x = xbest
General Formula for Error Propagation
y = ybest y
z = zbest z
q = q( x , y , z )
qbest = q( xbest , ybest , zbest )
q q q
q = x + y + z
for independent random
errors x, y, and z
main formula for error propagation
p p g
Final Exam: Monday, December 8, 2:00 - 2:50 pm, York Hall 2622
What: The exam will cover the material in the lectures and the labs.
Some of the questions will be similar to the homework problems
and lecture examples. Lab questions will include derivation
Part 2 The Rods is optional extra credit up to 2 points
Measure the radii R and r and the total mass
Mttotall = M + m
Measure I by torsion pendulum
Determine the density of the outer cylinder
M i the mass of the outer cylinder
find q if x and y are not independent
q for arbitrary x and y
x and y can be correlated
when x and y are independent xy = 0
Coefficient of Linear Correlation
do N pairs of (xi , yi) satisfy a linear relation ?
linear correlation c
period of pendulum
T = 2
two methods to find uncertainty
x1 , x2 , . , xN
N measurements of the quantity x
xbest = x
the best estimate for x the averag
A LABORATORY COURSE ON EXPERIMENTAL METHODS OF PHYSICS
2117 Natural Sciences Building
buto @p ys cs ucsd edu
Monday 3:00 - 5:00 pm
Lab TA Coordinator:
A student measures a quantity x many times and calculates the mean as x = 10 and
the standard deviation as = 1. What fraction of his readings would you expect to
find b t
fi d between 11 and 12?
G X , ( x ) =
e ( x X ) / 2
Prob( X x
Measure the density of the Earth
Learn to estimate and propagate errors
Measure moments of inertia
Statistical analysis. Use repeated measurements to reduce random errors
Design a shock absorber
Design something using mechanical sys
6. You want to combine your measurement of a spring constant (k = 17
5 N/m) with those from two other groups.
If two other methods yielded value of k = 22 2 V and 15 3 V, what
is the BEST WEIGHTED AVERAGE value and its uncertainty?
(Recall w = 1/.) State
5. Suppose you measure the height of the cliff in experiment 1ten times
with an average values h = 55.5 m and a standard deviation of 1.0 m.
(a) What is the probability of a measurement having a value of 53.4 m
given the above average and standard deviati
4. Two separate sets of the spring constant from experiment 3 gave
values of (6.33 0.08) N/m and (7.56 0.12) N/m.
(a) How do we decide whether the values agree? Calculate the
discrepancy in standard deviations.
(b) With what probability can the discrepanc
Practice Final for Physics 2BL
1. In laboratory #1 you determined the gravitational constant g by
measuring the period of a pendulum 10 times and measuring the
length of the pendulum string. The basic equation used in the
(a) Suppose your v
2. In experiment 2, you measure 5 values for the rolling time of a single
racket ball. Suppose you measure 3.092 s, 3.101 s, 3.098 s, 3.095 s
and 4.056 s.
(a) Calculate the BEST value for the rolling time.
(b) Calculate the STANDARD DEVIATION for the data