Uniform Circular Motion; Need help with deriving equations.

[n3w ton]

Homework Statement

Hi I'm doing a physics lab about uniform circular motion to measure frequency and to compare it to mass,radius and force tension.

(A & B) I did
(C,D, E) I need help

(a) What variables are being measured / manipulated in this lab? What type of relationship is being tested? (radius, mass, force tension/force causing centripetal force)

(b) Graph the relationship between the frequency of revolution and each of the following:
• the magnitude of the tension force [force causing the circular motion(centripetal force)]
• the radius of the circular path
• the mass of the object

**■→(c) Find the proportionalities between frequency of revolution and the variables in radius, mass, and force of tension/centripetal force.

**■→(d) Derive an equation for the frequency in terms of the tension, the radius, and the mass by combining your results from (c) and using your results from (b) to verify.

**■→(e) The following relationship gives the magnitude of the net force causing the acceleration of an object in uniform circular motion:
Fc = 4π²mrf²
Rearrange this equation to isolate the frequency. Compare this result with the equation you derived in (d). Indicate the likely causes for any discrepancies.

Data: http://i.imgur.com/dLpyP.png

Frequency vs Force Graph: http://i.imgur.com/fyFci.png

Frequency vs Mass Graph: http://i.imgur.com/GJ2ms.png

Frequency vs Radius Graph: http://i.imgur.com/JtxbR.png

Homework Equations

Fc = 4π²mrf²

The Attempt at a Solution

C) and D) I am stuck at

E)
Fc = 4π²mrf²
\sqrt{}\frac{Fc}{4π²mr}

 

[PeterO]

Homework Statement

Hi I'm doing a physics lab about uniform circular motion to measure frequency and to compare it to mass,radius and force tension.

(A & B) I did
(C,D, E) I need help

(a) What variables are being measured / manipulated in this lab? What type of relationship is being tested? (radius, mass, force tension/force causing centripetal force)

(b) Graph the relationship between the frequency of revolution and each of the following:
• the magnitude of the tension force [force causing the circular motion(centripetal force)]
• the radius of the circular path
• the mass of the object

**■→(c) Find the proportionalities between frequency of revolution and the variables in radius, mass, and force of tension/centripetal force.

**■→(d) Derive an equation for the frequency in terms of the tension, the radius, and the mass by combining your results from (c) and using your results from (b) to verify.

**■→(e) The following relationship gives the magnitude of the net force causing the acceleration of an object in uniform circular motion:
Fc = 4π²mrf²
Rearrange this equation to isolate the frequency. Compare this result with the equation you derived in (d). Indicate the likely causes for any discrepancies.

Data: http://i.imgur.com/dLpyP.png

Frequency vs Force Graph: http://i.imgur.com/fyFci.png

Frequency vs Mass Graph: http://i.imgur.com/GJ2ms.png

Frequency vs Radius Graph: http://i.imgur.com/JtxbR.png

Homework Equations

Fc = 4π²mrf²

The Attempt at a Solution

C) and D) I am stuck at

E)
Fc = 4π²mrf²
\sqrt{}\frac{Fc}{4π²mr}

Your graphs are not extensive enough - they must include the origin (0,0) - not necessarily as a point, but with the axes long enough for them to show up.

With graphical analysis, the only line you can confidently interpret is a straight line passing through the origin.

if y vs x is not straight, you can try y vs 1/x or y vs x² or or y vs 1/x² or y vs x² of y vs √x or y vs 1/√x to see if any of them are a straight line through the origin [or close - there may be uncertainties in your measurements]

suppose y vs 1/√x was such a straight line.

That means y is proportional to 1/√x or y = k/√x or y²x = k

 

[MrWarlock616]

uhmm.. time for one cycle is 1/frequency.

 

[PeterO]

uhmm.. time for one cycle is 1/frequency.

Looking at your results, I am not sure the figure you call frequency is in fact frequency.
It looks more like the Period to me - ie the time for one cycle.
You possibly need to follow the step you mention above.

 

[MrWarlock616]

Looking at your results, I am not sure the figure you call frequency is in fact frequency.
It looks more like the Period to me - ie the time for one cycle.
You possibly need to follow the step you mention above.

Yes exactly, that's what I said. The graphs are obviously wrong because he has used time period instead of frequency.
peter, I didn't ask this question..n3w ton did. :P