math tools: i.__________________ figures (digits) - tell you how ___________ a measurement is -...
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Math tools:
I. __________________ figures (digits)
- tell you how ___________ a measurement is
- _________ figures ________ precise
Ex: It is not that useful to
say that your height is
______________________
inches because your
height _____________ by
at least an ____________
during the day.
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Ex 1: Measure the length of a box:
L
L =
last digit is _____________
1 2 3 4 5 6
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Ex 2: Use a “better” ruler:
L
L =
last digit is ______________
1 2 3 4 5 6
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Ex 3: Measure the length of a different box:
L
L =
1 2 4 5 6 7
The precision is worthless because answer is_____________—not close to true or actual value.
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A. Figures (numbers) are significant if they are:1. ________________ numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9
2. any zeros that are:
a/ between any _________________ numbers: 509; or
b/ to the ___________ of a non-zero number AND
to the ___________ of the decimal point: 0.00790; or
c/ between a non-zero number and the __________
_________ : 10.
number # sig. figs.
number # sig. fig.
5.3 6.6070
202900 3.00 x 108
0.008 40
0.67 40.
Ex:
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B. Sig. figs. when multiplying or dividing:
C. Sig. figs. when adding or subtracting:
3.73 x 5.7 = 21
____ sig. figs.
____ sig. figs.
answer hasthe _________number of sig. figs., in thiscase: ____
3
2
lower
2
18.541+106.6 125.1
___ decimal places___ decimal places
answer has the _________number of ___________________ ,in this case: ____
3
1
lowerdecimal places
1
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II. Standard Scientific Notation:
A. Moving the decimal point to left
B. Moving the decimal point to right
616000 = 6.16 x 10
________ decimal pt.
Shift ______ to here by ___ places
implied5
exponent is ___________b/c number is _____ 1
positive
>
0.0070 = 7.0 x 10exponent is ___________b/c number is _____ 1
negative
<
5
-3
left
Shift ______ to here by ___ places3
right
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Ex: Convert to standard scientific notation
number scientific notation
43000
0.0290
2012
0.5
80
80.
4.3 x 104
2.90 x 10-2
2.012 x 103
5 x 10-1
8 x 101
8.0 x 101
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I. Units: In Regents Physics, we almost
always use the _____ (International System)
metric system. The ___________________ ,or
most basic, units in this system are:
SI
quantity unitabbrev-iation
length meter
current ampere
time second
mass kilogram
m
A
s
kg
The abbreviations spell _______________ (almost)"mAsk"
fundamental
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I. Prefixes: see PhysRT, pg. ____ at ___________ In all calculations, any prefix symbol on an SI unit must first be removed.
1 bottom
Ex: d = 15 nm rewrite as: d = 15 x _____ m
prefix _________
represents ____
with prefix without
5.3 km
1.7 cm
2.00 s
1.21 GW
8.6 kg
A trick b/ckg is alreadyan SI unit
__________ for
length (meters)
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I. Prefixes: see PhysRT, pg. ____ at ___________ In all calculations, any prefix symbol on an SI unit must first be removed.
1 bottom
Ex: d = 15 nm rewrite as: d = 15 x _____ m
symbol SI unitprefix _________
represents ____10-9
10-9
with prefix without
5.3 km
1.7 cm
2.00 s
1.21 GW
8.6 kg
5.3 x 103 m1.7 x 10-2 m
2.00 x 10-6 s
1.21 x 109 W
8.6 kg
A trick b/ckg is alreadyan SI unit
__________ for
length (meters)
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V. Converting Units: the power of "one"
Ex: Convert 60 miles to kilometers.Use the conversion factor: 1 mi =__________ km This can be written as either:
or
Multiplying by either of these two factors does
not change the ________________ (only the units)
because both factors equal _______ .
