning cylinders?

Several factors can influence the accuracy of determining the oscillation of a ruler resting on two spinning cylinders, including the precision of the measuring equipment, the consistency of the speed of the cylinders, and external factors such as air resistance or vibrations. It is important to control these factors as much as possible to obtain accurate results.

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