Question

This lab will introduce you to the concept of experimental error and propagation of error throughout calculations. It is highly recommended you read Appendix D before this lab. TIP: If a multi-step calculation involves performing addition/subtraction before multiplication/division, then you can find the associated error with the addition/subtraction calculation, then use that as input in the multiplication/division calculation. Consider the following calculation:x The following experimental values and their errors are obtained: a = 44.3, Aa = 1.2 b = 18.8, Ab = 3.1 c = 42.8 , Ac = 2.2 What is the absolute error in x (Ax)? Note we are not asking for the value of x itself, only its error. Report your answer to 2 significant figures.

Answer 1

absolute error in x = 0.13

Explanation

a = 44.3 +/- 1.2

b = 18.8 +/- 3.1

c = 42.8 +/- 2.2

(b - a) = (18.8 +/- 3.1) - (44.3 +/- 1.2)

(b - a) = (18.8 - 44.3) +/- (3.1 + 1.2)

(b - a) = -25.5 +/- 4.3

(b - a) / c = (-25.5 +/- 4.3) / (42.8 +/- 2.2)

absolute error = (25.5 / 42.8) * [(4.3 / 25.5) + (2.2 / 42.8)]

absolute error = (0.596) * (0.220)

absolute error = 0.131