Uniform Circular Motion frequency

[DevilTemptations]

Yesterday I did a lab with the purpose of determining the relationship between the frequency of revolution of an object in uniform circular motion and
1)the magnitude of the force (causing the circular motion)
2)the radius of the circular path
3)the mass of the object.

Well by graphing my observations, I was able to determine that the force is proportional to the frequency squared. The radius is proportional to the inverse of the frequency squared. The mass is also proportional to the inverse of the frequency squared.

By determing the line of best fit of these three graphs, I got the equations

Force=0.2639(frequency) - 0.1176
Radius=2.3983(frequency) + 0.1209
Mass=0.0343(frequency) - 0.0011

I also converted my proportionality statements into equations
frequency= force / k square rooted
frequency = k / radius square rooted
frequency = k / mass square rooted

Apparently I have to combine my "three results" to obtain an equation for the frequency in terms of the tension(force), the radius and the mass. It should provide the same answers if I checked it with data points as the equation SIGMA FORCE = 4PIE^2mrf^2 (There is obviousy going to be some disrepancies but it should be a close result)

HOW DO I COMBINE EQUATIONS?? HELP!

 

[Cross1]

I am doing the same lab but my data is not correct what data did you get?

 

[nlightner]

As a scientist, it is important to understand the relationship between different variables in an experiment. In this case, you have determined that the frequency of revolution in uniform circular motion is related to the force, radius, and mass of the object. To combine these equations, you can use the concept of dimensional analysis.

First, let's look at the equation you have provided: SIGMA FORCE = 4PIE^2mrf^2. This is known as the centripetal force equation, and it relates the force (tension) to the mass, radius, and frequency of the circular motion. In order to combine your equations, you will need to manipulate them to be in a similar form.

Starting with the equation for force, we can rearrange it to solve for frequency:

Frequency = force / k square rooted

Next, we can substitute this equation for frequency into the equation for radius:

Radius = 2.3983(frequency) + 0.1209
Radius = 2.3983(force / k square rooted) + 0.1209

We can do the same for the equation for mass:

Mass = 0.0343(frequency) - 0.0011
Mass = 0.0343(force / k square rooted) - 0.0011

Now, we can substitute these equations into the centripetal force equation:

SIGMA FORCE = 4PIE^2mrf^2
SIGMA FORCE = 4PIE^2(force / k square rooted)^2 * 2.3983(force / k square rooted) * 0.0343(force / k square rooted)

Simplifying this equation will give you an equation for frequency in terms of force, radius, and mass. It may be helpful to use dimensional analysis to ensure that all units are consistent throughout the equation.

I hope this helps you understand how to combine equations in a scientific context. Remember to always pay attention to units and make sure your equations are consistent. Good luck with your future experiments!