Department

PhysicsCourse Code

PHYSICS H90Professor

Jonathan Lee FengLecture

2This

**preview**shows half of the first page. to view the full**3 pages of the document.**Jessica Mangold

Physics H90

Professor Feng

Week 1 Lecture 2

1/9/19

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

answers

- 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

accurate?

- 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

bat?

- the velocity must depend on D = 400 feet, g = 9.8 m/s2, v = f(D, g)

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