Solution Found!
Refer to Exercise 5.a. Assume g = 9.80 m/s2 exactly, and
Chapter 3, Problem 15E(choose chapter or problem)
Refer to Exercise 5.
a. Assume \(g=9.80 \mathrm{~m} / \mathrm{s}^{2}\) exactly, and that \(L=0.855 \pm 0.005 \mathrm{~m}\). Estimate T , and find the relative uncertainty in the estimate.
b. Assume \(L=0.855 \mathrm{~m}\) exactly, and that \(T=1.856 \pm 0.005 \mathrm{~s}\). Estimate g, and find the relative uncertainty in the estimate.
Equation Transcription:
Text Transcription:
g=9.80 m/s^2
L=0.855{+/-}0.005 m
L=0.855 m
T=1.856{+/-}0.005 s
Questions & Answers
QUESTION:
Refer to Exercise 5.
a. Assume \(g=9.80 \mathrm{~m} / \mathrm{s}^{2}\) exactly, and that \(L=0.855 \pm 0.005 \mathrm{~m}\). Estimate T , and find the relative uncertainty in the estimate.
b. Assume \(L=0.855 \mathrm{~m}\) exactly, and that \(T=1.856 \pm 0.005 \mathrm{~s}\). Estimate g, and find the relative uncertainty in the estimate.
Equation Transcription:
Text Transcription:
g=9.80 m/s^2
L=0.855{+/-}0.005 m
L=0.855 m
T=1.856{+/-}0.005 s
ANSWER:
Answer:
Step 1 of 3:
a). The aim is to estimate T and to find the relative uncertainty in T.
Given, and
Here, L = 0.855,
Now, estimate the value of is
= 6.28 (0.2953)
= 1.856 s
Then, differentiate with respect to , we get
= (since