Transcript math ppt

Math Needed for Physics
Units,Metric prefixes, sig figs,
dimensional analysis, conversions
Physics units
•Length:
•Time:
•Mass:
meters (m)
seconds (s)
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
Prefix
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!
1. Picture
2. Info
3. Equation
4. 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?
a) 3 x 109 hertz
b) 3 billion hertz
c) 3,000 megahertz
d) 3,000,000,000 hertz
e) 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!)
a) 2
b) 4
c) 6
d) 8
e) 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:
a) kg m sec
b) m sec/kg
c) 1/ (kg m sec)
d) kg m/sec
e) Kg/m/sec