 #1
 91
 9
This isn't a homework question, but instead a question about an example in a book I'm reading, in prep for next semester. As such using the posting template is a bit of a miss. Hope that can be forgiven.
1. Homework Statement
I'm reading "An Introduction to Error Analysis" by John R Taylor during my spring vacation as brush up for my next semester. I encountered an example that doesn't make sense to me though. It goes through teaching 3 rules as follows:
(3.8)
(3.9)
(3.10)
Now the example it gives is as follows (leaving out units for ease):
##t = 1.6\pm0.1##
##h = 46.2\pm0.3##
Now it calculates ##g = \frac{2*h}{t^2}## and more importantly its uncertainty as follows:
$$\frac{\delta g}{g}=\frac{\delta h}{h}+2*\frac{\delta t}{t} = 0.007+2*0.063 = 0.133$$
as justifed by 3.8 and 3.10. However here is my problem; What about 3.9?
As far as I can see, the example completely forgets about the factor 2. With 3.9 in mind, ##x = \frac{h}{t^2}## shouldn't it be:
$$\frac{\delta g}{g}=2*\left(\frac{\delta h}{h}+2*\frac{\delta t}{t}\right)$$
What am I missing?
1. Homework Statement
I'm reading "An Introduction to Error Analysis" by John R Taylor during my spring vacation as brush up for my next semester. I encountered an example that doesn't make sense to me though. It goes through teaching 3 rules as follows:
Now the example it gives is as follows (leaving out units for ease):
##t = 1.6\pm0.1##
##h = 46.2\pm0.3##
Now it calculates ##g = \frac{2*h}{t^2}## and more importantly its uncertainty as follows:
$$\frac{\delta g}{g}=\frac{\delta h}{h}+2*\frac{\delta t}{t} = 0.007+2*0.063 = 0.133$$
as justifed by 3.8 and 3.10. However here is my problem; What about 3.9?
The Attempt at a Solution
As far as I can see, the example completely forgets about the factor 2. With 3.9 in mind, ##x = \frac{h}{t^2}## shouldn't it be:
$$\frac{\delta g}{g}=2*\left(\frac{\delta h}{h}+2*\frac{\delta t}{t}\right)$$
What am I missing?
Attachments

15.4 KB Views: 236

58.5 KB Views: 177

9.1 KB Views: 168