I'm trying to make up an automatic spreadsheet for my Physics students so they can enter the data and see everything calculated for them, but I ran into a snag.(adsbygoogle = window.adsbygoogle || []).push({});

I have two random variables,handtwith uncertainties Δh, and Δt, respectively.

The uncertainty in h is simply estimated, based on the precision and technique used to get the data.

The uncertainty in t is taken as the standard deviation of 4 trials of an experiment.

With these two numbers,handt, I'm generating the function [itex]a=2h/t^2[/itex]. (Derived from [itex]h=\frac{1}{2} a t^2[/itex].

Here's my question: What would be the standard method for figuring the uncertainty ina?

I'm thinking the uncertainty in [itex]t^2[/itex] is [itex]2 t \Delta t[/itex] and the uncertainty in [itex]h[/itex] is [itex]\Delta h[/itex], and then you'd multiply these together to get the uncertainty in [itex]a[/itex].

Then to get an idea of uncertainty, percentage-wise, you just take that and divide by the average value of [itex]a[/itex] which is [itex]2 h / \bar t^2[/itex].

Does that sound like the right approach? I'm troubled because I feel like there's an implied factor, [itex]\Delta h/h[/itex] in the final result is going to always decrease the uncertainty. If this is done correctly, the uncertainty in the heightshouldincrease the total uncertainty.

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# How do you find the uncertainty in a function of two variables?

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