Combining Equations for Lab report

[chroncile]

Homework Statement

I'm doing a lab report for frequency vs centripetal force and frequency vs radius. I have two tables and I have found the equations for both the graphs. When I combine the equations, should I make another table and how would it look like?

Homework Equations

f = c^0.5
f = r^-1

The Attempt at a Solution

I have two tables:

Table 1: Centripetal Force and Frequency for a constant radius of 60.7 cm and constant rotations of 10

Centripetal Force (0.1 N) Time Required (0.1 s) Average time (s) Period (for 1 rotation) (s) Frequency (Hz)
Trial 1 Trial 2 Trial 3
0.5 9.17 9.47 9.56 9.40 0.940 1.06
1.0 6.03 6.16 5.89 6.03 0.603 1.66
1.5 5.68 5.69 5.63 5.67 0.567 1.76
2.0 4.86 4.90 4.82 4.86 0.486 2.06
2.5 4.55 4.59 4.53 4.56 0.456 2.19
3.0 4.35 4.21 4.36 4.31 0.431 2.32

Table 2: Radius and Frequency for a constant centripetal Force of 1 N and constant rotations of 10
Radius (0.5 cm) Time Required
(0.1 s) Average time (s) Period (for 1 rotation) (s) Frequency (Hz)
Trial 1 Trial 2 Trial 3
52.2 4.84 4.97 4.66 4.82 0.482 2.07
55.7 5.56 5.68 5.68 5.64 0.564 1.77
61.1 6.01 5.96 5.75 5.91 0.591 1.69
64.9 5.95 6.09 6.01 6.02 0.602 1.66
69.1 6.20 6.30 6.15 6.22 0.622 1.61
75.4 6.87 6.77 6.50 6.71 0.671 1.49

 

[Delphi51]

Sounds like an interesting experiment.
I expect the graph of Fc vs f would be curved. How did you find its equation and what equation did you get?
Same for the f vs r graph.
Combining the two equations is kind of tricky; I think a 3rd graph would be quite helpful and the equations you got for the first two would suggest what to put on the axes of the 3rd graph.

 

[chroncile]

For frequency and centripetal force, I got a graph similar to y = ax^b and for frequency and radius, I got a graph that is similar to y = 1/x

When I put them together, I got a linear graph y = x

 

[Delphi51]

For frequency and centripetal force, I got a graph similar to y = ax^b

Okay, so is that Fc = af^b or f = aFc^b? You need it a little more specifically. Take a wild guess and try Fc = a*f².
(some people would take a peek at the list of equations for circular motion and notice that Fc = 4π²mrf² so Fc = constant*f² is it!)
You have to check that by graphing Fc vs f² and it should turn out to be a straight line to within experimental error. Maybe you are supposed to estimate your error in measurement and put an error bar or two on the graph. If you get a straight line, then you know
Fc is proportional to f².

for frequency and radius, I got a graph that is similar to y = 1/x

You mean f = b/r, right? You could try graphing f vs 1/r and see if you get a straight line.
I suspect you will have to try f² vs 1/r or f vs 1/r² to get that straight line.

If all that works out you will know f² is proportional to Fc and also that f² is proportional to 1/r. That suggests f² is proportional to Fc/r, and that you graph Fc vs r*f². A straight line there gives you the formula for how Fc varies with r and f.

 

[rwisz]

To combine the equations for frequency vs centripetal force and frequency vs radius, you can create a new table that includes the values for both variables. It would look something like this:

Combined Table: Frequency vs Centripetal Force and Radius

Centripetal Force (N) Radius (cm) Frequency (Hz)
0.5 60.7 1.06
1.0 60.7 1.66
1.5 60.7 1.76
2.0 60.7 2.06
2.5 60.7 2.19
3.0 60.7 2.32
1.0 52.2 2.07
1.0 55.7 1.77
1.0 61.1 1.69
1.0 64.9 1.66
1.0 69.1 1.61
1.0 75.4 1.49

This table allows you to see how the frequency changes with both the centripetal force and the radius. You can use this data to plot a graph of frequency vs both variables, which may provide further insight into the relationship between frequency, centripetal force, and radius. Additionally, you can use this table to calculate the average frequency for each combination of centripetal force and radius, which can help you determine any patterns or trends in the data. Overall, including a combined table can provide a more comprehensive understanding of the relationship between frequency, centripetal force, and radius in your lab report.