Write: 60 mi x _________ = km96.54
~100 km
1.609 km
1 mi
1.609
1.609 km
1 mi 1.609 km1 mi
one
actual value
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VI. Slope = m = ________y
x
10
20
40
30
2 4 6 8
Steps:
1. Draw a best fit line using a __________
1. Use two points on the
line to calculate m:
m = y = x
= ________
=
y2 – y1
x2 – x1
(x2, y2) = ( , )
(x1, y1) = ( , )
8 32
1 5
00
ruler
Steps:
1. Draw a best fit line using a __________
1. Use two points on the
line to calculate m:
32 - 58 - 1
3.9
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In PhysRT:
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I. Distances and displacements
Distance is ______________________________________
or __________________________________________________
Instead of _____________ , we will use _______ for
distance. We will use SI (international system)
units. The SI unit for distance is the _____________ .
Any other unit for distance must first be____________
________________________ before using any equation in
Regents Physics.
initialposition
finalposition
change in position =
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______________– quantities with ______________(size) only
Ex: distance d = 2.0 m
____________– quantities with magnitude and _________
Ex: displacement d = 2.0 m, west
Vectors are represented by ________________:
Distance d is a _______________.
Displacement d is a_____________________ .
distance =
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•must have arrow __________ for_________________
•use a ___________ to draw to scale as a straight line
•right or up is______________; down or left is ___________
•right =___________; up =_______________, etc
•any vector with same mag. and dir. is_______________
Ex: Draw d = 2.0 m, west. Use a scale of 1cm:1 m.
Ex: The vectors below are all _________________ because
they have the same _______________ and _______________:
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II. Adding Vectors
add using the ______________________method.
draw the _________________displacement ______ as
an ____________ from the ________ of A to the ________ of B
A = 2 m, E B = 3 m, E
Ex: Use a ruler to draw the vectors to the scale: 1 cm:1 m
A B
Resultant R = _________
R = _____________
Total distance traveled = _________
Resultant displacement =____________
Ex:
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Ex. What is B + A = ?AB
R = _____________
The __________________ displacement R =__________
magnitude of R: ___________
direction of R: _____________Notice that this new R is same as _________________
The ________________ in which vectors are added
__________________________ . This is true even if
you add ________________________________________ .
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Ex: If A = 3 m, east
Then –A = ___________
or = _________ (the ____________sign shows direction)
If X = Then -X =
Compared to X, -X has the same ________________ ,
but the opposite _____________________ .
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Find A – B = ____________
A = 2 m B = 3 m
A + (-B):
R =_________ = _________
Total distance traveled =___________
but resultant displacement = ______________
III. Subtracting vectors using the head to tail method.
Given:
mag. = ________
dir. = ________
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Ex: Using same vectors, what does B – A = ?
B = 3 m A = 2 m
B – A =_____________
R = __________ = _________
Total distance covered = ______________
Resultant displacement =______________Notice that the ____________________ here is exactly
__________________ to the one in the previous example.
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C
D Find C + D.
mag. of R = ____________
=___________
IV. Adding non-parallel vectors.
dir. of R:
starthere
R =_________________
Total distance =____________
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Ex: What is D + C?
R =__________________
starthere
R could also be written:
R = _______________________________________
mag. of R = ____________
=___________
dir. of R:
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Ex. Find C – D
R = __________________
D
C
Total distance =____________
starthere
mag. of R = ____________
dir. of R:
IV. Subtracting non-parallel vectors.
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Ex. Draw D- C
R = __________________
DC:
Total distance =____________starthere
mag. of R = ________
dir. of R:
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I. Time t is___________________________________It is a _____________________________
In physics, the time between two ___________ isis called the ___________________________ .
event 1occurs at t =
event 2occurs at t =
ti = ____________ time =
tf = ____________ time =
For example, if…
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Then the time interval: tf – ti = t equals
In Regents Physics, instead of ________ , we use
the symbol _____ for time intervals and often just
call it the ____________ . Remember that _____
represents ____________________________________ .
The basic unit for time is the __________________ .
