Solution Found!
Estimate U, and find the relative uncertainty in the
Chapter 3, Problem 20E(choose chapter or problem)
Estimate , and find the relative uncertainty in the estimate, assuming that \(X=5.0 \pm 0.2\) and \(Y=10.0 \pm 0.5\)
a. \(U=X \sqrt{Y}\)
b. \(U=2 Y / \sqrt{X}\)
c. \(U=X^{2}+Y^{2}\)
Equation Transcription:
Text Transcription:
X=5.0{+/-}0.2
Y=10.0{+/-}0.5
U=X{sqrt}Y
U=2Y/sqrt{X{
U=X^2+Y^2
Questions & Answers
QUESTION:
Estimate , and find the relative uncertainty in the estimate, assuming that \(X=5.0 \pm 0.2\) and \(Y=10.0 \pm 0.5\)
a. \(U=X \sqrt{Y}\)
b. \(U=2 Y / \sqrt{X}\)
c. \(U=X^{2}+Y^{2}\)
Equation Transcription:
Text Transcription:
X=5.0{+/-}0.2
Y=10.0{+/-}0.5
U=X{sqrt}Y
U=2Y/sqrt{X{
U=X^2+Y^2
ANSWER:
Solution :
Step 1 of 3:
Given and
Here ,
and
,
.
Our goal is :
We need to estimate U and the relative uncertainty in the estimate.
a).
b). and
c).
a).
Now we have to estimate U and the relative uncertainty in the estimate.
We know that and
Here ,
and
,
.
The estimate of U is
Therefore the estimate of U is 15.811.
Now computing the partial derivatives of .
Here we are differentiating with respect to X.
We know that x value.
Therefore
Then,
Now we are differentiating with respect to Y.
We know that Y value.
Therefore
Now we have to find the relative uncertainty in the estimate.
Then,
We substitute all the values in the above equation.
Therefore the relative uncertainty in the estimate is 0.4716.
Hence or
.