I get two different answers. Which one is correct?

[carloz]

Homework Statement

M = (a-b)/2 + a

a = 15
b=5

What is the uncertainty in M if the uncertainty in a and b is ±0.7?

Homework Equations

for c = a + b
Error in c =√[(error in a)^2 + (error in b)^2]

The Attempt at a Solution

Error in M = √[0.7^2 * 3] = 1.2124

The problem I am having is that we learn that the above formula can only work when the errors are independent of one another. the error in a is obviously not independent of the error in a. so i think I'm wrong.

What do you think?

Thank you.

 

[rock.freak667]

If I remember correctly, the errors work like this:

s= a+b ⇒ Δs=Δa + Δb

s= a-b ⇒ Δs= Δa + Δb

s=ab ⇒ Δs/s = Δa/a + Δb/b

So you can apply the first two as needed.

 

[carloz]

yes. but that only works when the uncertainties in a and b are independent. however in my equation for M, a appears twice. since the error of a is not independent of a, how do i go about finding the uncertainty?

thanks.

 

[shfreeman]

Why not just simplify your problem

(a-b)/2+a

into

(3a-b)/2

and then use the rules for the error of 3a+b. You don't need to worry about the independency of error a to error a.
This way I get

(3 Δa + Δb)/2 = 1.4

Or using the other rule [ √(Δa² + Δb²) ]

( √(9*Δa² + Δb²) ) / 2 ≈ 1.1068