physics for geniuses?

Question

within the precisions of a high school lab, do these data points at least somewhat support the relation that v^2 is proportional to Fc

from the equation v^2=Fc*r/m

Fc=.49 V=4.4 m/s
.98, 6.1
1.5, 7.1
2.0, 8.0

I see the Fc go up about .5 each time and with one exception, the velocity going up 1 each time....I just need help seeing how these points relate to the relationship v^2 is proportional to Fc

Answer 1

If v^2 is proportional to Fc, then v^2 = k*Fc, where k is a constant. For each of your values of v and Fc, calculate k = v^2/Fc;

You will get the following values for k:

39.51, 37.97, 33.61, 32

These average to 35.77 and the standard deviation is about 10%, which would be considered a good fit and that the formula

V^2 = 35.77*Fc fits those values pretty well.

Answer 2

The best way to visualize this is to graph the theoretical relationship you are considering in one color, and then mark your experimental values on the same graph in another color. You can see how well they correlate. Then try plotting the same thing on semi-log paper. See the references and others for free online graph paper you can print yourself.

This doesn't require genius.