Other units, such as ___________________________
must usually be converted into _________________
before solving any problems.
t = tf – ti =
The time interval will always be ______________ .
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II. speed v = _______________________________
=________________________________
=_________________________________
Ex:
Equation for v from PRT
(Physics Reference Tables):
Speed v can be ______________ (not changing), or
it can change. If it changes, the speed at any
instant is called the ____________________ speed.
The ______________speed, vavg = v is:
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…the 4 _____________________ (basic) units:
Ex: Jenny runs 95 meters in 15 seconds.
Find her average speed. Show all work.
____________ units are madeup of…..
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Ex. A car, initially moving at a speed of 25 m/s,increases its speed to 45 m/s in 3.0 seconds. What is its average speed during the 3.0 s?
vi = ____________ speed =
vf = ____________ speed =
This equation is NOT
in your PRT. You must
_____________________ .
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Word problem hints:
1/ If an object starts from rest: vi =
2/ If an object comes to rest: vf =
3/ If the speed of an object does NOT change,
v =
How far will the car in the last example
travel in 12 seconds?
Given:
Unknown:
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Ex. Units for speed v: units of ______________units of speed =
units of ______________
[v] =
Put a rectangle around units of distance,and an oval around units of speed:
m cm/s km/h mi
1/s ft/s in m/s2
mph km in/y m/s
cm h s km/h
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III. velocity v = _________________________________
mag. of the velocity = the ____________
Ex:
= ________________________________ __________________________________
velocity = ___________ + ________________
Draw velocity as an _________:
=
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average velocity:
Ex: Godzilla moves 5.0 x 102 meters east in 2.0 seconds. Find his average velocity.
If you assume that east is positive, you maywrite this velocity as:
Note: Speed and velocity have same _________
and use the same_______________:
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Ex: Ms. Rudd walks 1) 6.0 m east in 4.0 s, then runs 2) 2.0 m west in 0.50 s. Find her average speed in each part, and 3) the average speed over the entire time.
1) v = d/t
v = d/t
v = d/t
2)
3)
Why is the average speed over the entire timecloser to the answer for part _____ ?
d = the _____________ distance
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Now find the average velocities for each part ofthe previous example.
1) v = d/t
v = d/t
v = d/t
2)
3)
d = the __________________ here
d = _______________ d:
Why is the answer to 3) now ________ than what it was on the last slide?
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Uniform
motion
constant ________________
constant ______________
in______________________
Ex. A car leaks oil at a constant rate while
moving to the right in uniform motion. Sketch
the pattern of drops it leaves behind.
IV. Uniform motion:
or….
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acceleration, a = ____________________________
=______________________________
average a = where Δv =
Any time that _____________ changes, thereis___________________. And because:
velocity = +
changing either _____________ or ______________or _________ results in acceleration. In thissection, we only consider changes in __________ .The _________ speed changes, the _________ the a.
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Ex: Ms. Rudd accelerates her jet skis from a speed of 5.0 m/s to a speed of 17 m/s in 3.0 s. Find the magnitude of her acceleration.
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SI units for a:
other units:
Using brackets [ ] for units:
[a] =
From last problem:
a =
_________gainedeach _________
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Because a = _________ , the ________________
of a is the same as the __________________
of the ________________in v: v = vf - vi.
v =
Sincev ____ 0 (which is _________________),
then also the acceleration a ____ 0.
Ex 1: An object moving to the right
accelerates to a faster speed.
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Ex 2: An object moving to the right is
slowing down, or ________________________.
v =
Sincev ____ 0, then also a ____ 0.
Note that the direction of the acceleration
______________ always the same as the
direction of the ___________________ .
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Conclusions:1. If the ___________ and the________________ are in the __________ direction, then the object is _________________ ( __________________). 2. If the ___________ and the________________ are in _______________ directions, then the object is _________________ ( __________________).
Ex 3: An object moving up but slowing down:
v =
a is ______________ or_______________.
