Physics Math, Lab Theory Question

In summary, the lab today showed that Fc is inversely proportional to speed, but directly proportional to r. There are 2 r's in the top of the (mv^2) /r equation.
  • #1
mike_302
103
0
The lab we did today was to determine the relationship between radius, speed, mass, and frequency on the centripetal force in a given system. I am typing up my thesis now, and I am having trouble understanding something.

Fc=(mv^2)/r = m*4*pi^2*r*f^2 Given those two equal equations for centripetal force, I would be inclined to believe that centripetal force is INVERSELY related to centripetal force given the first equation, but at the same time, directly related to centripetal force, given the second equation.

So two questions here: Which one would it be, and why are there two equations providing different proportionalities?
 
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  • #2
mike_302 said:
The lab we did today was to determine the relationship between radius, speed, mass, and frequency on the centripetal force in a given system. I am typing up my thesis now, and I am having trouble understanding something.

Fc=(mv^2)/r = m*4*pi^2*r*f^2 Given those two equal equations for centripetal force, I would be inclined to believe that centripetal force is INVERSELY related to centripetal force given the first equation, but at the same time, directly related to centripetal force, given the second equation.

So two questions here: Which one would it be, and why are there two equations providing different proportionalities?

v = R * omega

so omega = v/R

Is that what has you confused? Also, your question seems to have some typos in it ("centipital force is inversely related to centripital force", rather that inversely related to ____ ?what?)
 
  • #3
oops, sorry. centripetal force would be inversely proportional to speed in the mv^2 / r equation, while it is directly proportional to r in m4(pi^2)rf^2 (btw, we have not seen/used v*omega... We are just aware of these equations for Fc)

So yes, the question still stands... Why is the proportionality different between Fc and r in the two different equations?

that is:
m4(pi^2)rf^2 = Fc
and
mv^2 / r = Fc
 
  • #4
mike_302 said:
oops, sorry. centripetal force would be inversely proportional to speed in the mv^2 / r equation, while it is directly proportional to r in m4(pi^2)rf^2 (btw, we have not seen/used v*omega... We are just aware of these equations for Fc)

So yes, the question still stands... Why is the proportionality different between Fc and r in the two different equations?

that is:
m4(pi^2)rf^2 = Fc
and
mv^2 / r = Fc

Actually the equation Fc = m*4*PI^2*r*f^2 is derived from the equation Fc = mv^2/r
Here is how the equation is derived:

Fc = mv^2/r

from the above equation we know that v = d/t. however since this is circular motion, we can say d = 2*PI*r. Hence subsituting (2*PI*r)/t for v:

Fc = m((2*PI*r)/t)^2/r

now expand and simpify:

Fc = (m*4*PI^2*r^2)/(t^2*r)

As you can see now that r can be canceled out from the equation. However since r in the numerator is squared there will be an r remaining in the numerator (This part should answer your question, no?):

Fc = m*4*PI^2*r/t^2

Now you will notice that there is t in the denominator. Since this is circular motion, it can be represented by a periodic function, thus the time can be represented as the Period of the motion:

Fc = m*4*PI^2*r/T^2

We know that the T = 1/f, thus f = 1/T, hence we can rewrite the equation as:

Fc = m*4*PI^2*r*f^2

Hopefully you noticed during that the r was canceled out from the denominator while the equation was derived, it is not so much a question of proportionality here but the method in which the equation was derived which produced the r variable to appear in both the numerator and the denominator.

Hopefully this helps...

Sekhar.B
 
  • #5
okay. So, in summary, what I think you are saying is that in mv^2, it is possible to derive another 2 radii out of there, and so in reality, in the (mv^2) /r equation, there are really 2 r's in the top... so it IS directly proportional to r, even in the (mv^2) /r equation, but the r's in the numerator are just hidden.
 
  • #6
Keep in mind that r, v, and f are not independent values. Yes, r appears in the numerator for one expression for centripetal force and in the denominator for the other. But that's only because of the relationship between r, v, and f. Make sure you can understand and write down the equation that relates these three quantities.

Another thing to consider is the dimensions of F. In one expression, the force looks like the kinetic energy divided by a distance r. In the other expression, it looks like a mass times a frequency squared times a distance r, which is a mass times an acceleration. With practice, both these ways of looking at the units for force should make sense to you.
 

FAQ: Physics Math, Lab Theory Question

What is the difference between physics and math?

Physics is a natural science that studies the behavior and properties of matter and energy in the universe. It uses mathematical equations to describe and predict the behavior of physical systems. Math, on the other hand, is a branch of science that deals with the study of numbers, quantity, and space. It provides the tools and language for expressing and manipulating physical concepts in physics.

Why is lab theory important in physics?

Lab theory is important in physics because it allows us to test and validate the theories and laws that we develop through mathematical equations. It also helps us to understand the limitations and uncertainties of these theories and to make improvements and advancements in our understanding of the physical world.

What skills are necessary for success in physics and math?

In order to be successful in physics and math, one must have a strong foundation in algebra, geometry, and calculus. It is also important to have critical thinking and problem-solving skills, as well as the ability to visualize and manipulate abstract concepts. Strong mathematical and analytical skills are crucial for understanding and applying the laws and theories of physics.

What are some common tools used in physics labs?

Some common tools used in physics labs include rulers, calipers, thermometers, timers, balances, voltmeters, and spectrometers. These tools are used to measure and record various physical quantities such as length, time, temperature, mass, voltage, and light intensity.

How can I apply physics and math in real life?

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