Homework #6
ME 236
I. Review Questions (Not Due)
1. Consider the equation H 
d 1 / 3
. If the uncertainty of each variable is the same fraction of
10k 1 / 5
their respective nominal value, what variable’s uncertainty has the largest effect on the
uncertainty in H?
a. 
b. d
c. k
d. H
2. Consider the function F  AB 0.5C 2 / 3 / D 4 / 7 , where A, B, C, and D are measured variables. If
all these variables have the same uncertainty (as a percentage of the nominal value), which
variable affects the uncertainty in the function F the most?
a. A
b. B
c. C
d. D
II. Homework (Due)
Turn in the following problems from the book, plus Problem 6A below.
6-1, 2, 3, 4, 8
6A. Earth’s gravity varies along its surface, and a large portion of this variation is from
centripetal acceleration due to the rotation of the earth. The centripetal acceleration at the
surface of the Earth can be calculated by
2
 2 
2
aR  
 RE cos  ,
 T 
where T = period of rotation of the Earth = 8.64x104 s (negligible uncertainty)
RE = radius of Earth = 6.37x106 m ± 1500 m
 = Latitude on Earth (radians)
a. If our latitude on Earth is 35 degrees, 17 minutes ± 1 degree (35.3 ± 1.0°), determine our local
centripetal acceleration and its uncertainty. Use dimensional uncertainty propagation. (Hint:
and recall that 180° = π radians)
b. If the local gravity (without rotation) is 9.806 m/s2, what is the local effective gravity, and its
uncertainty? (In doing so, make an assumption about the uncertainty in the value of gravity
without rotation, g = 9.806 m/s2.)