Calculate the uncertainty in the force

Question

F = ma

The uncertainty of m is ±0.05kg and the uncertainty in a is ±0.005 m/s²

The measured values of F, m and a are: m = 5.00kg, F = 15.0N and a = 3.000 m/s²

Answer 1

Hi Mafer A.,

Propagation of indeterminate error (which is what you are essentially dealing with, for a symmetrically-distributed error interval) can be done either by "brute force", i.e. calculate the limits exactly using the extremes of the possible values, or "elegantly", by propagation of variance (which is the scientifically preferred method). But since you are given "hard" limits here, you might as well do by brute force, i.e. as (5.00-0.05)*(3.000-0.005) and (5.00+0.05)*(3.000+0.005) N. Note that the resultant interval need not necessarily be +- exactly the same amount, from the nominal value!

For the better treatment of indeterminate error propagation, consult any on-line reference. Since you don't have any idea what the error intervals represent here (i.e., are they 90% confidence limits? are they standard deviations?), you cannot convert them into variances in order to do the "elegant" treatment.

-- Cheers, -- Mr. d.