P185 Error Analysis Worksheets 1
Revised 1/29/08
Error Analysis for Physics 185
Overall Goals:
1. Determine basic uncertainties: reading error, calibration error, and other errors.
2. Distinguish between systematic errors, random errors, and blunders.
3. Understand absolute and % errors.
4. Combine errors and compare numbers using uncertainties.
5. Propagate errors by formulas and direct substitution.
Lab Errror Analysis Goal
1 Galileo and the Pendulum Basic uncertainties
2 Free-fall Basic uncertainties
3 Motion Absolute and % errors
4 Fluid Flow Absolute and % errors
5 Newton’s 3rd Law Combine and compare errors
6 Moment of Inertia Combine and compare errors
7 Conservation of Momentum Propagate errors by direct substitution
.8 Simple Harmonic Motion Propagate errors by direct substitution
9 The Physical Pendulum Propagate errors by formulas
10 Velocity of Sound Propagate errors by formulas
P185 Error Analysis Worksheets 2
Revised 1/29/08
1. Error analysis for the simple pendulum: Determining basic errors
Your instructor will show you how to find uncertainties on quantities you measure
directly.
List the quantity measured and its units.
Least each error, with either units (for an “absolute” uncertainty), or a “%”.
Briefly indicate how you determined the errors.
Quantity Errors How determined
Reading
Calib.
Other
Reading
Calib.
Other
Reading
Calib.
Other
P185 Error Analysis Worksheets 3
Revised 1/29/08
2. Error analysis for the free-fall: Determining basic errors
Your instructor will show you how to find uncertainties on quantities you measure
directly.
List the quantity measured and its units.
Least each error, with either units (for an “absolute” uncertainty), or a “%”.
Briefly indicate how you determined the errors.
Quantity Errors How determined
Reading
Calib.
Other
Reading
Calib.
Other
Reading
Calib.
Other
P185 Error Analysis Worksheets 4
Revised 1/29/08
3. Error analysis for free-fall: Absolute and % Errors
Use your data from the free-fall experiment for this exercise.
Pick two successive values for x and t. Find the uncertainties on each x and t value.
To change between % to absolute for a measurement of “x” use:
abs %
% 100 abs x
x 100
Quantity READING CALIBRATION OTHER
Abs. % Abs. % Abs. %
xA
xB
tA
tB
P185 Error Analysis Worksheets 5
Revised 1/29/08
4. Error analysis for fluid flow: Absolute and % Errors
Find the uncertainties on each measured quantity, including units.
For time “t” find the uncertainty for part A and again for part B, since you may measure
these in different ways.
To change between % to absolute for a measurement of “x” use:
abs %
% 100 abs x
x 100
Quantity READING CALIBRATION OTHER
Abs. % Abs. % Abs. %
h
m
tA
tB
P185 Error Analysis Worksheets 6
Revised 1/29/08
5. Error analysis for Newton’s 3rd Law: Combining and Comparing
Pick the peak force from each force sensor for one collision. Find the uncertainties on
each F. Explain how you determined the errors. Compare using the uncertainties.
Find the impulse for each force sensor for one collision. Find the uncertainties on each
I. Explain how you determined the errors. Compare using the uncertainties.
To find the total error use: READING CALIBRATION OTHER
2 2 2
READ CAL OTHER
Abs % Abs % Abs % Abs %
FA
FB
IA
IB
P185 Error Analysis Worksheets 7
Revised 1/29/08
6. Error analysis for Moment of Inertia: Combining and Comparing
Find the uncertainties on your determination of the spindle diameter “D.” Explain how
you determined the errors:
Find the uncertainties on your determination of the time for the weight to fall “t.” Explain
how you determined the errors:
List the errors on D, t, d, and h. To find the total error use: READING CALIBRATION OTHER
2 2 2
READ CAL OTHER
Abs % Abs % Abs % Abs %
D
t
d
h
P185 Error Analysis Worksheets 8
Revised 1/29/08
7. Error analysis for Momentum: Propagating Errors by Substitution
Write the formula for p in terms of mA, mB, vA, and vB,: __________________________
Find the errors on each quantity used in your formula and find the total error on each.
READ CAL OTHER
Abs % Abs % Abs % Abs %
mA
mB
vA,I
vB,I
vA,F
vB,F
Use the uncertainty to find the largest and smallest value for p.
Quantity Value Max Value Min Value Abs. Unc
pINITIAL .
pFINAL
Are your results consistent with momentum being conserved? Explain.
P185 Error Analysis Worksheets 9
Revised 1/29/08
8. Error analysis for Harmonic Motion: Propagating Errors by Substitution
Write the formula for k in terms of T, m, and m’: _______________________________
Find the errors on each quantity used in your formula and find the total error on each.
READ CAL OTHER
Abs % Abs % Abs % Abs %
T1
m1
m´1
T2
m2
m´2
Use the uncertainty to find the largest and smallest value for k. Assume m’ = (1/3)m.
Quantity Value Max Value Min Value Abs. Unc
k1 .
k2
Are your results consistent? Explain.
P185 Error Analysis Worksheets 10
Revised 1/29/08
9. Error analysis The Physical Pendulum: Propagating Errors by Formula
Write the formula for k in terms of g, r, and T: _______________________________
Find the value of k for two data points: __________ , _________
Find the errors on each quantity used in your formula and find the total error on each.
Do this for both data points.
READ CAL OTHER
Abs % Abs % Abs % Abs %
g1
r1
T1
g2
r2
T2
Find the formula for (k). Show your work
Use the uncertainties in the table to find the largest and smallest value for each k.
k1: Max ________ Min ________ k2: Max ________ Min ________
Are your results consistent? Explain.
P185 Error Analysis Worksheets 11
Revised 1/29/08
10. Error analysis The Speed of Sound: Propagating Errors by Formula
Write the formula for v in terms of f and : _______________________________
Find the value of v for two data points. __________ , _________
Find the errors on each quantity used in your formula and find the total error on each.
Do this for both data points.
READ CAL OTHER
Abs % Abs % Abs % Abs %
f1
1
f1
1
Find the formula for (v). Show your work
Use the uncertainties in the table to find the largest and smallest value for each v.
v1: Max ________ Min ________ v2: Max ________ Min ________
Are your results consistent? Explain.