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Lecture 2

PHYSICS H90 Lecture 2: physicswk1lec2Premium

3 pages60 viewsWinter 2019

Course Code
Jonathan Lee Feng

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Jessica Mangold
Physics H90
Professor Feng
Week 1 Lecture 2
Back of the Envelope Calculations, Graphs, Data, How to Lie with Statistics
Dimensional Analysis
- use the fact that two sides of an equation must have the same dimensions
- checking that the units agree can help avoid mistakes, eliminate multiple choice
answers, etc.
- can be used to find an approx. answer with very little work & to understand how the
answers depend on input parameters (scaling)
Back of the Envelope
- exact answers are great, but often, a reasonable estimate is even better
- little work -> know what to expect & provide reality check on more precise
- especially powerful when used in conjunction with dimensional analysis
- components of a good back of the envelope calculation:
- get an estimate, with assumptions stated clearly
- identify the dominant sources of uncertainty
- estimate the uncertainty
- (sometimes) determine how your answer scales with input parameters
Example A: Trump Tax Code Photo Op
- Claim: “In 1960 the tax code was 20,000; now it is 185,000 pages” -> Are these photos
- consider the big pile of paper -> start with something we (roughly) know: 500 pages is
about 2 inches high
- know that Trump is about 80 inches tall
*see notebook for calculations
- calculated that estimate there are about 300,000 pages in the pile
- how sure am I of the facts that went into this calculation?
- dominant source of uncertainty: we can be pretty sure about the number of
stacks per pile. the number of inches per stack is, perhaps, uncertain by a fraction
factor of ~10%, & similarly with the number of pages per in
- what this means: when we estimated 80 in/stack, it could be 70 in/stack or 90 in/stack
- we estimate that our answer is probability correct to within a fractional
uncertainty of ~10%
- we cannot be off by a factor of 2, which is what would be required for Trump’s
statement to be correct
Example B: Home Run Ball
- a home run baseball travels 400 feet -> roughly how fast was it going when it left the
- the velocity must depend on D = 400 feet, g = 9.8 m/s2, v = f(D, g)
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