Calculating an equations error given the error of a single value

[buttermellow]

Say you had an equation like E = .5mv². If in an experiment the velocity is measured, but has an error of 10%, what would be the total error in calculating E?

 

[I like Serena]

Hi buttermellow, welcome to PF!

Is this a homework question?

If so, what do you think it should be?
That way we can help you better to understand how to calculate such errors...

 

[ZealScience]

What about m? Just use addition of percentage error here. While making product percentage errors are added, while making sums just add errors. After all, uncertainty of E depends on m as well.

 

[HallsofIvy]

There is an engineers rule of thumb that says that when measurements are added or subtracted their errors add. When measurements are multiplied or divided, their relative errors (error divided by the value) add.

If f= xy and x has error dx, y has error dy, then f could be as large as (x+ dx)(y+ dy)= xy+ xdy+ ydx+ dxdy. Neglecting the small dxdy (if dx and dy are small, dxdy will be much smaller), the error is xdy+ ydx so the relative error is (xdy+ ydx)/(xy)= dy/y+ dx/x.

With 0.5mv^2, for small errors dm and dv, the relative error is dm/m+ 2dv/v.