# Math Needed for Physics

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Math Needed for Physics
Units,Metric prefixes, sig figs, dimensional analysis, conversions

Length: meters (m) Time: seconds (s) Mass: kilograms(kg)
Physics units Length: meters (m) Time: seconds (s) Mass: kilograms(kg)

Length: meter(m) The meter is the length of the path travelled by
light in vacuum during a time interval of 1/ of a second. Related to Imperial Units: 1 meter = 3.28 ft = inches = 1.09 yards Note: Light is million times faster than sound!

time: second(s) The second is the duration of periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. Related to Imperial Units: Uhhh ... its a second. Note: It used to be based on the length of a day but that changes so it makes a bad basis for a fundamental unit.

mass: kilograms(kg) The kilogram equal to the mass of the international prototype of the kilogram. On Earth, 1.0 kg has a weight of 2.2 lbs. The kg is the only unit still based on a physical object. (not same as weight, which is a force!)

Sig figs Good news: 3-4 good digits on hw & tests
bad news: on labs it does matter Ex: Stop watch: 3 numbers possible meter stick: 5 numbers possible calculating speed: only 3 numbers left!

Prefixes for units Important: saves time, sounds smart! Example:
I ran a 5k in the race My computer has 2GBytes memory The lottery is 12 mega bucks Any more?

Prefixes you need to MEMORIZE
Symbol Amount as # Amount as exponent Giga G Billion 109 Mega M Million 106 Kilo K Thousand 103 Base 1 Milli m Thousandth 10-3 Micro Millionth 10-6 Great Mighty King bakes mini marshmellows?

Factor label method “T-charts” or “Conversion factors”
Use if units are not proper (m,sec, kg) Easy is just one: 2.2 miles = ? Meters 2.2 miles * m/mile= m Hard: convert a “double unit” Example: gravity makes you fall faster by about 9.8m/s per second. That’s 22mph /sec

Dimensional analysis Dimensions can be treated like algebraic variables, but you know this already… Which makes sense, a 2000 foot per second house or a 2000 square foot house? You know you multiply length in feet by width in feet and you get square feet, that’s all dimensional analysis means – the units make sense!

Fermi number Enrico Fermi – great order of magnitude estimator
Often used to teach dimensional analysis You estimate by giving exponent only, so 300,000,000 Americans is 3 x 108, so it becomes 8 Fermi number examples: How many people in this room (1), In this school (3)? How many m thick is a dime? (-3) Together: How many cashews eaten by Americans last month? How many dimes would it take to make a stack to the moon?

Bad graphing! Labels? Units? title? Slope? Don’t connect dots!

Using the 4-step method We just say in shorthand: PIES! Picture Info
Equation Solve

Using the 4-step method A systematic method of problem solving
Step 1: Picture the description (literally!) Step 2: List (WRITE) the knowns and unknowns in the form of variables Step 3: From your list, pick the equation to use and write it by itself Step 4: Plug in and solve with units

Using the 4-step method - Example
A car accelerates from an initial speed of 5 m/s to 20 m/s over a quarter mile (400 m). What was his rate of acceleration? Pick from among these equations: (Background info: v0 means initial velocity, vf means final velocity, Δx means distance, Δt means time, a means accleration) Hint: one equation can only solve one unknown Δx = v0 Δt + ½ aΔt2 vf = v0 + a Δt vf2 = v02 + 2a Δx Use dimensional analysis to come up with the proper units for acceleration (Hint: you cannot add apples and oranges, because addition requires identical units)

Memorized prefixes – Clicker Question!
Which of the following is NOT mathematically the same as 3 Gigahertz? 3 x 109 hertz 3 billion hertz 3,000 megahertz 3,000,000,000 hertz Trick question, they all are!

Fermi – Clicker Question!
What is the Fermi number for the number of people named John Williams in the USA? (1 in 30 males are named John, 1 in 250 people have the last name Williams, half the people are males). You only get that! (2 minutes…don’t share your answer please!) 2 4 6 8 10

Conversions: Find these: (w/o using google!) a. 2.2 mph = _________1 m/s b. 1 pound = _________ kg c. 1 km = ___________mile

Dimensional Analysis – Clicker Question!
Momentum is mass x velocity. The SI unit for mass is the kg (only SI unit with a prefix!). The SI units for distance and time are meters and seconds. Using dimensional analysis, find the proper units for momentum. (1 min.) Pick one of these choices with your clicker: kg m sec m sec/kg 1/ (kg m sec) kg m/sec Kg/m/sec