using linear least squares in excel

[whizbang]

the question is:

Assume that, for a fixed value of the radius, the centripetal acceleration depends on velocity in the following way:
a = k1 v^m
where m is an integer. For each value of r used plot lna versus lnv for your five acceleration values and fit to a straight line. From your fit, determine the value of the exponent m and its uncertainty.

I've got the plots and all of the information used to solve this problem, but I am confused as to how i would even go about it. Although the question is rather straight forward, I'm not experienced at all in this type of math, assuming i already have the fit, how would i determine the value of the exponent and its uncertainty?

 

[tkhunny]

You should ahve some materials in Linear Regression. You will need this information.

Since a = k * v^m is most certainly NOT linear, it will take a little effort to make linear methods applicable.

The answer is the logarithm

ln(a) = ln(k * v^m) = ln(k) + ln(v^m) = ln(k) + m*ln(v)

There we have it. ln(a) = ln(k) + m*ln(v) -- This should look very linear to you. This is why you were asked to plot ln(a) against ln(v), rather than a against v.