Physics 1140 Summer 2011
Homework Set #2
(Solutions)
For problems 1-5, show the algebraic representation for the uncertainty, any other necessary work, and give the
final answer in the Standard Format. Let x = 45 + 3, y = 4.3 + 0.5, and z = 12.3 + 0.6
1.
Uncertainty in sums/differences combined with uncertainty in a measurement times an exact number:
(equations 3.9 and 3.16)
f = x + 3y
f = 58 + 3
2. Uncertainty in products/quotients: (equation 3.18)
a.) r = (x)(z)
r = 550 + 50
b.) s = z/y
s = 2.9 + 0.4
3. Uncertainty in a power: (equation 3.26)
a.) g = z3
g = 1900 + 300
b.) h = x-1/5
h = 0.467 + 0.006
4. Uncertainty in a function of a single variable: (equation 3.23)
a.) t = 3y2 + y + 10
t = 480 + 40
b.) p = ln(x)
p = 3.81 + 0.07
5. Uncertainty in a function of several variables: (equation 3.47 aka: “The Master Rule”)
q(x, y, z) = 2x + 3y3 – (1/z2)
q(x, y, z) = 330 + 80
6. A student measures the speed of sound by performing the Doppler Experiment in the 1140 lab. The student
measures the speed of sound to be 345.8 + 0.9 m/sec, while the accepted value for the speed of sound in
the lab is 343.6 m/sec. Calculate the discrepancy and percent discrepancy between these two numbers. Is
the student’s measurement consistent with the accepted value? Why or why not?
Discrepancy = 2.2,
%Discrepancy = 0.6%
7. a.)A student is asked to find the angular momentum of a disk. The formula is: L = (1/2)MR2 , where the
mass M = 2.20 +0.10 kg, the radius R = 0.250 + 0.005 m, and the angular rotation rate  = 43.0 + 0.8
radians/sec. What is L + L, including units? Show all your work, and express your answer in Standard
Format.
L = 3.0 + 0.2 (kg m2)/sec
b.) Another student makes the same measurements of another disk that is supposed to be identical to the
first and makes the following measurements: M = 2.40 + 0.10 kg, R = 0.255 + 0.003 m, and  = 42.1 + 0.5
rad/sec. What is L + L for this second disk, including units? Show all of your work, and express your
answer in Standard Format.
L = 3.3 + 0.2 (kg m2)/sec
c.) Finally, compare the two angular momentums (find the discrepancy) and make a determination whether
these two disks are indeed identical. Each measurement agrees within uncertainties. The disks are likely
identical.