Question

I am working on a lab practical write up in which we have to measure the acceleration due to gravity by observing carts rolling down an incline. I have to plot a scatter plot and use a program with Linear Least Squares Fit to calculate the gradient of the graph and uncertainty for this value. This program works but I don't know how to combine the uncertainty given for the Linear Fit with the uncertainties associated with my input x and y values. Is there a way to do this?

Answer 1

We know what's the gradient its del(y)/del(x) lets denote it by m.So

This will be the form of fitted curve.

We want to calculate error in how it is associated with x,y.

Since we know that m is y/x means slope of curve.One way to calculate error propagation is as follow.

take ln both side

To calculate max error we take mod and replace - sign by +

so,

differentiate both sides partiallly

This will be the uncertainity in m given uncertainity Del(x) in x,Del(y) in y.

Here x,y will be any point on the curve we can take,usually it is taken to be lowest possible so that we can calculate max. uncertainity.

if don't get anything let me know and thumbs up.