Solution Found!
Refer to Exercise 19. Assume that for a certain bacterium,
Chapter 3, Problem 29E(choose chapter or problem)
Refer to Exercise 19. Assume that for a certain bacterium, \(r=0.8\pm0.1\ \mu\mathrm{m}\) and \(h=1.9\pm0.1\ \mu\mathrm{m}\).
a. Estimate \(S\), and find the relative uncertainty in the estimate.
b. Estimate \(V\), and find the relative uncertainty in the estimate.
c. Estimate \(R\), and find the relative uncertainty in the estimate.
d. Does the relative uncertainty in \(R\) depend on \(c\)?
Equation Transcription:
Text Transcription:
r = 0.8 pm 0.1 mu m
h = 1.9 pm 0.1 mu m
S
V
R
c
Questions & Answers
QUESTION:
Refer to Exercise 19. Assume that for a certain bacterium, \(r=0.8\pm0.1\ \mu\mathrm{m}\) and \(h=1.9\pm0.1\ \mu\mathrm{m}\).
a. Estimate \(S\), and find the relative uncertainty in the estimate.
b. Estimate \(V\), and find the relative uncertainty in the estimate.
c. Estimate \(R\), and find the relative uncertainty in the estimate.
d. Does the relative uncertainty in \(R\) depend on \(c\)?
Equation Transcription:
Text Transcription:
r = 0.8 pm 0.1 mu m
h = 1.9 pm 0.1 mu m
S
V
R
c
ANSWER:Solution:
Step 1of 5:
The shape of a bacterium is approximated by a cylinder of radius r and h capped on each by a hemisphere. The volume and surface area of the bacterium is given by
V =
S = (h + 2r)
Where r = 0.8and h = 1.9
0.1. Here the rate R at which the chemical is absorbed to the bacterium is R = c (S/V), where c is a constant of proportionality.
We have to find
- The estimate of S, and the relative uncertainty in the estimate.
- The estimate of V, and the relative uncertainty in the estimate.
- The estimate of R,and the relative uncertainty in the estimate.
- Whether the relative uncertainty of R depend on c.