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 1/299 792 458 of a second. Related to Imperial Units: 1 meter = 3.28 ft = 39.97 inches = 1.09 yards Note: Light is million times faster than sound!

time: second(s) The second is the duration of 9 192 631 770 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 µ 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 * 1610 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