How Can I Linearize a Velocity vs Force Graph in Circular Motion Analysis?

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SUMMARY

The discussion focuses on linearizing a Velocity vs Force graph in the context of circular motion analysis. The user has recorded data including hanging mass, time for 10 circles, period, force, and speed, and has performed a power regression on the data. The key equations involved are F=ma and a=v^2/r, which relate force, mass, acceleration, and velocity. The user seeks guidance on how to manipulate these equations to isolate variables for linearization.

PREREQUISITES
  • Understanding of circular motion principles
  • Familiarity with the equations of motion, specifically F=ma and a=v^2/r
  • Knowledge of linear regression techniques, particularly linear least squares regression
  • Experience with data analysis software, such as Quattro Pro
NEXT STEPS
  • Research linear least squares regression methods for data analysis
  • Explore the relationship between force, mass, radius, and velocity in circular motion
  • Learn how to manipulate equations to isolate variables for linearization
  • Investigate experimental uncertainty analysis techniques in physics
USEFUL FOR

Students and educators in physics, particularly those involved in laboratory experiments related to circular motion and data analysis. This discussion is beneficial for anyone looking to understand the linearization of experimental data in the context of force and velocity relationships.

Bryan Tran
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Homework Statement


In my circular motion lab, I have to find the Varying Force.
I have a constant Bob mass, and constant radius. I also have the data recorded of the Hanging mass, Time for 10 circles, period, force, and speed.
Then I had a velocity vs force graph which I plotted the data and found a power regression.

Now, I'm trying to linearize the data of a Velocity vs Force graph...

Homework Equations


F=ma
a=v^2/r

The Attempt at a Solution


The first part of the question is wanting to get me to get the two variables on one side of the equation and the constants on the other, but I'm not sure what equation has both Force and Velocity in it and can give me acceleration as a constant.. Unless I'm looking at it wrong, help?

I can't really attempt anything because I'm already stuck.
 
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Is your experiment like fig 3a.1 on the page http://www.physics.fsu.edu/users/ng/Courses/phy2053c/Labs/Expt03a/Expt03a-3.htm ?
 
Last edited by a moderator:
Yes, very similar! except it's for 10 rotations, not 15.
 
The page in the link ends with the tanatalizing statement:

Next week you will investigate the experimental uncertainty in your exponents with the aid of the computer program Quattro Pro and determine whether your values of n are consistent with simple fractions. You will then be able to discuss your results in comparison with the theoretical relationship between F M, R and V.

Can you find a link to next week's notes? - or any page that describes the format of your data?

If not, I think you'll have to provide such a description for me to be of any help because your question needs to be stated with more detail.
 
This PDF?: http://www.physics.fsu.edu/courses/Fall04/phy2053c/labs/centripetal.PDF
 
Last edited by a moderator:
I think this PDF describes the procedure. It's probably linear least squares regression: http://www.physics.fsu.edu/users/ng/Courses/phy2053c/Labs/Expt02b-03b/Expt02b-03b.pdf
 
Last edited by a moderator:
http://www.webassign.net/userimages/Linearization%20Practice%20-%20Circular%20Motion%20Lab.pdf?id=317339&db=v4net
Here's the PDF

But in this one it doesn't have velocity... Maybe that's what I'm suppose to do... not use velocity and just use the variable vs time
 

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