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_______________can be confusing, but remember:
1. The __________________ is always from the
_________________ to the _____________ points.
1.The ________________ always has the same
direction as the object's ____________________
(the _________ direction it __________________).
1.The ___________________ has a direction givenby the direction of the ____________ in the ______________ , which may or may not be thesame as the direction of the ________________ .
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a = 2.0 m/s2, east =
Ex: The _________________of the acceleration is
also called the ____________________.
scalar
…is the magnitude
of the…
vector
distance
speed
acceleration
In review:
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In word problems, remember:
1) “starts from rest” means
2) “comes to rest” means
1) When an object is in ______________motion,it means it has a _________________velocity. In that case: __________ and ____ = _____ = _____
1) up/right are___________________,
1) down/left are____________________.
Examples: The speed of _____________________given in the PhyRT are ___________________.
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Ex: A ball is dropped. It accelerates from rest to a speed of 29 m/s in 3.0 seconds. Finds its acceleration.
What are the magnitude and direction of a?
How much speed does the ball gain each second?
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Ex: What is the speed of a giraffe, initially movingat a speed of 21 m/s, that accelerates at 5.0 m/s2 for 2.0 s?
If it remains at this final speed, how long will ittake to travel 100. m?
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Ex: Chuck Norris accelerates from a speed of 4.0 m/s to 10. m/s in 4.0 seconds. Find his average speed during that time.
How far does he travel in the 4.0 s?
Why can't you use vi or vf to find d in this case?
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Graphical Analysis of motion in _________________
I. Distance and displacement.
What is the total distance moved?What is the resultant displacement?
d (m)
t (s)
20
10
5 10 15
Find the average speed in the 0-5 s interval.
Repeat for 5-10 s and 10-15 s.
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II. Uniform motion – ____________ is constant
d
t
slope =_____ = ________
slope =______________
speed = _______________
A. Graph of d vs. t
What would the graph of a slower object look like?
________d in each _____
How much slower is B?1 2
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v
t
B. Graph of speed __________ for uniform motion
slope =______
slope =________________
a =_________
What does the area shown represent?
area = L x W = = _____________ =_____________
units: ______ x ______ = _________
What about B?
slope =______
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a
t
C. Graph of a vs. t for uniform motion
In review: for __________________ Motion:
d
t t
v a
t
How would you graph B?
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paper
tape constant v
timer marks the tape at constant ________ intervals
As car moves, describe pattern of marks on tape.
Ex: tape timers
_____________ spaced b/c car moves the __________ d between each mark.
cart pulls tape________________
How would tape look if car was twice as fast?
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III. Non-uniform motion: ___________________ acceleration
d
t
slope of tangent is the______________________
The slope ___________
b/c speed v ___________
A. Graph of d vs. t for object beginning at rest
0
Object covers ________ din each________________
dashed linesare__________
________speed vi = ___ __________________
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v
t
A. Graph of speed v vs. t for __________________acceleration a beginning _______________ .
slope =________
= __________
slope = _______________
a = ______________
What does the area shown represent?
area = (1/2) bh = (½) ______________=__________
units: ______ x ______ = ______
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a
t
C. Graph of a vs. t for constant a
In review: For _________________________acceleration
d
t
v
t
a
t
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cartpaper
tape
As car moves, describe pattern of marks on tape.
Ex:
_______________ spaced b/c car moves _________distance d between each mark.
Timer tape for ___________________
How would tape look if car had more acceleration?
timer
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Compare ____________ to ________________motion:
d
t t
v a
t
d
t
v
t
a
t
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Ex. Answer the questions based on the graph atright.
d (m)
4
2 4 6t (s)
-8
What is the total distance traveled?
What is the resultant displacement?
Find the average speed in the first 2 s.
Find the average speed over the entire 6 s.
Find the average velocity over the entire 6 s.
0
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Ex: The graph below describes a UFO moving in a straight line.
A B
C
Find vavg, d, and a in regions A, B and C.
t (s)
v(m/s)
4.0 8.0 12
20.
40.