SYLLABUS FOR PHYSICS 2BL

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SYLLABUS FOR PHYSICS 2BL A COURSE ON LABORATORY
METHODS OF PHYSICS Instructor Professor Alex
Groisman 7254 Urey Hall Email
agroisman_at_ucsd.edu Office Hour Monday
900-1000 or catch me after class on Monday Lab
Instructor Sara Bodde E-mail sgbodde_at_gmail.com
Lecture Monday 500-550 pm Final exam
Monday, June 5, 500-550 pm, Warren 2001. (10th
week of classes) Text J. R. Taylor,
An Introduction to Error Analysis.
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Textbook
Introduction to Error Analysis, by Taylor. No
experimental information but good intro on how to
handle data once your experiment produces
some Full of Homework problems and helpful
examples.
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Grading

• Lab 1 15
• Lab 2 15
• Lab 3 20
• Lab 4 15
• Lab activity 5
• Homework 10
• Final exam 20

Labs 1, 2, 3 pre-lab and interview (short quiz)
by an instructor 3 work in the lab and
written lab report description of the
experiment, presentation of the data, error
analysis, discussion and conclusions 12

100
Lab 3 will be worth 20 of the total numeric
grade and will involve writing a formal report,
which has to be submitted in a printed form.
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Homework

• Problems listed on 2BL Spring 2006 Schedule
• All problems are from the book by Taylor
• Turn them in to TA in Lab as on schedule
• The problems in the final exam will be similar to
  the problems from your homework and will test
  your understanding of the error analysis.

There are 8 separate homework assignments, 3-4
problems in each, to be turned in on separate
pages during weeks 2-9. Although homework
problems are worth only 10, solving them on your
own will prepare you for the Final, which is
worth 20.
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Four Easy Experiments

• A different kind of lab course.
• No cookbook
• Student is responsible for measurement and
  presentation

• Measure the density of the earth.
• Measure simple things like lengths and times.
• Learn to estimate and propagate errors.
• Measure moments of inertia.
• Use repeated measurements to reduce random
  errors.
• Design, build, and test shock absorber.
• Get the bugs out of your mechanical system.
• Measure coulomb force and calibrate voltmeter.
• Reduce systematic errors in a precise
  measurement.

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The correct way to state the result of
measurement is to give a best estimate of the
quantity and the range within which you are
confident the quantity liesBest Estimate
Uncertainty.
L 1.7 0.2 cm - your best estimate for the
length is 1.7 cm, and you estimate its range of
probable values to be from 1.5 to 1.9 cm.
(measured value of x )
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Rule 1 for stating uncertainties experimental
uncertainties should almost always be rounded to
one significant figure.
(measured g ) 9.85 0.09328 m/s2 - WRONG
(measured g ) 9.85 0.09 m/s2 - CORRECT
Rule 2 for stating uncertainties the last
significant figure in any stated answer should
usually be of the same order of magnitude (in the
same decimal position) as the uncertainty.
L 1.668 0.3 cm - WRONG
L 1.7 0.3 cm - CORRECT
What should we do with this one?
(measured g ) 9.85387 0.11328 m/s2 -
9.9 0.1 m/s2 ?
If the 1st significant figure in the uncertainty
is 1 it is a good idea to keep two figures, dg
0.11 and
(measured g ) 9.85 0.11 m/s2
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Examples
1) (measured height )
2) (measured time )
3) (charge )
4) (wavelength )
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Examples
3) (charge )
4) (wavelength )
5) (momentum )
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Two types of measurement errors

• Random Errors
• Can be reduced by repeated measurements.
• Can also be estimated by repeated measurement.
• Example measure the fraction of people over 6
  by surveying 100 people from around the world.
• Systematic Errors
• Harder to estimate and reduce.
• Calibration errors, neglecting small corrections,
  or mistakes.
• Example measure the fraction of people over 6
  by surveying a group from France.

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Error Propagation
What is the perimeter of this figure?
p w x y z
You measure x, y, x, w and compute p.
How would you calculate the error on p?

• First, you estimate errors from x, y, x, w. They
  all are likely to be on the order of precision of
  the ruler, 1/32 or 0.75 mm.
• Next, you propagate them following certain rules
  to compute the error on p.

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Error Propagation
p w x y z
We estimate errors on x, y, z, and w as
What is our estimate of error on p?
Since ,
However, since dx, dy, dz and dw are all error
estimates, we do not know the signs of the actual
errors. Therefore, it could be
OR
We would normally use the rule of addition in
quadrature